Jihai Gu
email: ajihaigu@163.com

Hui Wang

Chengwen Wang
email: cchengwen_wang@yeah.net

Ming Pang

Jin Xiangyang
email: ejinxiangyang@126.com

The Parameter Optimization and Performance Analysis of the Suspension System in the Cab of a Heavy Truck

Keywords: cab suspension, vibration analysis, parameters optimization

In this paper, we conduct a vibration simulation analysis of the suspension system in the cab of a heavy truck in ADAMS. Through establishing the parametric vibration mechanics model of suspension system and using the vibration signal as the excitation signal in the simulation, and regarding rms value of the weighted acceleration as the evaluation indicators, we optimize and match the parameters of the suspension system.

Introduction

Heavy trucks need to work under bad conditions of the road, so in order to ensure the comfort of the cab, researchers should improve the vibration isolation performance of suspension system. Establishing accurate virtual prototype model combining with multi-body dynamics is the key to analyze the performance of avoiding vibration of the suspension system in the cab. The suspension system is a vibration system of many degrees of freedom by connecting the vehicle frame, the suspension elements with the cab. The main element of reducing vibration in the suspension of the cab is springs and dampers. Without changing the structure and position of the suspension system, the main parameters of influencing the elements of reducing vibration are the damping and stiffness of the vibration absorber. Therefore, the optimization and matching of the parameters of the stiffness and damping of the front and rear suspension systems is the main way to improve the vibration performance of the suspension system. In terms of the stiffness and damping of the suspension system in the cab of one heavy vehicle, we perform a parameter optimization and matching of the suspension system to reduce vibration with applying the theory of multi-body dynamics and the function of Design of Experiments, DOE in ADAMS.

2

Parametric Modeling of Virtual Prototype

2.1

The Establishment of Mechanical Model Excitation, quality, elasticity and damping are main factors which influence the vibration of the mechanical system. Therefore, if we get the four elements accurately, we can reflect the mechanical model of the physical process in a right way from the complex machine. For the scattering of the quality and elasticity of the actual vehicle system, we can't succeed in analyzing the continuous system in the analytic method, but change the scattering of the continuous system to several concentrated quality and then analyze with the springs and dampers connected [START_REF] Zhangchao | Simulation Research of the matching and Optimization on Vehicle Powertrain Mounting System[END_REF]. This paper regards the suspension system in the cab as the research subject as a whole, the mechanical model of the spatial vibration equivalent system in the spatial coordinate is shown in Fig. 1.

1.Cab 2.People-seat system 3.The front suspension system 4.The rear suspension system Fig. 1. The mechanic model of the suspension system in the cab Before establishing the dynamics model of the suspension system in the cab, we should acquire the geometric model parameters, quality parameters, mechanic parameters to ensure the correctness of the model and the accuracy of the simulation. All the main parameters are provided by the manufacturers and furthered tested by the degree of freedom after establishing system model in ADAMS. The acquired 47 degrees of freedom of the system mainly include:

⑴The stabilizer bar freedom: with being changed into 8 flexible elements, connected by 2 fixed hinge with the lower bracket, 12 degrees of freedom constricted, the degree of freedom from the stabilizer bar is 8x6-2x6=36.

⑵The degree of freedom of the cab and the suspension elements: 6 degrees of freedom.

⑶The degree of freedom of the seat: with constricting the movement of the seats and the cab, only one degree of freedom of vertical movement according to the cab remains of the seats.

⑷4 degrees of freedom of the vibration table: vertical direction

In ADAMS, we have to ensure the model is neither under under-constrained nor over-constrained. Under-constriction makes it hard for us to ensure the correctness of the simulation; a warning will be given in the simulation under over-constriction and the simulation cannot work normally. Through the verification of the degree of freedom and static equilibrium, the model is established accurately. Then we can conduct the following simulation.

The Establishment of Model Input Excitation

The excitation signal applies the vibration accelerating speed of the 4 test points under the suspension acquired from the road vibration test as the excitation input, as shown in Fig. 2. For the actual test signals are combined from the road roughness incentives, engine vibration, frame bending vibration and torsional vibration transmission, so we apply the actual signals as the stimulation excitation sources, making the simulation closer to the actual situation. With establishing the multi-body dynamics model of the suspension system in the cab in the multi-body mechanic software ADAMS, regarding the weighted rms acceleration value of the cab's seat as the assessment target output, selecting the actual signal of the vehicle at the speed of 60km/h as the excitation source in the simulation, and separately entering them into the lower excitation model of the front and rear suspension system of the model, we conduct a vibration simulation analysis of the suspension system.

The Vibration Simulation Analysis

We confirm the excitation input of the suspension system model in the cab, conduct a vibration simulation of the model and then choose the forced damped vibration analysis. We get the power spectrum after the analysis, as shown in Figure 3. The measured signals in the same position are shown in Fig. 4.

The Parameter Optimization of Vibration Based on DOE

Design of Experiments, DOE mainly does research in the influence of every design variable to performance of the prototype when several design variables change at the same time. It is a method to optimize the prototype model through tests. The design of experiments mainly includes the establishment of design matrix and the statistical analysis of test results [START_REF] Yuchangyang | Design of vibration isolating for commercial vehicle's cab suspension system based on DOE technology[END_REF].

The experiment scheme in the process of DOE is described by the test design matrix. The size of the test design matrix is related to the number of factors, the level of each factor and their way of arrangement and combination. Good test design can get enough test data from relatively less number of trials. Therefore, The construction of the design matrix of DOE is the key to the test design [START_REF] Zhangjiangrong | ADAMS Introduction and Improvement of Virtual Prototype Technology[END_REF]. The method of DOE combines orthogonal experiment design. To conduct the construction of the test design matrix with the tool of the orthogonal experiment design-the orthogonal table, thus reducing large amount of test work. Arrange for tests with orthogonal tables, that is, randomly arranging the test factors to various columns on the orthogonal table (blank columns allowed), and arrange the levels of factors to various lines on the orthogonal table. The provided DOE technical tools in ADAMS can efficiently fulfill the analysis process [START_REF] Chenliping | Dynamic analysis of mechanical system and ADAMS Application Tutorial[END_REF].

Determine the Experiment Scheme

(1) Select experiment factor Suspension system's stiffness, damping are main factors of influencing the comfort and smoothness of the cab. Therefore, we separately select the stiffness and damping parameters of the air spring damper of the front and rear suspension system in the cab as the experiment factors, they are separately front suspension stiffness Kf, damping Cf, rear suspension stiffness Kr and damping Cr.

The air spring damper of the suspension system in the cab is nonlinear damping elements. In order to simplify the operation, in the process of establishing dynamic model, the damper is regarded as the linear element. According to the document provided by the manufacturer, we select the front and rear suspension stiffness as 30N/mm, the damping as 1.8Ns/mm, as the initial values of the simulation models.

(2) Determine the scope of factor levels According to the test data of the air spring stiffness provided by the manufacturer, the stiffness in the DOE test ranges from 20 to 70 N/mm, and the damping ranges from 1.8~8Ns/mm.

(3) Construct experimental design matrix The orthogonal table is used in experiment design, we divide the range scope of stiffness of damping 20~70N/mm and 1.8~8Ns/mm into 6 equal parts and get the medium date of every factor, as shown in the following table 2.

  f K A   f C B   r K C   r C D 1 20 1.8 20

The Analysis of the Simulation and Optimization Results

With the minimum of the vibration power spectral peak of the seat as the optimized target, we conduct a DOE simulation calculation of the dynamics model in the suspension system. When the design variables are Kf=30N/mm,Cf=5.52Ns/mm, Kr=60N/mm,Cr=8.0Ns/mm, the optimized target value reaches the minimum. The group of optimized parameter is noted as scheme 1. Because the orthogonal test technology shrinks the test scale, so to avoid some schemes may be ignored, we conduct an range analysis of the data from the simulation [START_REF] Liuwenqing | Design of Experiments[END_REF]. The parameter data in the scheme 2 is shown in table 3.

Table 3. The comparison of the simulation optimization results

Scheme

  f K A   f C B   r K C   r C D Accelerated speed rms (m/s 2 )
The Compared with the original scheme, the assessed target values in scheme 1 and scheme 2 reduce separately by 20.41% and 20.43%. The final scheme 2 is the best optimized parameter: the front suspension stiffness is 30N/mm; the front suspension damping is 5.52Ns /mm; the rear suspension stiffness is 70N/mm; the rear suspension damping is 8Ns /mm.

We change the design variables to the optimized stiffness and damping values in the model and analyze the vibration simulation once again. Then we get the output power spectral density of the cab's seat and compare it with the original spectral. Fig. 5 is the curve before and after optimization, with the optimization fulfilling the target of avoiding vibration.

Conclusions

With applying the parameter match optimization method of the suspension system based on the dynamics modeling and vibration simulation, we succeed in reducing the vibration of the cab. With applying multi-body dynamics theory, we establish the dynamics model. Through the vibration simulation and parameter optimization of the suspension system in the cab, we get a group of optimized stiffness and damping values of the performance of avoiding vibration: the front suspension stiffness value is 30N/mm; the front suspension damping value is 5.52Ns /mm; the rear suspension stiffness value is 70N /mm; the rear suspension damping value is 8Ns /mm. The simulation results show that with the group of suspension parameter, the weighted acceleration RMS of the cab's seat is reduced by 20.43% compared with the original vehicle index, which improves the stability of the model vehicle and reduces the vibration.

2 .

 2 (a) Power spectrum of the lower left front suspension (b)Power spectrum of the lower right front suspension (c) Power spectrum of the lower left rear suspension (d) Power spectrum of the lower right rear suspension Fig.Model excitation signal

Fig. 3 .Fig. 4 .

 34 Fig.3. The power spectrum of the simulation test

Fig. 5 .

 5 Fig.5. The comparison of simulation results

Table 1 .

 1 The comparison of the main peak frequencies from simulation and the measured test Although the peak frequencies change a little in the result from the simulation, they are still the main peak frequencies of vibration. The corresponding frequencies are basically consistent with the peak frequencies of the actual signals, proving that the vibration state of the simulation model can simulate the vibration of the vehicle cab's actual state.

	The main peak frequencies	The main peak frequencies
	from simulation in	from measured test(Hz)
	ADAMS(Hz)
	0.1995	-
	1.9907	1.953
	4.7769	4.688
	9.0558	8.984
	33.6347	-

Table 2 .

 2 The level factor values of test factors

	Factors
	L
	evel

Acknowledgment

This research was supported by the Science and Technology Research Foundation from the Education Department of Heilongjiang Province (No. 12521130).


Chunjing Si
email: smallx1002@sina.com

A Dynamic Knowledge Models of Nitrogen Fertilizer and Computer System for Cotton

Keywords: nitrogen management, influence factors, dynamic knowledge models, decision support system

Through analyzing the newest research results about nitrogen management of cotton and experimental results, and on the basis of the different effects of cotton yield, plant height and leaf area, a dynamic knowledge model for decision making on total nitrogen and their distribution among main growth stages of cotton under different environments and yield targets was developed with the principles of nitrogen balance and by integrating the factors of climate, soil, yield and so on. A comprehensive and intelligent computer system for cotton management was established using VC++6.0 and SQL Server 2003.

Introduction

As nitrogen is one of the important components of protein, which is also the important element making up of cellular plasm, so to speak, life activities cannot be formed without nitrogen. The nutrition level of nitrogen fertilizer has a very essential influence on cottons' growth and development, which not only limits the height of cotton leaves, but also cotton yields. In the case of lacking the nitrogen fertilizer, cottons take on a slow and weak growth, with undersized and thin stems, cotton buds and bolls with a high expulsion rate and rare bolls; in the case of using too much or improperly fertilizing in different growth periods of cottons, sugars formed by organic nutrition consume too much with little accumulation, excessive vegetative growth and increasing expulsion. Fertilization of abundant nitrogen fertilizers will not only decrease the utilization rate of fertilizer and increase its cost, but also cause adverse effects to the environment. Different treatments of nitrogen fertilizer have certain influence on the growth of cotton organs and the yields. So, it will be of much importance for guiding the agricultural production to create accurate and effective nitrogen management models and design and develop them into systems.

Materials and methods

Experiment design

The experiment is conducted in agricultural experiment station (with latitude of 40°32' N and longitude of 81°18' E) of Tarim University in Xinjiang Province in April, 2011. With a height above the sea level of 900-950 meters and of warm temperate desert climate, the experimental zone locates in the upper and middle reaches of Tarim River, graced with rich resources of water and soil, dry weather, abundant sunlight and four distinctive seasons. For nearly 30 years, the area has an average annual precipitation of 40.1-82.5 mm, with little rain in summer and little snow in winter, an average annual temperature of 10.7℃ and a total annual sunshine duration of 2900 hours, suitable for the growth of long-staple cotton. The cottons are planted by means of plot, with a planting density of 12200 plants per mu. The experimental soil is loam, with 14g/kg organic content, 0.5g/kg total nitrogen, 85mg/kg effective nitrogen, 14mg/kg available phosphorus and 75mg/kg rapidly available potassium. The experimental variety is the New Sea 21 of long-staple cotton, with a plot area of 132m 2 . This experiment designs five nitrogen fertilization treatments, namely, 0, 180, 240, 300, 360kg/hm 2 , with the amount of base fertilizer holding 45% of the total fertilization amount, and the remainder being top dressing/nitrogen application, respectively in the periods from the bud period to the flower and boll stage and 3 fertilization proportions with water of 15%, 25% and 15%. Besides, the phosphorus and potassium fertilizers in the base fertilizer separately are P 2 O 5 138 kg/hm 2 and K 2 O 72 kg/ hm 2 . The experiment is arranged in random groups, with 3 repeated treatments in each group. The samples make up of the following table

Experimental method

In the main growth period, seedling stage, bud stage, flower and boll stage and boll period, samples are respectively taken in the time between 10:00-12:00 am on the corresponding dates. Each nitrogen fertilizer treatment area randomly selects 3 representative cotton plants (5 plants in the bud period), and measures related data from the selected plant samples. The plant height of cotton: the plant heights of cotton are measured with rulers on June 9 th , June 17 th , July 2 nd , July 17 th and September 15 th . The length and width of cotton leaves: the length and width of the largest leaves in representative plants are measured with rulers on June 9 th , June 17 th , July 2 nd , July 17 th and September 15 th . The leaf area: according to the quantitative functional relationship between pulse length and leaf area in cotton leaves applied in Literature [START_REF] Xinyu | The Quick Calculation of the Long-staple Cotton Leaf Area by Look-up Table[END_REF], the leaf area is solved.

With the pulse length x as the independent variable and the leaf area y as the dependent variable, the quadratic regression equation of one variable y=2.4337-0.4328x+0.8265x 2 is established.

3 The influence of nitrogen fertilizer on the growth of long-staple cotton

The influence of nitrogen fertilizer on the yield of long-staple cotton

The research literature [3][START_REF] Junyi | Cotton Nutrition Fertilization and Diagnosis[END_REF][START_REF] Shuchun | Cotton Nutrition and Fertilization[END_REF] show there is certain quantitative relationship existing between nitrogen fertilizer NR and the target of yield TY (kg/ha), which can be expressed in the following linear function:

181 . 17 1062 . 0    TY NR * * 8313 . 0  R (1)
The literature [START_REF] Xiaojing | Diagnostic Study on Nitrogen Nutrition Status in Cottons[END_REF] proves that under the condition of border irrigation in southern Xinjiang area, different amounts of nitrogen fertilization have influences on the boll number of each cotton plant, the weight of each boll and the yield of seed cottons. This research suggests that under different nitrogen treatments, there is certain difference in the boll number of each cotton plant, the weight of each boll and the yield of seed cotton. Thereinto, the relationship of the boll number of each cotton plant and nitrogen treatments accords with quadratic curve equation. At first, the yield of seed cotton increases with the increasing amount of nitrogen fertilization, but when the nitrogen level reaches N3, the yield takes on downtrend. By simulating and matching the nitrogen fertilizer effect of cottons with quadratic equation of one variable, the experimenter concludes the correlation between the amount of nitrogen fertilization and the cotton yield as follows:

9 . 1962 6895 . 2 0039 . 0 2     x x y * * 2 9576 . 0  R (2)
In the equation, y refers to the yield and x the amount of nitrogen fertilization.

The influence of nitrogen fertilizer on plant height and leaf area of the long-staple cotton

The experimental result (seen in Chart 3) shows that with the advancement of long-staple cotton's growth process, there is no difference in different nitrogen fertilizer treatments in periods of seedling and bud, that the growth processes of cotton in the beginning of flowering and at full-blossom stage are both a little delayed and that in the full-blossom stage, the heights of front plants rapidly increase and after that, the difference in plant height with different nitrogen treatments gradually increases with the growth process. 4 The dynamic knowledge model of nitrogen management

The establishment of the model/the modeling

Based on the widely collecting and consulting the latest literatures about the cultivation, the soil science and plant nutrition of the long-staple cotton, by means of the principle of system analysis and mathematical modeling method, the experiment builds the relevant quantitative mathematical model of nitrogen management and develops the cotton nitrogen management system based on dynamic knowledge model, and finally tests the correctness of this model with practical applications and optimizes the model with understanding and analyzing the feedback information from the system.

Descriptions of model algorithm

The amount of soil nitrogen supply in season

The amount of soil nitrogen supply in season: SN ON ION   In the equation, ON refers to the supply amount of reducible N element in season and ION the supply amount of irreducible N element in season. [START_REF] Xiaoping | The Influence of Cultivation Pattern on Cottons[END_REF]. the supply amount of reducible N element in season  1000 365

08 . 0        SNUE t N SBW SPD TSN ON (3)
In the equation, TSN refers to the real total amount of N element in the soil (g• kg -1 ); SPD the thickness of the top layer (cm); SBW the volume (g• kg -1 ). The utilization rate of the fertilizer in season is affected by the fertilizer variety, fertilizing method, weather conditions and soil environment and so on. Under the conventional fertilizing technique, the utilization rate of fertilizer in season is generally 32. 5%±2. 5%. Recently, as a new fertilizing technique, drip fertigation has obtained/achieved much development. Because the fertilizer is quantitatively applied with water, the solubleness of the fertilizer and the close fertilization are increased, thus improving the fertilizer efficiency and the utilization rate of nitrogen fertilizer reaches 50. 5%±3. 5%. According to the fertilization pattern and past experience, users can determine the utilization rate of corresponding fertilizers in season. N (t) refers to the total number of standardized days under water temperature effect:

  ' ' ' 1 2 365 ( ) ( ) ( ) N t N t N t N t     N (



. Thereinto, STA20 is the soil temperature when the plough layer is 20 cm thick. Fw (t) is the influence function of moisture to nitrogen fertilization.

  0.2 ( ) () 0.2 0.8 ( ) () 1 0.6 ( ) 0 ( ) D D O O D w O S S O S W t W W t W W t W W W F t W t W W t W W W W t W                       (5)
WD is the wilting moisture content; WO the optimum soil moisture content under mineralization; Ws saturated moisture content of soil; W(t) the actual moisture content of soil.

(2). The supply amount of irreducible N element in season 10 ION AOVN SPD SBW    

In the equation, AOVN is the content of irreducible N element and effective nitrogen in the top layer of soil; SPD the thickness of the topsoil (cm); SBW soil capacity (g• kg -1 ).

The necessary/needed amount of N under specific yields

The necessary amount of N under specific yields URN (kg

                                        (7)
In the equation, TYmax is the yield potential under the earliest time of suitable sowing period; YM the average yield in the first three years; YLPP the production potential of production technology.

The fertilizing ratio of organic N to inorganic N OINR1:OINR2

(1) The fertilization amount of organic N

            ' max ' 1 max ' max 5
                           (8)
In the equation, TY (kg/hm 2 ) is used to calculate the realizable yield potential of users; TYmax is the yield potential under the earliest time of suitable sowing period; OMC the organic material content in the soil (g/kg). LA is the age of transplanted leaves after PS correcting the seeding method, whose value is:

     Otherwise seeding direct 5 . 2 LA A L ,LA
                                  (11)
In the equation, LA is the age of transplanted leaves after PS correcting the seeding method; TY(kg/hm 2 )is used to calculate the realizable yield potential of users; TYmax is the yield potential under the earliest time of suitable sowing period. CLAYC is the content of the physical clay (%), whose value is listed in Chart 4 as follows:

                                  (13) (4). The full-blossom stage             ' max
                                  (14) (5). The boll stage            ' max
                                  (
             (16)

Verification of the model

By systemically using the meteorological data, soil bank, commercial variety, perennial production data of 5 areas with different latitudes like Alear City, Bachu, Bytown, and Shihezi, the experimenter designs management schemes of cotton nitrogen in normal years for these areas and then compares with the cotton cultivation mode in local use to find that they are basically consistent, which suggests this system is of good practicality and accuracy.

The design and development of nitrogen management system

By understanding and refining document literatures and expert knowledge, combining with field trials and dynamic knowledge model of nitrogen management, with the help of programming language VC++6.0 and data platform SQL 2000, the experiment designs and develops nitrogen management system based on dynamic knowledge model, which mainly covers 4 modules. The first three modules simulate the influences of different nitrogen treatments on such parameters as the yield of long-staple cotton, the plant height and leaves. Thereinto, the module of production estimation realizes the influences of 5 nitrogen treatments on the number of bolls in each cotton plant, the weight of each boll and the seed cotton yield, further realizing the estimation of long-staple cotton yield; by analyzing the influences of 5 nitrogen treatments on long-staple plants, the module of plant height prediction concludes to predict the plant height by the fertilization amount of nitrogen fertilizer; by the influences of 5 nitrogen treatments on leaf number and leaf area, the leaf parameter estimation module concludes to estimate related parameters of leaves according to the fertilization amount of nitrogen fertilizer. According to input parameters by users, nitrogen management module can help users calculate the amount of soil nitrogen supply in season, the necessary amount of nitrogen under specific yields, and the fertilization proportion of long-staple cotton in different growth stages under drip fertigation.

Conclusion

By understanding and refining document literatures and expert knowledge, combining with field trials, the study analyzes the influences of nitrogen fertilizer on relevant parameters such as the cotton yield, plant height and leaves, further giving out the dynamic knowledge model of nitrogen management and designs and develops the cotton nitrogen management system based on dynamic knowledge model. Proved by practical applications, dynamic knowledge model is of good practicality and accuracy, and the system is characterized by fast and convenient uses, practicality and universality. In the future studies, the system will strengthen the study on the influence of nitrogen fertilizer on other cotton organs and be able to make better service for production.

4 . 2 . 4 .

 424 refers to the age of transplanted leaves (9) (2) The fertilization amount of inorganic N OINR 2 OINR 2 10-OINR 1 (10) The drip fertigation In different growth stages of cotton, the ratio of base fertilizer to top-dressing; the drip fertigation ratio in base fertilizer, bud stage, the beginning of flowering, the full-blossom stage, boll stage and early flocculant stage, namely,

Table 1 .

 1 1: Schemes of every fertilization treatment in the experiment

	Treat	Total amount		Base fertilizer		Topdressing nitrogen fertilizer
	ment	N	P 2 O 5	K 2 O	N	P 2 O 5	K 2 O	1 st (6.1 0)	2 nd (7.1 5)	3 rd (8.20)
	N0	0	138	72	0	138	72	0	0	0
	N1	180	138	72	81	138	72	27	45	27
	N2	240	138	72	108	138	72	36	60	36
	N3	300	138	72	135	138	72	45	75	45
	N4	360	138	72	162	138	72	54	90	54

Table 2 .

 2 The influence of different amounts of nitrogen fertilizer on cotton yields

	Treatment	Boll numbers of each plant(No./plant)	Weight of each plant(g)	Yield of seed cotton(kg./hm 2 )
	N0	7.6	2.9	4562.2
	N1	8.3	2.8	4810.7
	N2	8.4	2.9	5042.5
	N3	8.5	3.1	5454.5
	N4	8.4	3.0	5216.4

Table 3 .

 3 The influence of different nitrogen levels on plant height, leaf number and leaf area

	Treatmen t	Plant height(cm )	True leaf number(leaf number/plant )	Leaf area (cm 2 /plant )	Plant height(cm )	True leaf number(leaf number/plant )	Leaf area (cm 2 /plant )
		(Stage of 4 leaves) May 21th	(Stage of 5 leaves) May 21th
	N0	4.0	3.5	61.2	5.1	4.8	109.8
	N1	4.1	3.6	64.3	5.6	5.0	118.5
	N2	4.3	3.8	84.5	6.1	5.0	133.0
	N3	3.1	3.5	59.8	5.7	5.1	122.3
	N4	3.6	3.5	55.7	5.4	5.0	114.5

  t) I refers to the number of standardized days under the effect of water and the temperature of Number i, whose value is: If the value of

			i PDT (psychological development time the variety accumulates
	gradually under actual sowing dates) is taken and fixed from 0 to 144, then
								' ( ) i N t	( ) F t F t ( ) T w 	(4)
	Otherwise, its value is 0.
	FT (t) is the influence function of temperature to nitrogen fertilization, whose value
							20 STA	30
	is    T F t	8	e	0.058	20 STA		10

  

  • hm -2 )In the equation, TY (kg/hm 2 ) is used to calculate the realizable yield potential of users.

			N UR		1		e	 0.0004 418.5966 4151.962  TY   	(6)
	TY	YM	1	max 4 TY YLPP YM YLPP	YM YM	1 1	4 4 YLPP YM YLPP YLPP YM YLPP	max max TY TY

Table 4 .

 4 The soil texture and the corresponding values of CLAYC

	Soil texture	CLAYC value
	Sandy soil	7.5
	Sandy loam	15
	Light loam	25
	Middle loam	37.5
	Heavy loam	52.5
	Clay	65


Yan Li

Yangren Wang

Shuhong Sun

Simulation Study of Winter Wheat Photosynthate Distribution Effect on Controlled Water and Fertilizer Measure

Keywords: photosynthate, mechanism model, winter wheat, dry weight

From the morphological characteristics of crop growth, the mechanism model of photosynthate distribution based on the dynamic ralationship between root,shoot,leaf and grain is proposed in this paper. And the method of the determining model parameters with the field experiment data is proposed. The root-cap growth equilibrium coefficient, the shoot-leaf growth equilibrium coefficient, the grain-shoot growth equilibrium coefficient, the water stressed coefficient and the nutrient stressed coefficient are obtained by the nonlinear program according to the measured dry matter of the winter wheat root,shoot,leaf and grain in 2008 in the irrigation experiment station of Tianjin argricultutal university and the objective function of the minimum absolute error sum on the simulated and measured dry weight.And they are verified by the the winter wheat measured data in the irrigation experiment station of Tianjin argricultutal university in 2009. The results show that the simulated value and observed data of the dry weight of root, stem, leaf and grain are consistent. The correlation coefficients ( R 2 ) of the comparison between simulated and measured value of the root,shoot, leaf and grain dry weight on every treatments were all over 0.81. It shows that the model on the simulation of the root, shoot, leaf and grain in this paper is reasonable.It provides a theoretical basis on reasonable farmland irrigation and fertilization.

Introduction

The Chinese and foreign scholars have done a lot of work on the tendency of the wheat growth for forties years and proposed many crop growth models. But, the existing wheat growth simulation models also have some shortcomings. Especially, the photosynthate allocation in the existing crop growth models is a empirical model. This has affected the development and application of the crop growth models to a certain extent.It is further studied and developed a mechanistic model. It need to be improved its explanatoriness [START_REF] Xiu-Liang | Study on Simulation of Wheat Phenological Development[END_REF][START_REF] Mei-Cun | Study on Simulation Model of Wheat Stem Top Primordia Development[J][END_REF][START_REF] Yan | Simulation Study of Winter Wheat Photosynthate Distribution Effect on Controlled Water and Fertilizer Measure[END_REF][START_REF] Yun | Review on Development of Foreign Crop Growth Models[J][END_REF][START_REF] Roger | New and Traditional Methods for the Analysis of Unreplicated Experiments[END_REF].

2.Creation of the model

Hypothesis of the model

According to the same stretch law of the crop growth, there are several following hypotheses in the establishment of the distribution coefficient model on the winter wheat photosynthate.

(1)Balance hypothesis of the stem-leavf growth

l sl s y x W K W C Q   1 1 (1)
Where W l is the dry matter weight of the leaves, kg/hm 2 ;W s is the dry matter weight of the stems, kg/hm 2 ;Q,C are the Nitrate average concentration (g/kg)and the average volumetric moisture content (cm 3 /cm 3 )in the soil of 0-100cm depth, respectively. x 1 and y 1 are the index. K sl is a proportionate coefficient related to the crop species and the growing period. In this paper, the coefficient of the stem-leave growth balance was defined. It is one of the crop hereditary parameters related to the crop species and the environmental factors.

(2)Balance hypothesis of the seed-stem growth

s se e y x W K W C Q   2 2 (2)
Where W e is the dry matter weight of the seed, kg/hm 2 ; x 2 and y 2 are the index.The remaining symbols are the same meaning as the former.K se is a proportionate coefficient related to the crop species ,the growing period and the environmental factors. In this paper, the coefficient of the seed-stem growth balance was defined. It is one of the crop hereditary parameters.

(3)Balance hypothesis of the root-shoot functions

  d e s l r y x P W W W A S W C Q       3 3 (3)
Where W r is the dry matter weight of the roots, S is the absorbing water velocity of the roots, P d is the canopy photosynthetic rate. x 3 and y 3 are the index.Because the whole crop growth was analysed, the absorbing water velocity of the roots(S) was equal to the actual transpiration rate of the crop (T a ). In this paper, A related to the species , the variety characteristics of the crops and the environmental factors was defined as the coefficient of the root-shoot growth balance. It is one of the genetic parameters of the crops.

(4) The composition of the roots, stems leaves and seeds was not significant difference. The substrate of the growth was transformed the dry matter with the conversion efficiency Y g . The rest (1-Y g ) was consumed by the respiration [START_REF] Shi Jian-Zhong | Mechanism Model on Assimilate Distribution of Plant Vegetative Stage [J][END_REF][START_REF] Liu Tie-Mei | Quantitative Simulation on Dry Matter Partitioning Dynamic in Wheat Organs[J][END_REF][START_REF] Ai-Wang | Irrigation quota of the main crops in the northern region [M[END_REF][START_REF] Wei-Xing | System simulation and intelligent management of crop[END_REF].

Through the one day's accumulation of the photosynthate, the dry matter weight increment of the roots, stems, leaves and seeds(dW r, dW s , dW l , dW e ) were as following

g d r r Y P f dW    g d s s Y P f dW    g d l l Y P f dW    g d e e Y P f dW   
The dry matter increment of the plant (dW) can be described as [START_REF] Yun | Review on Development of Foreign Crop Growth Models[J][END_REF] Where P d is the total amount of one day photosynthate, Y g is the conversion efficiency of the photosynthate.

Deduction of the model

It is supposed that the dry matter weight of the various parts of the plants is W l , W s , W r , W e in the t time. The canopy photosynthetic rate is P d , the absorbing water velocity of the roots is S , the plant is in a growth equilibrium state in the t time. It can be described as equation ( 1), (2) and (3).

d g e l s r P Y dW dW dW dW dW      
In the t+⊿t time, the various parts of the plant is W l +dW l , W s +dW s , W r +dW r , W e +dW e and still in a function equilibrium state. It is described as,

  l l sl sl s s y x dW W dK K dW W C Q     ) ( ) ( 1 1 +   s s se se e e y x dW W dK K dW W C Q     ) ( ) ( 2 2 +     d e e s s l l r r y x P dW W dW W dW W dA A S dW W C Q           ) ( 3 3
The before-mentioned 3 formulas were arranged and the high-level infinitesimal(dK se •dW s , dK sl •dW l , dA•dW s , dA•dW l and dA•dW e ) was omitted.

That is obtained,

2 1 2 1 1 1 / )] ( [ y y x x l sl sl l se y x se s e C Q dW K dK W K C Q dK W dW           (5) 1 1 / ) ( y x l sl sl l s C Q dW K dK W dW     (6) (7)
Substituted equation ( 5), ( 6) and ( 7) into equation ( 4) , the mechanism model of the crop photosynthate will be obtained.

The distributive coefficient of the roots was calculated as

(8-1)
The distributive coefficient of the stems was calculated as, (

The distributive coefficient of the leaves was calculated as, (

The distributive coefficient of the seeds was calculated as, (8-4)

    3 3 2 2 2 2 3 2 1 3 2 1 ] [ y x d l s e l sl sl l se se s y x l sl y x sl l y y y x x x d r C SQ dA P W W W dW K dK W K dK W C Q dW K C Q dK W C Q S P A dW                         
Y C SQ dA W W W dK W K W C Q K dK W K dK W C Q dW K C Q dK W Y C Q S A f                                 3 3 1 1 2 2 2 2 3 2 1 3 2 1 ] [ g d x sl l sl s y x sl sl l s Y P C Q dK W K W C Q K dK W f        1 1 1 g d sl l sl s y x l Y P dK W K W C Q f     1 1 g d y y x x sl l sl s y x sl sl l se y x se s e Y P C Q dK W K W C Q K dK W K C Q dK W f             2 1 2 1 1 1 1 1
) (

Determine of the organ quality and economic yield

According to the before-metioned concept of the photosynthate distributive coefficient, the dry matter of the roots, stems, leaves and seeds are calculated as follows, (9-1)

(9-2) (9-3) (9-4)
Where W r,i , W s,i, W l,i and W e,i are the dry matter weight of the roots, stems, leaves and seeds on the i day, kg/hm 2 . P d,i and Y g,i are the amount of the photosynthate(kg/hm 2 ) and the transformation efficiency of the photosynthate. W r,i-1 , W s,i-1 , W l,i-1 and W e,i-1 are the dry matters of the roots, stems, leaves and seeds on the i-1 day (kg/hm 2 ). f r,i , f s,i , f l,i and f e,i are the photosynthate distributive coefficients of the roots, stems, leaves and seeds on the i day.

Calculation of the water and nutrient stressed coefficients

(1)the water stressed coefficient. Where it is calculated with the power function.

(10)

Where T ai is the crop transpiration on the i day in the water stressed condition(mm/d).

T pi is the potential crop transpiration(mm/d). σis the sensitivity index of the crop growth and yield in the water shortage condition, it also is called the water shortage sensitivity index. The crop transpiration T ai is equal to the water amount of the crop root absorption.

(2)the nutrient stressed coefficient. Where it is also calculated with the power function.

(11)

Where λis the sensitivity index of the crop growth and yield in the nutrient shortage condition, it also is called the nutrient shortage sensitivity index.

(12)

i g i d i r i r i r Y P f W W , , , 1 , ,      i g i d i s i s i s Y P f W W , , , 1 , ,     i g i d i l i l i l Y P f W W , , , 1 , ,      i g i d i e i e i e Y P f W W , , , 1 , ,     1 0            i pi ai I FW T FW       t R FN tpyN          W P t P t R crtN N tpyN / , 1 min 
Where P N (t) is the crop Nitrogen content on the t time (%). P crtN (W) is the critical crop Nitrogen content, it is also the Nitrogen minimum amount of the crop growth in the no Nitrogen stressed condition (%), it is calculated as follows [START_REF] Kang | Simulation of Biomass Formation and Nitrogen Uptake in Winter Wheat under Different Water and Nitrogen Supply[END_REF],

        W crtN e W P 26 . 0 3 1 35 . 1 (13)
Where

  W W , 1 max  
, W is the dry matter accumulation on the computed time (t/hm 2 ).

Accumulate of the organ dry matter

The crop photosynthate simulation in the water and nutrient stressed condition is calculated as follows. First of all, the potential crop photosynthate is calculated in the no water and nutrient stressed condition, it multiplied by the water and nutrient stressed coefficients then, the crop photosynthate on the one day is calculated as follows,

i i dmi di FN FW P P    (14)
Where P dmi is the amount of the photosynthate in the no water and nutrient stressed condition on the i day(kg/hm 2 ). P di is the amount of the photosynthate in the water and nutrient stressed condition on the i day(kg/hm 2 ).FW i and FN i is the water and nutrient stressed coefficient, respectively. Formulate ( 14) is calculated the amount of the crop photosynthate on the i day, and then it is multiplied by the distribution coefficients of the photosynthate for the organs (the roots, stems, leaves and seeds), the dry weight of the organs are acquired on the i day, and then it is added to the the amount of the photosynthate on the previous day, the sum accumulated every day is the final photosynthate cumulative value. The dry weight of the roots, stems, leaves and seeds is calculated as formulate (9).

Model Examination

Experimental Execution

Winter wheat phased draught experiment is performed in the irrigation experiment station of Tianjin Agricultural University. The experiment station is located at Lat.39°08′, Long. 116°57′, sea-level elevation is 5.49m and groundwater level is 3.70-1.06 m. The experimental field covers an area of approximately 1 hm 2 . Water for irrigation is groundwater transmitted by plastic hose and is metered. Winter wheat variety 6001 is selected for experiment. Based on local rainfall of the experiment station and water demand of the crop and by referring to previous experimental and research results, it is determined to carry out treatment as per winter wheat water-fertilizer double factorial experiment. Irrigation is divided into 5 levels (240mm, 180mm, 120mm, 60mm and non-irrigation) and is made at wintering, jointing, earing and filling stages. Fertilizer is applied at 4 levels (750kg/hm 2 , 450 kg/hm 2 , 150 kg/hm 2 and non-fertilizing). Compound fertilizer with total primary nutrient of no less than 54% is used as base fertilizer and is applied to soil with seeding; carbamide with 46% nitrogen content is used as top dressing and is applied along with jointing irrigation, i.e. fertilizer application is immediately followed by irrigation. Considering survey meter is used to observe soil moisture content at depth 0-180cm by layers, 20cm per layer. Measurement is made at seeding, wintering, regreening, jointing and harvesting stages against each treatment. Generally, measurement is made once every 10 days before jointing and is conducted at the same time with dry weight measurement after jointing. Additional measurement is made before irrigation and after rainfall (daily precipitation more than 30mm).

Model Examination

Minimizing sum of absolute value of the error between simulated and measured values of dry weight is used as the the objective function. For programming solution to solve indexes of shoot-leaf growth equilibrium coefficient K sl , root-cap growth equilibrium coefficient A and grain-shoot growth equilibrium coefficient K se

  partial combination of base fertilizer and top dressing, 8 treatments are designed in 2008. A part of treatments are adjusted in 2009 on the basis of experiment in 2008 and number of treatment is increased to 10. For experiment made in 2008, it is seeded on Sep. 25, 2007 and harvested on Jun. 14, 2008. Precipitation during the experiment is 187.4mm. For experiment made in 2008, it is seeded on Oct. 7, 2008 and harvested on Jun. 15, 2009. Precipitation during the experiment is 84.6mm. Seeding rate is 187.4kg/hm 2 in 2008 and 2009. Seeding is made mechanically with 25cm row spacing and approximately 5cm depth. Neutron

x 1

 1 =0.3265, y 1 =0.1858, x 2 =0.0499, y 2 =0.01731, x 3 =-0.3675, y 3 =-0.5639 and solve water and nutrient stressed coefficients λ=0.5695,σ=0.5026 with dry weight of root, shoot, leaf and seed measured by experiment made in winter wheat experimental field at the west capmpus of Tianjin Agricultural University in 2008. Scatter plot of simulated and measured values is drawed with 126 series data of 21 winter wheat zones in 2009. Compared between simulated and measured values of dry weight of root, shoot, leaf and seed in whole growth period of winter wheat is shown in figure 1~4 as medium water medium nutrient. Related coefficients are 0.9998, 0.8142, 0.898 and 0.8726 respectively. It is shown that simulation of organs of winter wheat is reasonable.

Fig. 1

 1 Fig.1 Comparison between simulated and measured value of root dry weight

Fig. 2 Fig. 3 Fig. 4 .Conclution 1 . 2 .

 23412 Fig.2 Comparison between simulated and measured value of shoot dry weight

Acknowledgment

Funds for this research was provided by the Scientific Research Development Foundation of Tianjin Agricultural University No.2012N06 and the National Science and Technology Support Program No. 2012BAD08B01.


Rong Tao

Senbin Yang

Wei Tan

Changqing Zhang

Secure Gateway of Internet of Things Based on AppWeb and Secure Sockets Layer for Intelligent Granary Management System

Keywords: gateway, internet of things, intelligent granary management system, AppWeb, secure sockets layer

To develop an intelligent granary management system (IGMS) based on Internet of Things (IOT), secure gateway of IOT (IOTGW), the key component in the system, is designed and achieved. According to the functional requirements of IOTGW in IGMS, embedded Web server is adopted as a lightweight approach for accessing perception devices and interacting with heterogeneous networks. The design scheme based on ARM chip and embedded Web server is given and the hardware and software architectures of IOTGW are investigated in detail. By comparing the major performances, AM3352, Linux, AppWeb, SQLite and C language are chosen for IOTGW implementation. In order to protect the sensitive information transmitted between the client and server, the secure sockets layer (SSL) protocol is added in AppWeb, and the compilation and transplantation of AppWeb with SSL are given detailedly. Experiment shows that the IOTGW can access different types of perception devices and actuators widely, exchange information between the perception layer and network layer safely, and control the perception nodes remotely, so the management of granary becomes convenient, efficient and intelligent.

Introduction

Granary is a storehouse or room in a barn for threshed grain, and grain reserve has become a key issue concerning about people's livelihood and national defense. In order to reduce unnecessary losses caused by animals, floods, fires, etc in the process of grain storage, granary monitoring system is applied subsequently. The original method is manual inspection by sampling, which is time-consuming, inaccurate and inefficient. The second generation technique is electronic detection using computer and bus standard, that is, electronic monitoring equipments such as temperature and humidity sensors are installed to collect the temperature and humidity data of granary, and bus standard, take RS485, RS422 or fieldbus for example, is adopted to transmit these data to the monitoring computer [START_REF] Kun | Design of a Wireless Granary Temperature Monitoring System[END_REF]. This technique improves the accuracy of monitoring data and reduce the costs of granary management, however, there are some disadvantages including low transmission rate, weak system reliability, difficult for remote communication and big workload of wiring. With the rapid development of communication and network technology, the third generation monitoring system is featured by networking, in other words, short-range wireless communication technologies such as Wireless Sensor Network (WSN) are employed to connect monitoring equipments and collect data, meanwhile, long-range wired and wireless communication technologies such as Internet and mobile communication system are used to convey sensor data and control commands remotely [START_REF] Zhang Zhen | Research of Granary Monitoring System Based on Wireless Sensor Network[END_REF]. In this way, the management level of automation and information is improved greatly. Nevertheless, the system's scalability and intelligence are not good enough for it's not easy to increase the number or type of monitoring nodes, or to obtain, fuse and process monitoring information in real time and actively. To address these issues, Internet of Things (IOT) is introduced to granary monitoring as a new technique [START_REF] Xu Baisen | Research on architecture of the Internet of Things for grain monitoring in storage [C[END_REF].

Internet of Things is a dynamic global network infrastructure with self configuring capabilities based on standard and interoperable communication protocols where physical and virtual "things" have identities, physical attributes, virtual personalities and use intelligent interfaces, and are seamlessly integrated into the information network. IOT is characterized by more thorough sense and measure, more comprehensive interoperability and intelligence, whose application areas cover modern agriculture, infrastructure construction, public security, environment protection, intelligent industry, urban management and other fields [START_REF] Atzori | The Internet of Things: a survey[END_REF].

Restricts of time, space, region and human to real-time monitoring of granary can be broken through by using the technology of IOT, and the IOT-based granary monitoring system can collect, memorize and transmit the parameters including food temperature, humidity, gas concentration, insect and water content to the control center as well as execute the orders from the control center [START_REF] Xie Yanxin | Application of network of things technologies on granary monitoring system[END_REF]. Baisen Xu et al. analyzed the information function model and architecture reference model of IOTbased grain monitoring system, which is composed of four layers: perception layer, transport layer, processing layer and application layer [START_REF] Xu Baisen | Research on architecture of the Internet of Things for grain monitoring in storage [C[END_REF]. However, they only discussed the related key technical problems theoretically, the methods and steps of system implementation were not given. [START_REF] Peng | Design of a granary monitoring system based on Internet of Things[END_REF] proposed a wireless LAN monitoring system adopting intelligent granary monitoring, which is consisted of a central monitoring station, a wireless relay station and wireless collection points. The multifunction real time data is collected by collection points made by ARM11 embedded processor, and then they were sent to the wireless relay station by ZigBee wireless module. The wireless relay station was responsible for monitoring and preserving the information from the collection points, and sending the comprehensive information to the central monitoring station by WiFi module. The received data was processed by the central monitoring station to realize the monitoring of the real-time information of granary working status. However, the wireless relay station has many deficiencies. Firstly, it can only access these collection points supporting ZigBee protocol, and the collecting information is confined to temperature, humidity, oxygen and pest pictures; Secondly, it can't manage or control the collection equipments; Thirdly, it communicates with the central monitoring station only by WiFi, which has small network coverage, high cost and susceptible radio channel; Finally, its security is poor, for it lacks authentication, encryption and other information security measures. Furthermore, many granary monitoring systems based on IOT given in other literatures exist above defects more or less.

In order to maximize the advantages of IOT, achieve broad access and management of perception devices and secure information transmission, gateway of Internet of Things (IOTGW) should be exploited to replace the wireless relay station. Therefore, this paper focuses on the design and implementation of secure IOTGW for the Intelligent Granary Management System (IGMS).

Intelligent Granary Management System Based on Internet of Things

IOT Architecture of Intelligent Granary Management System

The requirements of intelligent granary management system are as follows: First of all, the environment of grain storage should be monitored dynamically and adjusted automatically, i.e. temperature, humidity, gas conditions of granary and the extent of food mildew can be sensed in real time and storage conditions will be adjusted by automatic adjustment system accordingly; In the next place, dynamic perception of quantity and location of grain can be achieved for efficient inventory management; Last but not least, personnel access and pest invasions should also be apperceived to ensure the security of granary.

According to the above requirements, the IOT-based architecture of IGMS is shown in Fig. 1, which can be divided into three layers: perception layer, network layer and application layer. The perception layer aims to acquire, collect and process the data from perception devices including RFID label, GPS, camera, temperature sensor, humidity sensor, infrared sensor and gas sensor, and control the actuators such as heater, fan and dehumidifier. The major communication protocols between these equipment and IOTGW are ZigBee, Bluetooth, WiFi and USB. The network layer aims to transfer the data collected from perception layer and commands issued by application layer in a large area or long distance, which is constructed based on the Internet (via Ethernet and GPRS). Data processing and services providing are two major purposes of the application layer. The data from network layer is handled by corresponding management systems and then various services including tracking, identification, monitoring and data management will be provided to granary manager.

Analysis of IOTGW in Intelligent Granary Management System

As shown in Fig. 1, it's difficult to connect different devices in perception layer and communicate with Internet, for it lacks of uniform standardization in communication protocols and sensing technologies [START_REF] Hao | A brief introduction to IoT gateway [C[END_REF]. Therefore, IOTGW is introduced to carry out data communication between the two kinds of networks by coping with both the protocol transformation and the device heterogeneity throughout IOT network. In other words, IOTGW is the bridge to connect the perception layer with network layer, which has the following functional requirements: 1) Broad access. The perception devices and actuators should be integrated through IOTGW, namely, the IOTGW can access devices with different protocols including ZigBee, Bluetooth, WiFi and USB.

2) Protocol conversion. The core protocol of Internet is HTTP/IP, which is different from the protocols of perception layer in many aspects such as data formats, data rate and data meaning. In order to exchange information between these two layers, the IOTGW should fuse heterogeneous networks and support protocol interworking seamlessly including conversion of data messages, events, commands and time synchronization. 3) Manageable capability. The management of IOTGW contains perception nodes management and gateway device management. The former aims to acquire the node's identification, status and properties, and to realize remote startup, shutdown, control and diagnosis, the latter aims to realize the gateway device's configuration, supervision, upgrade and maintenance. 4) Information security. The information transmitted in the network may affect the granary security, and they are transmitted by wireless channel, therefore, safety precautions should be taken to ensure information security.

Design of IOTGW Based on ARM and Embedded Web Server

Design Elements and Principles

There are already some researches on the design and implementation of IOTGW system. Qian Zhu et al. proposed an IOTGW system based on Zigbee and GPRS protocols according to the typical IOT application scenarios and requirements from telecom operators, and the implementation of prototyping system based on ARM9 and Python were given [START_REF] Qian | IOT gateway: bridging wireless sensor networks into Internet of Things[END_REF]. Till Riedel et al. used Web service based interface descriptions paired with a model driven approach to achieve a high flexibility at a low runtime overhead when designing message based communication within an Internet of Things. The experiments with an industrial servicing use case showed that Web Services and standard HTTP communication based gateways for sensor nodes can integrate multiple concurrent IOT systems [START_REF] Riedel | Using Web service gateways and code generation for sustainable IoT system development[END_REF]. In a word, IOTGW plays a leading role in the IOT systems, and the technologies of ARM and Web service are helpful for its development.

An embedded Web server is a component of a software system that implements the HTTP protocol. The embedded Web server technology is the combination of embedded device and Internet technology, which provides a flexible remote device monitoring and management function based on Internet browser and it has become an advanced development trend of embedded technology. Through this embedded Web server user can access their equipments remotely [START_REF] Sarika Chhatwani | Embedded Web server[END_REF]. There are some advantages to using embedded Web server to design IOTGW: 1) HTTP is a well studied crossplatform protocol and there are mature implementations freely available; 2) Web browsers are readily available with all computers and mobile phones, and other utility software are needless in the application layer; 3) With the usage of Web service, interacting with a perception device becomes as easy as typing a URI in a Web browser. Consequently, embedded Web server can be adopted as a lightweight approach for accessing perception devices and interacting with heterogeneous networks. Moreover, the general problem of using embedded Web services is that even light-weight implementations are too resource heavy for many IOT systems.

The IOTGW is designed with three main principles in mind: simplicity, extensibility and modularity. Simplicity and extensibility refer to users can extend and customize the IOTGW to their needs. Modularity means that internal components of the IOTGW can interact only through small interfaces, thus allowing the evolution and exchange of individual parts of the system.

Architecture of Hardware and Software

According to above elements and principles, hardware architecture of IOTGW system is shown in Fig. 2.

Perception

Fig. 2. Hardware architecture of IOTGW system

As shown in Fig. 2, the hardware architecture is composed of five major modules: minimum ARM system, interface module, transmission module, LCD touch screen and power source, each responsible for a well defined set of tasks. Minimum ARM system is the kernel of the IOTGW, which provides the utilities of processing, control and storage. Embedded Web server with TCP/IP protocol suite is built in the ARM processor, and some web application programs, take protocol conversion, message parsing and device management for example, are written in ARM. The interface module makes the IOTGW accessible to different perception devices. With the help of software, these devices can be controlled and managed by appointing unique IP address, and their heterogeneity is shielded. The Ethernet and GPRS transmission module realizes the data transmission based on Internet by the means of wired and wireless respectively. The heterogeneity between these two protocols and perception devices is shielded too, so data and command can be exchanged and understood between perception layer and network layer. The LCD touch screen is used for output and input of data, command and status, which are useful during equipment debugging and testing. After the IOTGW is in proper working order, the LCD touch screen can be removed. The power source supplies direct current (DC) for all IOTGW components, such as 3.3V, ±5 V, and the source type contains electric supply and battery.

In order to implement the IOTGW's functionalities, the software is designed as Fig. 3. As shown in Fig. 3, Embedded Operating System (EOS) is installed on the hardware platform firstly, and then three functional blocks including data exchange, protocol conversion and equipment management are programming under the EOS.

Data Exchange

Implementation of Secure IOTGW Based On AppWeb with Secure Sockets Layer

Selection of System Platform and Tools

Selection of ARM chip. The AM3352 microprocessor, based on the ARM Cortex-A8, is the product of Texas Instruments. The device supports Linux and Android operating systems and has excellent features including enhanced microprocessor unit, additional peripheral interfaces and real-time clock [START_REF]AM335x ARM Cortex-A8 Microprocessors[END_REF]. Consequently, we choose AM3352 as the hardware platform, corresponding, Linux, which is leading, free and open source EOS, is adopted for hardware resources management and program running control.

Selection of embedded Web server. The common open source embedded Web servers which support Linux EOS are AppWeb, Goahead, Boa, Thttpd, Lighttpd, Shttpd and Mini_httpd. The comparisons of their major performances are shown in table 1.

Table 1. Performances comparisons of common embedded Web servers

Server

Benefits and features Memory usage Security and reliability

In view of the requirements of IOTGW in the IGMS, such as high security, large requests, multi-business types and easy maintenance, the AppWeb is selected as the embedded Web server because of its extended security and higher performance [START_REF]Appweb for Dynamic Applications[END_REF].

Selection of embedded database. SQLite, which is contained in a small (about 350 KB) C programming library, is a software library that implements a selfcontained, serverless, zero-configuration, cross-platform, transactional SQL database engine. It has some outstanding features, such as 1) Transactions are atomic, consistent, isolated, and durable (ACID) even after system crashes and power failures; 2) Faster than popular client/server database engines for most common operations; 3) Implements most of SQL92; 4) Several processes or threads may access the same database concurrently. So SQLite is employed accordingly.

Selection of development language. Common Gateway Interface (CGI) applications can be written in a number of different languages, such as C, C++, Java, PHP, Python and PERL. C is a structured, procedural programming language that has been widely used both for operating systems and applications and that has been standardized as part of the Portable Operating System Interface (POSIX). C is employed to write the CGI scripts for the following reasons: 1) CGI programs written in C are stable and secure for the program is compiled and unmodifiable; 2) Linux is written in C with built-in C compiler, and it's a waste of resource to install other languages' compiler; 3) The scripts generated by C are relatively small and have faster execution speed; 4) The logic interactions of the hardware must use the C language;. In a word, the system platform and tools for IOTGW implementation are AM3352 + Linux + AppWeb + SQLite + C language.

The development of IOTGW system includes the realization of hardware and software, and the specific contents are as shown in Fig. 2 and Fig. 3 respectively. to space constraints, the following focuses on the core part of the secure IOTGW development-compilation and transplantation of AppWeb with Secure Sockets Layer (SSL).

Compilation and Transplantation of AppWeb with SSL

In the IGMS, the communication between the server and the client contains the device status, user data, control commands and other sensitive information, so it's necessary to configure the secure transmission system in the AppWeb. The Secure Sockets Layer is a commonly-used protocol for managing the security of a message transmission on the Internet. SSL uses the public-and-private key encryption system from RSA, which also includes the use of a digital certificate, to establish the security of connection between the client and server and to prevent eavesdropping and tampering. Therefore, the SSL protocol is added in AppWeb to establish an encrypted data connection, and the main steps are as follows.

Building the cross compile environment. The host computer is a general-purpose PC running the Linux operating system, which communicates with the target, AM3352, via a serial port and network connection. The prepared cross compilation tool chain (cross-3.2.tar.bz2) can be downloaded from "ftp://ftp.arm.linux.org.uk/". In order to make the arm-linux cross compiler ready to use, the toolchain is decompressed and environment variable PATH is modified by following codes.

After the cross compilation tool chain is installed, the Configure file is modified by following commands.

The IP addresses of host computer and target board are in the same segment, for example, the former is 192.168.1.6 and the latter is 192.168.1.15. The TFTP service is enabled to download the kernel image and file system mirroring to the target board. Using the NFS, the file directory of host computer is mounted to the target board via export CC="/usr/local/arm/bin/arm-linux-gcc" export AR="/usr/local/arm/bin/arm-linux-ar" export LD="/usr/local/arm/bin/arm-linux-ld" export RANLIB="/usr/local/arm/bin/arm-linux-ranlib" export STRIP="/usr/local/arm/arm-linux-strip" export CC_FOR_BUILD="gcc" tar xvzf cross-3.2.tar.bz2 export PATH=/usr/local/arm/3.2/bin:$PATH "sudo mount 192.168.1.15:/tftpboot/mnt/nfs", consequently, host files can be directly read and written on the target board and application programs can be debugged expediently.

Download and decompression of source. The AppWeb source package and MatrixSSL open source are downloaded from "http://appwebserver.org/" and "http://www.matrixssl.org/" respectively, and then the following commands are executed to decompress them.

Cross compilation of AppWeb with MatrixSSL.

The CPU types of host computer and target board are i686 and ARM Cortex-A8, so the Configure commands are as follows.

The cross compilation result is shown in Fig. 4.

Fig. 4. Cross compilation result of AppWeb with MatrixSSL

Then, the executable and configuration files of AppWeb and dynamic and static linking libraries of MatrixSSL will be generated.

Transplantation of AppWeb with MatrixSSL. The files in /etc/appweb, such as appweb.conf, conf/, groups.db, users.db, mime.types, are moved to working directory firstly, then the appweb.conf is modified as follows.

Open the Web service. Finally, the Web service is enabled via "./appweb -f appweb.conf &", and the AppWeb server can be visited in PC browser by "httpS://192.168.1.15:4443", as shown in Fig. 5.

./configure --host=arm-Cortex-A8-linux --build=i686-pc-linux --port=80 --type=RELEASE --enable-log --disable-shared-libc --disable-access-log --disable-shared --enable-static --enable-multi-thread --disable-test --disable-samples --prefix=/usr/appweb --webDir=/var/www --with-cgi=builtin --with-copy=builtin --with-auth=builtin --with-esp=builtin --with-upload=builtin --with-matrixssl=builtin --with-ssl=builtin --with-matrixssl-dir=/usr/local/matrixssl/src --with-matrixssl-libpath=/usr/local/matrixssl/src --with-matrixssl-iflags="-I/usr/local/matrixssl/src" --with-matrixssl-libs=libmatrixsslstatic make tar -xvzf appweb-4.

Conclusions and Future Work

Internet of Things is a huge global information system composed of hundreds of millions of objects that can be identified, sensed and processed based on standardized and interoperable communication protocols. The IOT based granary management can intelligently process the perception devices' state, provide management and control for decision-making, and even make them cooperate with each other autonomously without manager's intervention. IOTGW plays an important role in IGMS, which facilitates the seamless integration of perception objects and Internet, and the ServerRoot "." ErrorLog "logs/error.log" DocumentRoot "/var/www" LoadModulePath "/usr/appweb/modules" Listen 80 <if SSL_MODULE> Listen 4443 </if> <if SSL_MODULE> LoadModule ssl libsslModule <if MATRIXSSL_MODULE> LoadModule matrixSsl libmatrixSslModule </if> </if> LoadModule cgi libcgiModule AddHandler cgiHandler .cgi .cgi-nph .bat .cmd .pl .py ScriptAlias /cgi-bin/ "$DOCUMENT_ROOT/cgi-bin" SSLCertificateFile "$SERVER_ROOT/server.crt" SSLCertificateKeyFile "$SERVER_ROOT/server.key.pem" management and control with perception devices. This paper presents a secure IOTGW based on AppWeb and MatrixSSL, which has guarantee of information security in addition to achievement of data forwarding, protocol transformation and device control. Furthermore, the IOTGW framework is flexible, making it usable for many applications, such as smart home, industrial monitoring, smart grid, monitoring and so on. In future works, the IOTGW will be put into practice to build a county intelligent granary management system, then improvement and production will be considered.

Fig. 1 .

 1 Fig. 1. IOT architecture of IGMS

Fig. 3 .

 3 Fig. 3. Software architecture of IOTGW system

Fig. 5 .

 5 Fig. 5. Interface of video surveillance in the browser

Acknowledgment

This work has been funded by Advance Research Project of Xi'an Communications Institute under grant No.XATYB013. The authors would like to thank Prof. Yanpu Chen for his help and valuable comments.

AppWeb

Over 4500 requests per second (r/s); Supports HTTP/1.0, HTTP/1.


M Nagayama

Thanh Nam Nguyen

On the ω-limit set of a nonlocal differential equation proposed by

We study the ω-limit set of solutions of a nonlocal ordinary differential equation, where the nonlocal term is such that the space integral of the solution is conserved in time. Using the monotone rearrangement theory, we show that the rearranged equation in one space dimension is the same as the original equation in higher space dimensions. In many cases, this property allows us to characterize the ω-limit set for the nonlocal differential equation. More precisely, we prove that the ω-limit set only contains one element.

Introduction

The aim of this present paper is to study the ω-limit set of solutions of the initial value problem (P )

           u t = g(u)p(u) -g(u) Ω g(u)p(u) Ω g(u)
x ∈ Ω, t ≥ 0, u(x, 0) = u 0 (x)

x ∈ Ω.

Here Ω ⊂ IR N (N ≥ 1) is an open bounded set, g, p : IR → IR are continuously differentiable and u 0 is a bounded function. More precise conditions on g, p and u 0 will be given later. A typical example is given by the functions g(u) = u(1 -u) and p(u) = u. In this case, the equation becomes

u t = u 2 (1 -u) -u(1 -u) Ω u 2 (1 -u) Ω u(1 -u)
.

Problem (P ) has been originally proposed by M. Nagayama [START_REF] Nagayama | [END_REF] to express bubble motion with chemical reaction where the volume constraint is considered. By integrating the equation in (P ), it is easy see that solutions of (P ) satisfy the mass conservation property: Ω u(x, t) dx = Ω u 0 (x) dx for all t ≥ 0.

We refer to Proposition 2.2 for a rigorous proof of this property.

We will consider Problem (P ) under some different hypotheses on the initial function u 0 . Problem (P ) possesses a Lyapunov functional whose form depends on the hypothesis satisfied by u 0 (see section 4 for more details).

In this paper, we always consider the following hypotheses on the functions g and p:

p ∈ C 1 (IR) is strictly increasing on IR, g ∈ C 1 (IR), g(0) = g(1) = 0, g > 0 on (0, 1) and g < 0 on (-∞, 0) ∪ (1, ∞).

We suppose that the initial function satisfies one of the following hypotheses: (H 1 ) u 0 ∈ L ∞ (Ω), u 0 (x) ≥ 1 for a.e. x ∈ Ω, and u 0 ≡ 1. (H 2 ) u 0 ∈ L ∞ (Ω), 0 ≤ u 0 (x) ≤ 1 for a.e. x ∈ Ω, and Ω g(u 0 (x)) dx = 0. (H 3 ) u 0 ∈ L ∞ (Ω), u 0 (x) ≤ 0 for a.e. x ∈ Ω, and u 0 ≡ 0. Note that Hypothesis (H 1 ) (and also (H 3 )) implies that Ω g(u 0 ) = 0.

Before defining a solution of Problem (P ), we introduce the notation F (u) := g(u)p(u) -g(u) Ω g(u)p(u) Ω g(u)

.

(

) 1
Definition 1.1. Let 0 < T ≤ ∞. The function u ∈ C 1 ([0, T ); L ∞ (Ω)) is called a solution of Problem (P ) on [0, T ) if the three following properties hold

(i) u(0) = u 0 , (ii) Ω g(u(t)) = 0 for all t ∈ [0, T ), (iii) du dt = F (u) for all t ∈ [0, T ).
The ω-limit sets are important and interesting objects in the theory of dynamical systems. Understanding their structure allows us to apprehend the long time behavior of solutions of dynamical systems. In this paper, we characterize the ω-limit set of solutions of Problem (P ), which is defined as follows:

Definition 1.2. We define the ω-limit set of u 0 by

ω(u 0 ) := {ϕ ∈ L 1 (Ω) : ∃t n → ∞, u(t n ) → ϕ in L 1 (Ω) as n → ∞}.
In the above definition, we do not use the L ∞ -topology to define ω(u 0 ) because the solution often develops sharp transition layers which cannot be captured by the L ∞ -topology. Note also that as we will see in Theorem 2.5, solutions of (P ) are uniformly bounded so that the topology of L 1 is equivalent to that of L p with p ∈ [1, ∞). For convenience, we refer to the books [START_REF] Robinson | Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors[END_REF][START_REF] Temam | Infinite-Dimensonal Dynamical Systems in Mechanics and Physics[END_REF] for studies about dynamical systems as well as the structure of ω-limit sets.

An essential step to study ω(u 0 ) is to show the relative compactness of the solution orbits in L 1 (Ω). In local problems, the standard comparison principle can be applied to obtain the uniform boundedness of solutions. Furthermore, in local problems with a diffusion term, such as local parabolic problems, the uniform boundedness of solutions implies the relative compactness of solution orbits in some suitable spaces by using Sobolev imbedding theorems. However, the above scheme cannot be applied to Problem (P ), due to the presence of the nonlocal term as well as to the lack of a diffusion term.

By careful observation of the dynamics of pathwise trajectories (i.e. the sets {u(x, t) : t ≥ 0} for x ∈ Ω), we show the existence of invariant sets and hence the uniform boundedness of solutions. The difficulties connected with the lack of diffusion term will be overcome by using ideas presented in [START_REF] Hilhorst | On the large time behaviour of the solutions of a nonlocal ordinary differential equation[END_REF]. More precisely, applying the rearrangement theory, we introduce the equi-measurable rearrangement u and show that it is the solution of a onedimensional problem (P ) (see section 3). Since the orbit {u (t) : t ≥ 0} is bounded in BV (Ω ), where Ω := (0, |Ω|) ⊂ IR, it is relatively compact in L 1 (Ω ). We then deduce the relative compactness of solution orbits of Problem (P ), by using the fact that

u(t) -u(τ ) L 1 (Ω) = u (t) -u (τ ) L 1 (Ω ) . (2)
Note that the inequality u(t) -u(τ ) L 1 (Ω) ≥ u (t) -u (τ ) L 1 (Ω ) follows from a general property of the rearrangement theory. The important point is that (2) involves an equality.

An other advantage of considering Problem (P ) is that the differential equations in (P ) and (P ) have the same form. Therefore we will study the ω-limit set for Problem (P ) rather than for Problem (P ). Although (P ) possesses many stationary solutions, the one-dimensional structure of Problem (P ) allows us to characterize its ω-limit set, and then deduce results for that of (P ).

The organization of this article is as follows: In section 2, we prove the global existence and uniqueness of the solution as well as its uniform boundedness. Next in section 3, we recall and apply results from the arrangement theory presented in [START_REF] Hilhorst | On the large time behaviour of the solutions of a nonlocal ordinary differential equation[END_REF] to obtain the relative compactness of the solution in L 1 (Ω). In section 4, we prove that Problem (P ) possesses Lyapunov functionals and use them together with the relative compactness of the solution to show that ω(u 0 ) is nonempty and consists of stationary solutions. Moreover, these stationary solutions are step functions. More precise properties of these functions are given in Theorems 4.4 and 4.5. In section 5, we suppose that one of the hypotheses (H 1 ) or (H 3 ) holds and prove that ω(u 0 ) only contains one element.

If Hypothesis (H 2 ) is satisfied, the properties obtained in Theorems 4.4 and 4.5 are not sufficient to show that ω(u 0 ) contains one element even in one space dimension. This is an open problem and we conjecture that if (H 2 ) holds, then ω(u 0 ) only contains one element.

2 Existence and uniqueness of solutions of (P )

Local existence

First we proves the local Lipschitz property of the nonlocal nonlinear term F , given by ( 1), in the space L ∞ (Ω).

Lemma 2.1 (Local Lipschitz continuity of F ). Let v ∈ L ∞ (Ω) be such that Ω g(v(x)) dx = 0. Then there exist a L ∞ (Ω)-neigbourhood V of v and a constant L > 0 such that F ( v) is well-defined for all v ∈ V and that F (v 1 ) -F (v 2 ) L ∞ (Ω) ≤ L v 1 -v 2 L ∞ (Ω) , for all v 1 , v 2 ∈ V. Proof. Since g is continuous, the map v → Ω g(v) is continuous from L ∞ (Ω) to L ∞ (Ω). It follows that there exist a constant α > 0 and a neighbourhood V of v such that Ω g( v) ≥ α for all v ∈ V. (3)
Without loss of generality, we may choose

V := { v ∈ L ∞ (Ω) : v -v L ∞ (Ω) ≤ ε},
for a constant ε > 0 small enough. We set

c := v L ∞ (Ω) + ε, f (s) := g(s)p(s), and
K := max sup [-c,c] |f (s)|, sup [-c,c] |g(s)|, sup [-c,c] |f (s)|, sup [-c,c] |g (s)| .
Then the following properties holds and will be used later: For all v 1 , v 2 ∈ V,

f (v 1 ) -f (v 2 ) L ∞ (Ω) ≤ K v 1 -v 2 L ∞ (Ω) , (4)
and

g(v 1 ) -g(v 2 ) L ∞ (Ω) ≤ K v 1 -v 2 L ∞ (Ω) .
We have

F (v 1 ) -F (v 2 ) = [f (v 1 ) -f (v 2 )] -     g(v 1 ) Ω f (v 1 ) Ω g(v 1 ) -g(v 2 ) Ω f (v 2 ) Ω g(v 2 )     = [f (v 1 ) -f (v 2 )] - g(v 1 ) Ω f (v 1 ) Ω g(v 2 ) -g(v 2 ) Ω f (v 2 ) Ω g(v 1 ) Ω g(v 1 ) Ω g(v 2 ) =: A 1 - A 2 A 3 ,
where

A 1 := f (v 1 ) -f (v 2 ), A 2 := g(v 1 ) Ω f (v 1 ) Ω g(v 2 ) -g(v 2 ) Ω f (v 2 ) Ω g(v 1 ),
and

A 3 := Ω g(v 1 ) Ω g(v 2 ).
In the sequel, we estimate A 1 , A 2 and A 3 . First the inequality (4) yields

A 1 L ∞ (Ω) ≤ K v 1 -v 2 L ∞ (Ω) . (5)
Next we write A 2 as

A 2 = g(v 1 ) Ω f (v 1 ) Ω g(v 2 ) -g(v 2 ) Ω f (v 1 ) Ω g(v 2 ) + g(v 2 ) Ω f (v 1 ) Ω g(v 2 ) -g(v 2 ) Ω f (v 2 ) Ω g(v 2 ) + g(v 2 ) Ω f (v 2 ) Ω g(v 2 ) -g(v 2 ) Ω f (v 2 ) Ω g(v 1 ),
or equivalently,

A 2 = [g(v 1 ) -g(v 2 )] Ω f (v 1 ) Ω g(v 2 ) + g(v 2 ) Ω [f (v 1 ) -f (v 2 )] Ω g(v 2 ) + g(v 2 ) Ω f (v 2 ) Ω [g(v 2 ) -g(v 1 )],
which in turn implies that

A 2 L ∞ (Ω) ≤ 3K 3 |Ω| 2 v 1 -v 2 L ∞ (Ω) . (6)
As for the term A 3 , we apply (3) to obtain

|A 3 | ≥ α 2 > 0. (7)
Combining ( 5), ( 6) and ( 7), we deduce that

F (v 1 ) -F (v 2 ) L ∞ (Ω) ≤ K + 3K 3 |Ω| 2 α 2 v 1 -v 2 L ∞ (Ω) .
This completes the proof of Lemma 2.1.

Proposition 2.2. Let u 0 ∈ L ∞ (Ω) satisfy Ω g(u 0 ) = 0. Then Problem (P ) has a unique local-in-time solution. Moreover, we have

Ω u(x, t) dx = Ω u 0 (x) dx for all t ∈ [0, T max (u 0 )), (8)
where T max (u 0 ) denotes the maximal time interval of the existence of solution.

Proof. Since F is locally Lipschitz continuous in L ∞ (Ω), the local existence follows from the standard theory of ordinary differential equations. We now prove [START_REF] Temam | Infinite-Dimensonal Dynamical Systems in Mechanics and Physics[END_REF]. Integrating the differential equation in Problem (P ) from 0 to t, we obtain

u(t) -u 0 = t 0 u t (s) ds = t 0 F (u(s)) ds. It follows that Ω u(x, t) dx - Ω u 0 (x) dx = t 0 Ω F (u) dxds = 0,
where the last identity holds since

Ω F (u) dx = 0.
This completes the proof of the lemma.

Lemma 2.3. If T max (u 0 ) < ∞ and lim sup t↑Tmax(u 0 ) F (u(t)) L ∞ (Ω) < ∞, then u(T max (u 0 )-) := lim t↑Tmax(u 0 ) u(t) exists in L ∞ (Ω) and Ω g(u(T max (u 0 )-)) = 0.
Proof. For simplicity we write T max instead of T max (u 0 ). Set

M := lim sup t↑Tmax F (u(t)) L ∞ (Ω) < ∞.
Then there exists 0 < T < T max such that

F (u(t)) L ∞ (Ω) ≤ 2M for all t ∈ [T, T max ).
Consequently, for any t, t ∈ [T, T max ), with t < t , we have

u(t) -u(t ) L ∞ (Ω) ≤ t t F (u(s)) ds ≤ 2M |t -t |.
Thus {u(t)} is a Cauchy sequence so that the limit u(T max -) := lim t↑Tmax u(t) exists in L ∞ (Ω). If Ω g(u(T max -)) = 0, then, by Lemma 2.2, we can extend the solution on [T max , T max + δ), with some δ > 0, which contradicts the definition to T max . This completes the proof of the lemma.

Global solution

In this subsection, we fix u 0 ∈ L ∞ (Ω) satisfying Ω g(u 0 ) = 0 and denote by [0, T max ) the maximal time interval of the existence of solution. Set

λ(t) = Ω g(u)p(u) Ω g(u) for all t ∈ [0, T max ), (9)
and study solutions Y (t; s) of the following auxiliary problem:

(ODE)

   Ẏ = g(Y )p(Y ) -g(Y )λ(t), t > 0, Y (0) = s, (10)
where Ẏ := dY /dt. We remark that the function u satisfies u(x, t) = Y (t; u 0 (x)) for a.e. x ∈ Ω and all t ∈ [0, T max ).

(11)

Lemma 2.4. Let s < s and let 0 < T < T max . Assume that Problem (ODE) possesses the solutions Y (t; s), Y (t; s) ∈ C 1 ([0, T ]), respectively. Then

Y (t; s) < Y (t; s) for all t ∈ [0, T ]. (12)
Proof. Since Y (0; s) = s < s = Y (0; s), the assertion follows immediately from the backward uniqueness of solution of (ODE).

Theorem 2.5. Assume that one of the hypotheses (H 1 ), (H 2 ), (H 3 ) holds.

Then Problem (P ) possesses a global solution u ∈ C 1 ([0, ∞); L ∞ (Ω)). Moreover:

(i) If (H 1 ) holds, then for all t ≥ 0,

1 ≤ u(x, t) ≤ ess sup Ω u 0 a.e. x ∈ Ω. ( 13
) (ii) If (H 2 ) holds, then for all t ≥ 0, 0 ≤ u(x, t) ≤ 1 a.e. in Ω. ( 14
) (iii) If (H 3 ) holds, then for all t ≥ 0, ess inf Ω u 0 ≤ u(x, t) ≤ 0 a.e. x ∈ Ω.
Proof. For simplicity, we set

a := ess inf Ω u 0 , b := ess sup Ω u 0 .
We only prove (i) and (ii). The proof of (iii) is similar to that of (i).

(i) First, we show that (13) holds as long as the solution u exists and then deduce the global existence from Lemma 2.3. Let Y (t; s) be the solution of (ODE). We remark that b ≥ 1 and that Y (t, 1) ≡ 1 for all t ∈ [0, T max ). The monotonicity of Y (t; s) in s implies that as long as u, Y (t; b) both exist

1 ≡ Y (t, 1) ≤ Y (t; u 0 (x)) = u(x, t) ≤ Y (t; b) a.e. x ∈ Ω. ( 15
)
The first inequality above implies the first inequality of (13) as long as the solution u exists. It remains to prove the second inequality of (13). To that purpose, it suffices to show that

Y (t; b) ≤ b (16)
as long as the solution Y (t; b) exists. In view of (15), we have 1 ≤ u(x, t) ≤ Y (t; b). Then the definition of g and the monotonicity of p imply that

g(Y (t; b)) ≤ 0, g(u(x, t)) ≤ 0, p(Y (t, b)) ≥ p(u(x, t)),
for a.e. x ∈ Ω. As a consequence,

Ẏ (t; b) = g(Y (t, b))(p(Y (t; b)) -λ(t)) ≤ 0. Hence Y (t, b) ≤ Y (0; b) = b,
which completes the proof of (16). Thus (13) is satisfied as long as the solution u exists.

Next we show that the solution u exists globally. Suppose, by contradiction, that T max < ∞. We have for all t ∈ [0, T max ),

|λ(t)| ≤ Ω |g(u)p(u)| Ω g(u) = Ω |g(u)| |p(u)| Ω |g(u)| ≤ max{|p(1)|, |p(b)|}.
It follows that there exists C > 0 such that F (u(t)) L ∞ (Ω) ≤ C for all t ∈ [0, T max ). By Lemma 2.3, u(T max -) := lim t↑Tmax u(t) exists in L ∞ (Ω) and

Ω g(u(T max -)) = 0.
Since u(x, t) ≥ 1 for a.e x ∈ Ω, t ∈ [0, T max ), u(x, T max -) ≥ 1 for a.e.

x ∈ Ω. Hence Ω g(u(T max -)) = 0 if and only if u(x, T max -) ≡ 1. The mass conservation property (cf. ( 8)) yields Ω u 0 = |Ω|. Hence u 0 (x) = 1 for a.e x ∈ Ω. This contradicts Hypothesis (H 1 ) so that T max = ∞.

(ii) Since Y (t, 1) ≡ 1, Y (t, 0) ≡ 0, we deduce that

0 ≡ Y (t, 0) ≤ Y (t; u 0 (x)) = u(x, t) ≤ Y (t, 1) ≡ 1 a.e. x ∈ Ω.
This implies (14) as long as the solution u exists. We now prove that T max = ∞. Indeed, suppose, by contradiction, that T max < ∞. Since 0 ≤ u(x, t) ≤ 1 for a.e. x ∈ Ω, and all t ∈ [0, T max ), g(u(x, t)) ≥ 0 for a.e. x ∈ Ω, and all t ∈ [0, T max ). Therefore

|λ(t)| ≤ Ω |g(u)p(u)| Ω g(u) = Ω g(u) |p(u)| Ω g(u)
≤ max{|p(0)|, |p(1)|}, for all t ∈ [0, T max ). It follows that there exists C > 0 such that F (u(t)) L ∞ (Ω) ≤ C for all t ∈ [0, T max ). By Lemma 2.3, u(T max -) := lim t↑Tmax u(t) exists in L ∞ (Ω) and

Ω g(u(T max -)) = 0.
This implies that u(T max -) only takes two values 0 and 1. Or equivalently, Y (T max -; u 0 (x)) only takes two values 0 and 1. Thus the backward uniqueness of the solution of the initial value problem (ODE) implies that u 0 (x) only takes two values 0 and 1; hence Ω g(u 0 ) = 0. This contradicts Hypothesis (H 2 ) so that T max = ∞.

The result below follows from the proof of Theorem 2.5.

Corollary 2.6. Assume that one of the hypotheses (H 1 ), (H 2 ), (H 3 ) holds and let λ(t) be defined by (9). Then there exists C > 0 such that

|λ(t)| ≤ C for all t ∈ [0, ∞).
3 Boundedness of the solution and one-dimensional associated problem (P )

All the results in this section are similar to those of [2, Section 3]. We recall and state some important results. Let w be a function from Ω to IR and let Ω := (0, |Ω|) ⊂ IR. The distribution function of w is given by µ w (s) := |{x ∈ Ω : w(x) > s}|. Theorem 3.3. Let one of the hypotheses (H 1 ), (H 2 ), (H 3 ) hold. We define

u (y, t) := (u(t)) (y) on Ω × [0, +∞). ( 18
)
Then u is the unique solution in

C 1 ([0, ∞); L ∞ (Ω )) of Problem (P ) (P )              dv dt = g(v)p(v) -g(v) Ω g(v)p(v) Ω g(v) t > 0, v(0) = u 0 .
Moreover, for all t ≥ 0,

u (y, t) = Y (t; u 0 (y)) for a.e. y ∈ Ω , ( 19
)
and the assertions (i), (ii), (iii) of Theorem 2.5 hold for the function u .

Lemma 3.4 ([2, Lemma 3.7]). Let u be the solution of (P ) with u 0 ∈ L ∞ (Ω) and let u be as in (18). Then

u (t) -u (τ ) L 1 (Ω ) = u(t) -u(τ ) L 1 (Ω) , (20)
for any t, τ ∈ [0, ∞).

Corollary 3.5 ([2, Corollary 3.9]). Let {t n } be a sequence of positive numbers such that t n → ∞ as n → ∞. Then the following statements are equivalent

(a) u (t n ) → ψ in L 1 (Ω ) as n → ∞ for some ψ ∈ L 1 (Ω ); (b) u(t n ) → ϕ in L 1 (Ω) as n → ∞ for some ϕ ∈ L 1 (Ω) with ϕ = ψ.
The following proposition follows by similar results in [2, Lemma 3.5 and Proposition 3.10]. Proposition 3.6. Let one of the hypotheses (H 1 ), (H 2 ), (H 3 ) hold. Then {u(t) : t ≥ 0} is relatively compact in L 1 (Ω) and the set {u (t) : t ≥ 0} is relatively compact in L 1 (Ω ).

4 Lyapunov functional and ω-limit set for (P )

We define three Lyapunov functionals according to whether the initial function satisfies either Hypothesis (H 1 ), (H 2 ) or (H 3 ). More precisely, we define for i = 1, 2, 3 the functional E i by

E i (u) = (-1) i+1 Ω P(u), (21)
where

P(s) = s 0 p(τ ) dτ.
Lemma 4.1 (Lyapunov functional). Assume that the hypotheses (H i ) holds either for i = 1, or for i = 2, or for i = 3. Then (i) There exists C > 0 such that for all τ 2 > τ 1 ≥ 0,

E i (u(τ 2 )) -E i (u(τ 1 )) = (-1) i+1 τ 2 τ 1 Ω g(u)(p(u) -λ(t)) 2 dxdt ≤ -C τ 2 τ 1 Ω |u t | 2 dxdt ≤ 0. (ii) E i (u(•)
) is continuous and non increasing on [0, ∞), and the limit E i∞ := lim t→∞ E i (u(t)) exists.

Remark 4.2. Note that the solution orbit {u(t) : t ≥ 0} is uniquely defined by the initial function u 0 . Hence E i∞ -the limit of the Lyapunov functional a long the solution orbit-is also uniquely defined by the initial function. We will use the quantity E i∞ to make a constrain for all elements in the ω-limit set (see Proposition 4.3 (ii) below) then use it to characterize the ω-limit set.

Proof of Lemma 4.1. (i) We only give the proof for the case i = 1. We have

d dt E 1 (u(t)) = d dt Ω P(u) dx = Ω p(u)u t dx.
Since

Ω u t dx = 0, it follows that d dt E 1 (u(t)) = Ω (p(u) -λ(t))u t dx = Ω g(u)(p(u) -λ(t)) 2 dx. ( 22
) Set C = - 1 min s∈[1,ess sup u 0 ] g(s) > 0.
Then, since for all t ≥ 0, 1 ≤ u(t) ≤ ess sup u 0 a.e. in Ω, we have, for all t ≥ 0,

- 1 C ≤ g(u(t)) ≤ 0 a.e. in Ω.
As a consequence, for all t ≥ 0, g(u(t)) ≤ -Cg 2 (u(t)) a.e in Ω.

Substituting this inequality into (22) yields

d dt E 1 (u(t)) ≤ -C Ω g 2 (u)(p(u) -λ(t)) 2 dx = -C Ω |u t | 2 dx ≤ 0,
which proves (i).

(ii) As a consequence of (i), E i (u(•)) is continuous and nonincreasing. Moreover, E i is bounded from below. Therefore there exists the limit of E i (u(t)) as t → ∞, which completes the proof of (ii). Proposition 4.3. Assume that one of the hypotheses (H i ), (i = 1, 2, 3) holds. Then (i) ω(u 0 ) a nonempty set in L 1 (Ω).

(ii) Let E i∞ be given in Lemma 4.1, we have

E i (ϕ) = E i∞ for all ϕ ∈ ω(u 0 ). ( 23
)
In other words, E i (•) is constant on ω(u 0 ).

(iii) Any element ϕ ∈ ω(u 0 ) either satisfies Ω g(ϕ) dx = 0 or is a stationary solution of Problem (P ).

Proof. (i) follows from Proposition 3.6. (ii) Let ϕ ∈ ω(u 0 ) and let t n → ∞ be a sequence such that

u(t n ) → ϕ in L 1 (Ω) as n → ∞.
Since {u(x, t n )} is uniformly bounded, the convergence u(t n ) → ϕ implies

E i (u(t n )) → E i (ϕ) as n → ∞.
Hence in view of Lemma 4.1 (ii) we have

E i (ϕ) = lim n→∞ E i (u(t n )) = E i∞ . (iii) Assume that Ω g(ϕ(x)) dx = 0;
we show below that ϕ is a stationary solution of Problem (P ). Let {t n } be a sequence such that t n → ∞ and

u(t n ) → ϕ in L 1 (Ω) as n → ∞. (24)
It follows from Lemma 4.1 that

+∞ 0 Ω |u t | 2 dxdt ≤ 1 C (E i (u 0 ) -lim t→∞ E i (u(t)) < +∞. Thus lim n→∞ tn+1 tn Ω |u t | 2 dxdt = 0.
It follows that for t ∈ [0, 1],

u(t n + t) -ϕ L 1 (Ω) ≤ u(t n + t) -u(t n ) L 1 (Ω) + u(t n ) -ϕ L 1 (Ω) ≤ tn+t tn u t L 1 (Ω) + u(t n ) -ϕ L 1 (Ω) ≤ t 1 2 |Ω| 1 2 tn+t tn Ω |u t | 2 dxdt 1 2 + u(t n ) -ϕ L 1 (Ω) → 0
as n → ∞. Hence for all t ∈ [0, 1],

u(t n + t) → ϕ in L 1 (Ω) as n → ∞.
Set f (s) = g(s)p(s); then the uniform boundedness of u (cf. Theorem 2.5) implies that for all t ∈ [0, 1],

f (u(t n + t)) → f (ϕ), g(u(t n + t)) → g(ϕ) in L 1 (Ω).
as n → ∞. Note that Ω g(ϕ) = 0 implies

λ(t n + t) := Ω f (u(t n + t)) Ω g(u(t n + t)) → Ω f (ϕ) Ω g(ϕ)
as n → ∞.

It follows that for all

t ∈ [0, 1] Ω F (u(t n + t)) dx → Ω F (ϕ) dx as n → ∞,
where F is defined by [START_REF] Ambrosio | Functions of bounded variation and free discontinuity problems[END_REF]. On the other hand, the uniform boundedness of u(x, t) and Corollary 2.6 imply that F (u(x, t)) is uniformly bounded. Thus

Ω F 2 (u(t n + t)) dx → Ω F 2 (ϕ) dx as n → ∞, for all t ∈ [0, 1]
. By Lebesgue's dominated convergence theorem, we have

1 0 Ω F 2 (u(t n + t)) dxdt → 1 0 Ω F 2 (ϕ) dxdt as n → ∞. Since 1 0 Ω F 2 (u(t n +t)) dxdt = tn+1 tn Ω F 2 (u(t)) dxdt = tn+1 tn Ω |u t | 2 dxdt → 0, as n → ∞, it follows that 1 0 Ω F 2 (ϕ) dxdt = 0.
This yields F (ϕ) = 0 a.e. in Ω, or equivalently,

g(ϕ)     p(ϕ) -Ω g(ϕ)p(ϕ) Ω g(ϕ)     = 0 a.e. in Ω.
Therefore ϕ is a stationary solution of Problem (P ).

In two following theorems, we obtain a more precise form and constraints of the elements in the ω-limit set.

Theorem 4.4. Assume that one of hypotheses (H i ), (i = 1, 2, 3) holds and let ϕ ∈ ω(u 0 ). Then:

(i) If (H 1 ) holds, then 1 ≤ ϕ ≤ ess sup Ω u 0 and ϕ is a step function. More precisely, ϕ = µχ A 1 + χ Ω\A 1 , where µ > 1, A 1 ⊂ Ω, |A 1 | = 0. (ii) If (H 2 ) holds, then 0 ≤ ϕ ≤ 1 and ϕ is a step function. More precisely, ϕ = χ A 1 + νχ A 2 , where 0 < ν < 1, A 1 , A 2 ⊂ Ω, with A 1 ∪ A 2 ⊂ Ω and A 1 ∩ A 2 = ∅. (iii) If (H 3 ) holds, then ess inf Ω u 0 ≤ ϕ ≤ 0 and ϕ is a step function. More precisely, ϕ = ξχ A 1 , where ξ < 0, A 1 ⊂ Ω, |A 1 | = 0.
Proof. We only prove (i); the proofs of (ii) and (iii) are similar. Since for all t ≥ 0, 1 ≤ u(t) ≤ ess sup Ω u 0 a.e. in Ω, it follows that 1 ≤ ϕ ≤ ess sup Ω u 0 a.e. in Ω.

Note that since Ω ϕ = Ω u 0 > |Ω|, ϕ ≡ 1. Therefore Ω g(ϕ) < 0. It follows from Proposition 4.3 (iii) that ϕ is a stationary solution of (P ), namely

Since we know the existence of a function ϕ , we also know that the system (26) possesses a solution. We show below that it is unique. Indeed, we deduce from (26) that P(µ) -P( 1 Hence G is strictly increasing on (1, ∞). It follows that the equation (28) admits at most one solution µ > 1. Furthermore, in view of Remark 4.2, the right-hand-side of (28) is uniquely defined by the initial function u 0 . Thus µ is uniquely defined by the initial function. Therefore also a 1 is uniquely determined. The knowledge of the constants µ and a 1 completely determines the stationary solution ϕ , so that ω(u 0 ) only contains one element.

Next we show that ω(u 0 ) only contains one element. Since ω(u 0 ) only contains one element, u (t) converges to ϕ as t → ∞. Consequently, u (t) is a Cauchy sequence in L 1 (Ω ). By Lemma 3.4, u(t) is also a Cauchy sequence in L 1 (Ω). This implies that u(t) converges as t → ∞ and hence ω(u 0 ) only contains one element.

The following result is an immediate consequence of Theorem 5.1 and the uniform boundedness of u.

Definition 3 . 1 .

 31 The (one-dimensional) decreasing rearrangement of w, denoted by w , is defined on Ω = [0, |Ω|] by w (0) := ess sup(w) w (y) = inf{s : µ w (s) < y}, y > 0. (17) Remark 3.2. The function w is nonincreasing on Ω and we have µ w (s) = µ w (s) for all s ∈ IR. Moreover, if a ≤ w(x) ≤ b a.e. x ∈ Ω, then a ≤ w (y) ≤ b for all y ∈ Ω .

  the monotonicity of p yieldsϕ = µχ A 1 + χ Ω\A 1 , for some constant µ > 1 and A 1 ⊂ Ω. Moreover |A 1 | = 0 since ϕ ≡ 1.Hence using the mass conservation property and recalling that m 0 := Ω u 0 , we obtainµa 1 + |Ω| -a 1 = m 0 P(µ)a 1 + P(1)(|Ω| -a 1 ) = E 1∞ ,or equivalently, (µ -1)a 1 = m 0 -|Ω| (P(µ) -P(1))a 1 = E 1∞ -P(1)|Ω|.

2 = s 1 [

 21 monotonicity of p to deduce that G (s) = p(s)(s -1) -(P(s) -P(1)) (s -1) p(s) -p(τ )]dτ (s -1) 2 > 0 for s > 1.

Corollary 5 . 2 .

 52 Let (H i ) hold for i = 1 or 3. Then for all p ∈ [1, ∞), u(t) → ϕ in L p (Ω) as t → ∞,where ϕ is given in Theorem 5.1.

Acknowledgements

The author would like to thank Prof. Danielle Hilhorst for many helpful discussions.

Theorem 4.5. Assume that one of hypotheses (H i ), (i = 1, 2, 3) holds. Let ϕ ∈ ω(u 0 ) and let E i∞ be given in Lemma 4.1 (ii). We set m 0 := Ω u 0 . Then (i) If (H 1 ) holds, then

Proof. We only prove (i). The other cases can be proven in a similar way. We apply (23) for i = 1 to obtain

Hence (i) follows from (25), the mass conservation property and Theorem 4.4.

5 Large time behavior of the solution of (P )

In this section, we only suppose Hypotheses (H 1 ), (H 3 ). (ii) Let (H 3 ) hold. Then ω(u 0 ) only contains one element, denoted by ϕ. Moreover, ϕ is a step function of the form ϕ = ξχ A 1 with A 1 ⊂ Ω, and ξ < 0.

Proof. We only prove (i). First we prove that ω(u 0 ) only contains one element. Note that (cf. Corollary 3.5) any element of ω(u 0 ) has the form ϕ with ϕ ∈ ω(u 0 ). Since ϕ is non-increasing, Theorem 4.4 implies that there exist 0 < a 1 ≤ |Ω|, µ > 1 such that ϕ = µχ (0,a 1 ) + χ (a 1 ,|Ω|) .

It follows from (23) and a standard property in the rearrangement theory (cf.

[2, Proposition 3.1 (iii)]) that Ω P(ϕ ) = Ω P(ϕ) = E 1∞ .