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Lyapunov exponent

In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector $$\delta \mathbf{Z}_0$$ diverge (provided that the divergence can be treated within the linearized approximation) at a rate given by

$$ | \delta\mathbf{Z}(t) | \approx e^{\lambda t} | \delta \mathbf{Z}_0 | $$

where $$\lambda$$ is the Lyapunov exponent.

The rate of separation can be different for different orientations of initial separation vector. Thus, there is a spectrum of Lyapunov exponents—equal in number to the dimensionality of the phase space. It is common to refer to the largest one as the maximal Lyapunov exponent (MLE), because it determines a notion of predictability for a dynamical system. A positive MLE is usually taken as an indication that the system is chaotic (provided some other conditions are met, e.g., phase space compactness). Note that an arbitrary initial separation vector will typically contain some component in the direction associated with the MLE, and because of the exponential growth rate, the effect of the other exponents will be obliterated over time.

The exponent is named after Aleksandr Lyapunov.

Definition of the maximal Lyapunov exponent
The maximal Lyapunov exponent can be defined as follows: $$ \lambda = \lim_{t \to \infty} \lim_{|\delta \mathbf{Z}_0| \to 0} \frac{1}{t} \ln\frac{| \delta\mathbf{Z}(t)|}{|\delta \mathbf{Z}_0|}$$

The limit $$|\delta \mathbf{Z}_0| \to 0$$ ensures the validity of the linear approximation at any time.

For discrete time system (maps or fixed point iterations) $$ x_{n+1} = f(x_n) $$, for an orbit starting with $$x_0$$ this translates into: $$\lambda (x_0) = \lim_{n \to \infty} \frac{1}{n} \sum_{i=0}^{n-1}  \ln | f'(x_i)| $$

Definition of the Lyapunov spectrum
For a dynamical system with evolution equation $$\dot{x}_i = f_i(x)$$ in an n–dimensional phase space, the spectrum of Lyapunov exponents $$ \{ \lambda_1, \lambda_2, \ldots, \lambda_n \} \,, $$ in general, depends on the starting point $$x_0$$. However, we will usually be interested in the attractor (or attractors) of a dynamical system, and there will normally be one set of exponents associated with each attractor. The choice of starting point may determine which attractor the system ends up on, if there is more than one. (For Hamiltonian systems, which do not have attractors, this is not a concern.) The Lyapunov exponents describe the behavior of vectors in the tangent space of the phase space and are defined from the Jacobian matrix $$ J_{ij}(t) = \left. \frac{ d f_i(x) }{dx_j} \right|_{x(t)} $$ this Jacobian defines the evolution of the tangent vectors, given by the matrix $$Y$$, via the equation $$ \dot{Y} = J Y $$ with the initial condition $$Y_{ij}(0) = \delta_{ij}$$. The matrix $$Y$$ describes how a small change at the point $$x(0)$$ propagates to the final point $$x(t)$$. The limit $$ \Lambda = \lim_{t \rightarrow \infty} \frac{1}{2t} \log (Y(t) Y^T(t)) $$ defines a matrix $$\Lambda$$ (the conditions for the existence of the limit are given by the Oseledets theorem). The Lyapunov exponents $$\lambda_i$$ are defined by the eigenvalues of $$\Lambda$$.

The set of Lyapunov exponents will be the same for almost all starting points of an ergodic component of the dynamical system.

Lyapunov exponent for time-varying linearization
To introduce Lyapunov exponent consider a fundamental matrix $$ X(t)$$ (e.g., for linearization along a stationary solution $$x_0$$ in a continuous system), the fundamental matrix is $$ \exp\left( \left. \frac{ d f^t(x) }{dx} \right|_{x_0} t\right) $$ consisting of the linearly-independent solutions of the first-order approximation of the system. The singular values $$\{\alpha_j\big(X(t)\big)\}_{1}^{n}$$ of the matrix $$X(t)$$ are the square roots of the eigenvalues of the matrix $$X(t)^*X(t)$$. The largest Lyapunov exponent $$\lambda_{\mathrm{max}}$$ is as follows $$  \lambda_{\mathrm{max}}= \max\limits_{j}\limsup _{t \rightarrow \infty}\frac{1}{t}\ln\alpha_j\big(X(t)\big). $$ Lyapunov proved that if the system of the first approximation is regular (e.g., all systems with constant and periodic coefficients are regular) and its largest Lyapunov exponent is negative, then the solution of the original system is asymptotically Lyapunov stable. Later, it was stated by O. Perron that the requirement of regularity of the first approximation is substantial.

Perron effects of largest Lyapunov exponent sign inversion
In 1930 O. Perron constructed an example of a second-order system, where the first approximation has negative Lyapunov exponents along a zero solution of the original system but, at the same time, this zero solution of the original nonlinear system is Lyapunov unstable. Furthermore, in a certain neighborhood of this zero solution almost all solutions of original system have positive Lyapunov exponents. Also, it is possible to construct a reverse example in which the first approximation has positive Lyapunov exponents along a zero solution of the original system but, at the same time, this zero solution of original nonlinear system is Lyapunov stable. The effect of sign inversion of Lyapunov exponents of solutions of the original system and the system of first approximation with the same initial data was subsequently called the Perron effect.

Perron's counterexample shows that a negative largest Lyapunov exponent does not, in general, indicate stability, and that a positive largest Lyapunov exponent does not, in general, indicate chaos.

Therefore, time-varying linearization requires additional justification.

Basic properties
If the system is conservative (i.e., there is no dissipation), a volume element of the phase space will stay the same along a trajectory. Thus the sum of all Lyapunov exponents must be zero. If the system is dissipative, the sum of Lyapunov exponents is negative.

If the system is a flow and the trajectory does not converge to a single point, one exponent is always zero—the Lyapunov exponent corresponding to the eigenvalue of $$L$$ with an eigenvector in the direction of the flow.

Significance of the Lyapunov spectrum
The Lyapunov spectrum can be used to give an estimate of the rate of entropy production, of the fractal dimension, and of the Hausdorff dimension of the considered dynamical system. In particular from the knowledge of the Lyapunov spectrum it is possible to obtain the so-called Lyapunov dimension (or Kaplan–Yorke dimension) $$ D_{KY} $$, which is defined as follows: $$ D_{KY}= k + \sum_{i=1}^k \frac{\lambda_i}{|\lambda_{k+1}|} $$ where $$ k $$ is the maximum integer such that the sum of the $$ k $$ largest exponents is still non-negative. $$ D_{KY} $$ represents an upper bound for the information dimension of the system. Moreover, the sum of all the positive Lyapunov exponents gives an estimate of the Kolmogorov–Sinai entropy accordingly to Pesin's theorem. Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, which is based on the direct Lyapunov method with special Lyapunov-like functions. The Lyapunov exponents of bounded trajectory and the Lyapunov dimension of attractor are invariant under diffeomorphism of the phase space.

The multiplicative inverse of the largest Lyapunov exponent is sometimes referred in literature as Lyapunov time, and defines the characteristic e-folding time. For chaotic orbits, the Lyapunov time will be finite, whereas for regular orbits it will be infinite.

Numerical calculation
Generally the calculation of Lyapunov exponents, as defined above, cannot be carried out analytically, and in most cases one must resort to numerical techniques. An early example, which also constituted the first demonstration of the exponential divergence of chaotic trajectories, was carried out by R. H. Miller in 1964. Currently, the most commonly used numerical procedure estimates the $$L$$ matrix based on averaging several finite time approximations of the limit defining $$L$$.

One of the most used and effective numerical techniques to calculate the Lyapunov spectrum for a smooth dynamical system relies on periodic Gram–Schmidt orthonormalization of the Lyapunov vectors to avoid a misalignment of all the vectors along the direction of maximal expansion. The Lyapunov spectrum of various models are described. Source codes for nonlinear systems such as the Hénon map, the Lorenz equations, a delay differential equation and so on are introduced.

For the calculation of Lyapunov exponents from limited experimental data, various methods have been proposed. However, there are many difficulties with applying these methods and such problems should be approached with care. The main difficulty is that the data does not fully explore the phase space, rather it is confined to the attractor which has very limited (if any) extension along certain directions. These thinner or more singular directions within the data set are the ones associated with the more negative exponents. The use of nonlinear mappings to model the evolution of small displacements from the attractor has been shown to dramatically improve the ability to recover the Lyapunov spectrum, provided the data has a very low level of noise. The singular nature of the data and its connection to the more negative exponents has also been explored.

Local Lyapunov exponent
Whereas the (global) Lyapunov exponent gives a measure for the total predictability of a system, it is sometimes of interest to estimate the local predictability around a point $x_{0}$ in phase space. This may be done through the eigenvalues of the Jacobian matrix $J^{0}(x_{0})$. These eigenvalues are also called local Lyapunov exponents. (A word of caution: unlike the global exponents, these local exponents are not invariant under a nonlinear change of coordinates).

Conditional Lyapunov exponent
This term is normally used regarding synchronization of chaos, in which there are two systems that are coupled, usually in a unidirectional manner so that there is a drive (or master) system and a response (or slave) system. The conditional exponents are those of the response system with the drive system treated as simply the source of a (chaotic) drive signal. Synchronization occurs when all of the conditional exponents are negative.

Software

 * R. Hegger, H. Kantz, and T. Schreiber, Nonlinear Time Series Analysis, TISEAN 3.0.1 (March 2007).
 * Scientio's ChaosKit product calculates Lyapunov exponents amongst other Chaotic measures. Access is provided online via a web service and Silverlight demo.
 * Dr. Ronald Joe Record's mathematical recreations software laboratory includes an X11 graphical client, lyap, for graphically exploring the Lyapunov exponents of a forced logistic map and other maps of the unit interval. The contents and manual pages of the mathrec software laboratory are also available.
 * Software on this page was developed specifically for the efficient and accurate calculation of the full spectrum of exponents. This includes LyapOde for cases where the equations of motion are known and also Lyap for cases involving experimental time series data.  LyapOde, which includes source code written in "C", can also calculate the conditional Lyapunov exponents for coupled identical systems.  It is intended to allow the user to provide their own set of model equations or to use one of the ones included.  There are no inherent limitations on the number of variables, parameters etc.  Lyap which includes source code written in Fortran, can also calculate the Lyapunov direction vectors and can characterize the singularity of the attractor, which is the main reason for difficulties in calculating the more negative exponents from time series data.  In both cases there is extensive documentation and sample input files.  The software can be compiled for running on Windows, Mac, or Linux/Unix systems.  The software runs in a text window and has no graphics capabilities, but can generate output files that could easily be plotted with a program like excel.

title: Lyapunov exponent


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List of tunnels by country

The list of tunnels includes any road tunnel, railway tunnel or waterway tunnel anywhere in the world.

Afghanistan

 * Salang Tunnel

Andorra

 * Envalira Tunnel, road
 * Pont Pla Tunnel, 1.26 km, road
 * Sant Antoni Tunnel, 280 m, road
 * Dos Valires Tunnel, 3 km, road

Argentina

 * Cristo Redentor Tunnel
 * Raúl Uranga – Carlos Sylvestre Begnis Subfluvial Tunnel

Azerbaijan

 * Ziya Bunyadov tunnel Baku
 * Darnagul tunnel Baku
 * 20 January tunnel Baku
 * Kalbajar Tunnel

People's Republic of China
Specifically notable tunnels in the People's Republic of China include:
 * Line 6 (Chengdu Metro), 68.2 km (42.4 mi), longest metro/rapid transit tunnel
 * Wushaoling Tunnel, 21 km long dual bore railway
 * Zhongnanshan Tunnel, 18 km long dual bore roadway
 * Fenghuoshan tunnel, at 5 km above sea level, the highest elevation rail tunnel in the world

Colombia

 * Tunel del Toyo (under construction) 9.84 km
 * La Línea Tunnel 8.65 km
 * Occidente Tunnel 4.6 km
 * Buenavista Tunnel 4.6 km
 * Sumapaz Tunnel 4.1 km
 * Daza Tunnel 1.7 km
 * Túnel Polvorín 1.6 km
 * Girardota Tunnel 850 m
 * La Llorona Tunnel 470 m
 * Bijagual Tunnel 185 m
 * Boquerón Tunnel 2.4 km
 * Santa Rosa Tunnel 1.5 km
 * Tunnel 5 1.6 km
 * Tunnel 3 1.4 km
 * Túnel Guacapate 1.2 km

Denmark

 * Great Belt Fixed Link, railway, 8.0 km
 * Copenhagen Metro, metro rail, M2 line, 7,4 km (Fasanvej–Lergravsparken)
 * Øresund Connection, road and rail, 4.05 km
 * Boulevard Line, Copenhagen, railway, 1.8 km
 * Limfjordstunnelen

Egypt

 * Ahmed Hamdi Tunnel, under the Suez Canal between Suez and Ismailia.

Estonia

 * Ülemiste Tunnel, road, 320 m

Finland

 * Raisiotunneli Raisio
 * Myllyahde tunneli Turku
 * Kehä II tunneli Kauniainen
 * Korpilahti railway tunnel, near Jyväskylä
 * Päijänne Water Tunnel, 1982
 * Savio Rail Tunnel, 13.5 km, opened in 2008

France

 * Channel Tunnel to the United Kingdom (railway through the English Channel), at 50.5 km (31.4 mi)
 * International Tunnel de Bielsa-Aragnouet France – Spain: total length 3.07 km, diameter 7.5 m, 100 m minimum distance between one after another vehicles, asphalt lane 6 m wide, for vehicles high max 4.3 m, max speed 60 km/h (37 mi/h)
 * Fréjus Rail Tunnel
 * Fréjus Road Tunnel
 * Mont Blanc Tunnel
 * Pont de l'Alma Tunnel (built under the River Sena – along its length, perpendicular to the length of the bridge, with reinforced concrete columns between the two traffic lanes, road: forbidden for pedestrians)
 * Rove Tunnel, southern section of the Marseilles–Rhône Canal, 7.2 km (4.5 mi) long and 22 m (72 ft) wide, Bouches-du-Rhône dept., SE France; opened 1927. Starting near the village of Le Rove, it cuts through the Chaîne de l'Estaque at sea level. It is considered one of the greatest pieces of engineering since the Panama Canal. Longest canal tunnel in the world.
 * Col de Tende Road Tunnel
 * Col de Tende Rail Tunnel

Georgia

 * Roki Tunnel (3.73 km road)
 * Rikoti Tunnel (1.72 km road)

Germany
e.g.:
 * Rennsteig Tunnel
 * Engelberg Tunnel
 * Old Elbe Tunnel
 * New Elbe Tunnel

Gibraltar

 * Dudley Ward Tunnel

Greece
Road tunnel in operation:
 * Aktio–Preveza Undersea Tunnel (road), Connects Aktio and Preveza, under Aktion Channel, 1.20 km
 * Artemisio Tunnel (road), double tunnel, under Mount Artemision, 1.40 km
 * 76 tunnels of Egnatia motorway, most notably in parts of Epirus and Western Macedonia, combined length of 99 km, the longest of which are Driskos Tunnel 4.6 km, Metsovo Tunnel 3.5 km, Dodoni Tunnel 3.6 km, Kastania Tunnel 2.2 km, Anilio Tunnel 2.1 km
 * Road Tunnels of E94 part Athens–Corinth, point Kakia Skala, combined length of 6 km

Road tunnel under construction:
 * Tempe Tunnel
 * Platamonas Tunnel

Railway tunnel in operation:
 * Tempe Tunnel 5.5 km
 * Platamonas Tunnel 4.3 km
 * Perama Tunnel 3.5 km
 * Kakia Skala Tunnel 2.4 km

Railway tunnel under construction:
 * Kalidromos Tunnel
 * Othrios Tunnel
 * Domokos Tunnel
 * Panagiopoulos Tunnel
 * Aegio Tunnel

Iceland
No metro, but some long road tunnels, including Hvalfjörður Tunnel at 5.8 km (3.6 mi) and some longer, and the longest (non-road) hydroelectric tunnel in Europe, one of the longest tunnels of any kind in the world, at Kárahnjúkar Hydropower Plant at 39.7 km (24.7 mi)

India

 * Dr. Syama Prasad Mookerjee Tunnel Longest Road Tunnel in India
 * Atal Tunnel
 * Banihal Qazigund Road Tunnel
 * Pir Panjal Railway Tunnel (Banihal Tunnel)
 * Maliguda Tunnel
 * New Katraj Tunnel
 * Punarjani Guha
 * trivandrum port tunnel
 * Jaipur Tunnel
 * Kuthiran Tunnel
 * Anakkampoyil-Kalladi-Meppadi tunnel
 * Zoji-la Tunnel
 * Sela Tunnel

Isle of Man

 * Great Laxey Mine Railway tunnel

Israel

 * Carmel Tunnels
 * Traffic Tunnels on road number 60 from Jerusalem to Gush Etzion
 * Traffic Tunnels on road number 6 (crossing Israel)
 * Railway tunnels (under construction) on new line Tel Aviv–Jerusalem
 * Gaza Strip smuggling tunnels
 * Siloam Tunnel
 * Jerusalem Water Channel
 * Western Wall Tunnel

Italy

 * Fréjus Rail Tunnel
 * Fréjus Road Tunnel
 * Mont Blanc Tunnel
 * Traforo del Gran Sasso
 * Great St Bernard Tunnel
 * Simplon Tunnel
 * Col de Tende Road Tunnel
 * Col de Tende Rail Tunnel

Japan

 * Seikan Tunnel, 53.9 km (33.5 mi)

Lithuania

 * Kaunas Railway Tunnel
 * Paneriai Railway Tunnel

Luxembourg

 * Gousselerbierg Tunnel
 * Grouft Tunnel
 * Markusbierg Tunnel
 * René Konen Tunnel
 * Stafelter Tunnel

Macau

 * Túnel do Monte da Guia
 * Túnel da Colina de Taipa Grande
 * Túnel do Canal da Taipa

Macedonia

 * Bukovik Tunnel, railway, 7.05 km

 * veles tunnel 500 m
 * veles tunnel 300 m

 * demir kapija tunnel 800 m

Malaysia

 * SMART Tunnel – 3.3 km (highway); 9.7 km (water passage)
 * Genting Sempah Tunnel – 900 m (highway)
 * Larut Tunnel – 2.9 km (rail)
 * Menora Tunnel – 800 m (highway)
 * Penchala Tunnel – 700 m (highway)
 * Kelana Jaya Line (light metro) – 2.9 km (underground rail section)
 * Sungai Buloh–Kajang Line (light metro) – 9.5 km (underground rail section)
 * Sungai Buloh–Serdang–Putrajaya Line (light metro) – 13.5 km (underground rail section)

Montenegro
Road tunnels in operation
 * Sozina Tunnel 4.19 km
 * Ivica Tunnel 2.21 km
 * Sutorman Tunnel 1.97 km (used as railway tunnel from 1908 to 1959, very narrow, only one car, rarely used)
 * Vrmac Tunnel 1.64 km
 * Lokve Tunnel 1.12 km
 * Budoš Tunnel

Road tunnels under construction
 * Vjeternik Tunnel 3.0/2.86 km (two tubes)
 * Klisura Tunnel 2.81 km
 * Kosman Tunnel 2.67/2.55 km (two tubes)
 * Vežešnik Tunnel 2.47/2.41 km (two tubes)
 * Mala Trava Tunnel 1.90/1.88 km (two tubes)
 * Jabučki Krš Tunnel 1.46/1.36 km (two tubes)
 * Ibarac Tunnel 1.19 km

Railway tunnels in operation
 * Sozina Tunnel 6.17 km
 * Trebješica Tunnel 5.17 km
 * Mojkovac Tunnel 3.24 km
 * Ostravica Tunnel 3.13 km
 * Šljivovica Tunnel 2.20 km

Morocco

 * Tunnel du Legionaire

Panama

 * Las Esclavas Tunnel

Pakistan
Road tunnels in operation
 * Attabad Tunnels, on N-35 Karakoram Highway is a series of five tunnels in Gilgit-Baltistan
 * Abbottabad Tunnels on Hazara Motorway M-15
 * Kohat Tunnel on N55 Indus Highway
 * Lowari Tunnel on N-45 Nowshera-Chitral Highway
 * Malakand Tunnel on N-45 Nowshera–Chitral Highway
 * Nahakki Tunnel is a tunnel from Peshawar to Mohmand Agency via Bajaur
 * Neelum–Jhelum Hydropower Tunnel
 * Swat Tunnel on Nowshera–Swat Expressway
 * Quetta Tunnel at the entrance of Quetta on N-25 National Highway near Lak Pass.

Railway tunnels in operation
 * Khojak Tunnel, is a railway tunnel connecting Rohri with Chaman
 * Lahore Metro Orange Line Tunnel in Lahore

Philippines

 * Subic Tunnel (road)
 * Marcos Highway Tunnel (road)
 * Antipolo Tunnel (road)
 * Cebu tunnel (road)
 * Purle line tunnel (rail)

Poland

 * "Tunel" ("the Tunnel"), 813 m, on the Warsaw–Kielce–Kraków line, between Sędziszów and Słomniki
 * Wałbrzych–Jedlina, 1.60 km, rail
 * Warsaw Metro rail
 * Warsaw Cross-City Line, 2.31 km, rail
 * Warsaw, road city tunnel (Wisłostrada), 930 m southbound, 889 m northbound
 * Gdańsk, road under water tunnel, 1.38 km, Tunel_pod_Martw%C4%85_Wis%C5%82%C4%85
 * Laliki, road mountain tunnel, 678 m, Tunel_Emilia
 * Kraków, road city tunnel, 230 m, Tunel_Rafa%C5%82a_Kalinowskiego_w_Krakowie
 * Kraków, tram city tunnel, 1.42 km, Tunel_Krakowskiego_Szybkiego_Tramwaju

Puerto Rico

 * Minillas Tunnel
 * Vicente Morales Tunnel

Romania

 * Teliu Rail Tunnel 4.37 km
 * Talasmani Rail Tunnel 3.33 km
 * Pasul Şetref Rail Tunnel 2.39 km
 * Danes Rail Tunnel 969 m
 * Capra-Bâlea Road Tunnel, 884 m (connects the historic regions of Transylvania and Wallachia), Transfăgărășan
 * Sighisoara Rail Tunnel 401 m
 * Sacel Highway Tunnel, 340 m, A1 motorway (Romania)
 * Transfagarasan KM 60 Tunnel, 172 m, Transfăgărășan

Russia

 * Severomuysky Tunnel (15.34 km), Buryatia
 * Baikal (Daban) tunnel (6.69 km), Irkutsk Oblast
 * Gimry tunnel (4.30 km), Dagestan
 * Lefortovo tunnel, 3.2 km, Moscow
 * North-Western Tunnel, 2.8 km, Moscow

Singapore

 * Mass Rapid Transit (Singapore)
 * Chin Swee Tunnel
 * Kampong Java Tunnel
 * Kallang–Paya Lebar Expressway
 * Fort Canning Tunnel
 * Marina Coastal Expressway

Slovenia

 * Dekani Tunnel – 2.18/2.19 km, A1 road
 * Golovec Tunnel – 530/595 m, A1 road/E57 road
 * Kastelec Tunnel – 2.29/2.24 km, A1 road
 * Karavanke Tunnel (Karawanken Tunnel) – 7.86 km, A2 road/E61 road
 * Trojane Tunnel – 2.84/2.93 m, A1/E57 road
 * Šentvid Tunnel – 1.07/1.05 m, A2/E61 road
 * Bohinj Tunnel – 6.33 km, rail tunnel on the way Jesenice – Nova Gorica
 * Tunnels on the Slovenian motorways

Switzerland

 * Gotthard Base Tunnel, 57.09 km (35.5 mi) railway tunnel through the Alps

Taiwan

 * Baguashan Tunnel (Provincial Highway No. 76)
 * Baguashan Tunnel (Taiwan High Speed Railway)
 * Central Tunnel (South-link line)
 * Hsuehshan Tunnel (National Highway No. 5)
 * Xinguanyin Tunnel (North-link line)
 * Yuchang Tunnel (Yuchang Highway)
 * Taipei Metro
 * Kaohsiung Mass Rapid Transit

Tanzania

 * TAZARA Railway – 22 tunnels; 1.5 mi

Thailand

 * Chong Khao Tunnel (235.90 m rail tunnel on Southern line in Nakhon Si Thammarat province)
 * Huai Mae Lan Tunnel (130.20 m rail tunnel on Northern line in Phrae province)
 * Khao Phang Hoei Tunnel (230.60 m rail tunnel on Northeastern line in Lopburi and Chaiyaphum provinces)
 * Khao Phlueng Tunnel (362.44 m rail tunnel on Northern line in Uttaradit and Phrae provinces)
 * Khun Tan Tunnel (1362.10 m rail tunnel on Northern line in Lampang and Lamphun provinces)
 * Mongkolrit Tunnel (268 m road tunnel in Betong, Yala province)
 * Pang Tup Khop Tunnel (120.09 m rail tunnel on Northern line in Uttaradit province)
 * Phra Phutthachai Tunnel (1.20 km rail tunnel on freight-only Eastern line in Saraburi province)
 * Mae Taeng–Mae Ngat–Mae Kuang Diversion Tunnel 23 km (waterway) underconstruction
 * MRT Blue Line 25.8 km (underground rail section)
 * MRT Orange Line 13.8 km (underground rail section) – underconstruction
 * Khao Yai – Thap Lan Tunnel (250 m and 180 m road tunnel, total of 430 m in Prachinburi Province, for wildlife overpass)

United Arab Emirates

 * Airport Tunnel, Dubai (road)
 * Al Shindagha Tunnel, Dubai (road)
 * Wadi Al Helo Tunnel (between Sharjah – Kalba approximately 1.6 km)

United Kingdom

 * Channel Tunnel to France (railway through the English Channel), at 50.5 km (31.4 mi)

Vietnam

 * Hải Vân Tunnel, the longest tunnel in Southeast Asia at 6.28 km (3.90 mi).
 * Sài Gòn River Tunnel
 * Cu Chi Tunnels

Zambia

 * TAZARA Railway – 22 tunnels; longest 1.5 mi

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: List of tunnels by country


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Wadhurst

Wadhurst is a market town in East Sussex, England. It is the centre of the civil parish of Wadhurst, which also includes the hamlets of Cousley Wood and Tidebrook. Wadhurst is twinned with Aubers in France.

Situation
Wadhurst is situated on the Kent–Sussex border seven miles (11 km) east of Crowborough and about seven miles (11 km) south of Royal Tunbridge Wells. Other nearby settlements include Ticehurst, Burwash, Mayfield and Heathfield in East Sussex, and Lamberhurst, Hawkhurst and Cranbrook in Kent.

Physically, Wadhurst lies on a high ridge of the Weald – a range of wooded hills running across Sussex and Kent between the North Downs and the South Downs. The reservoir of Bewl Water is nearby. The River Bewl, which is a sub-tributary of the River Medway, and the Limden rise within the civil parish of Wadhurst.

History
The name Wadhurst (Wadeherst in early records) is Anglo-Saxon and most probably derives from Wada which is believed to be the name of a Saxon tribe which occupied the area and began the clearing of the forests in the 7th or 8th century. There is an Anglo-Saxon manor known as Bivelham which lay between the parishes of Wadhurst and Mayfield.

Although Wadhurst was almost certainly in existence at the time of the Domesday survey in 1086, it was part of the Archbishop of Canterbury's land and was therefore not mentioned. The earliest record relating to the area is a reference in the Cartulary of Battle Abbey to "Snape in the parish of Wadhurst".

Henry III granted Wadhurst its charter in 1253, allowing Wadhurst to hold a market every Saturday and a fair on 29 June, the feast of St Peter and St Paul.

In the 16th, 17th and 18th centuries Wadhurst, as did many towns and villages in the Weald, had a thriving iron industry. Two of the large Georgian buildings on the High Street, Hill House and The Old Vicarage, were both ironmasters' houses, along with a number of other large houses on the outskirts of Wadhurst. In the church of St Peter and St. Paul there are several iron ledger-stone memorials of ironmasters, which are unique to this area.

During the First World War, Wadhurst lost 149 men, out of a total village population of 3,500. The worst losses were during the Battle of Aubers Ridge, when 25 men from Wadhurst were killed in one day: nearly 80% of the men from Wadhurst who went into no man's land that day. Wadhurst is now actively twinned with Aubers.

In March 2023, Wadhurst was named by The Sunday Times as the best place to live in the United Kingdom.

Governance
An electoral ward with the same name exists. The population of this ward at the 2011 census was 5,181.

Buildings and people
Wadhurst is a small market town, and has kept a very good range of shops considering its size. It has a traditional butcher, baker, ironmonger, hairdresser, bank, post office, gift shop, and several pubs. The population of the ward was 4,883 at the 2011 Census. In 2020, the population estimate is 4,025 according to the Office for National Statistics.

There are three buildings of particular architectural interest in the town itself, and a number of old manor houses and farms nearby. The Church of St. Peter and St. Paul dominates the centre of the town. Wadhurst's heritage as a centre of the iron industry is shown by the many iron gravestones in the church. There are two early Georgian houses on the High Street, the Old Vicarage and Hill House. On the outskirts is the 19th-century Wadhurst Castle. The parish church is medieval and includes work from the 12th to the 15th centuries; there is a shingled spire and a vaulted porch. There is little of interest inside apart from 30 inscribed iron tomb slabs dating from 1614 to 1790.

The rest of the town is in a variety of vernacular styles, from the 13th century onwards; and little in the centre of the town is very modern apart from a range of shops which replaced the Queens Head Hotel, demolished in the crash of a Gloster Meteor in January 1956 in which four people were killed.

The Victorian era saw the town expand towards the new railway station, about 1.5 mi north of the town. The station, the highest in southern England, is on the line from London Charing Cross to Hastings via Tunbridge Wells, and was opened in 1851 by the South Eastern Railway. The resulting expansion brought the hamlets of Sparrow's Green, Turners Green and Best Beech Hill into the town. In addition to the railway, there are buses to Tunbridge Wells, Crowborough and Hastings, as well as community transport and 'rail link' buses to Ticehurst and Mayfield.

In the centre of Wadhurst there are two churches: St. Peter and St. Paul is an Anglican church; parts of it date from the 12th century. Wadhurst Methodist Church is no longer used as a church. There is a Catholic church in Mayfield Lane attached to the Sacred Heart School. The three churches also participate in Churches Together, an interdenominational organisation, along with St John the Baptist, an Anglican church in Tidebrook, and St Peter in Stonegate. Church Street contains a row of 13th- and 14th-century cottages which are reputed to be the oldest properties in Wadhurst. Some apparently were built as a cloister to St. Peters and St. Paul's Church.

There are also two early 19th-century former Strict Baptist chapels of similar design in the hamlets of Pell Green (Rehoboth Chapel) and Shover's Green (the Shover's Green Baptist Chapel). Both are listed at Grade II.

Wadhurst has two schools in the state-maintained sector: a Church of England primary school (with a nursery) in Sparrow's Green and Uplands Academy, a secondary school and sixth form. The latter also has an affiliated youth and community centre. In addition, in Mayfield Lane there is an independent Catholic preparatory school, Sacred Heart. Wadhurst also used to be the site of Bellerbys College (formerly known as Wadhurst College and Micklefield Wadhurst), a private girls' school on Mayfield Lane that has been defunct since about 2004.

Wadhurst United F.C.
Wadhurst United F.C. (based at the Recreation Ground, South View Road) is Wadhurst's local football team. They were formed in 1890 and joined the Sussex County League Division Three in 2004. They left the league after the 2005–06 season, to rejoin the East Sussex Football League. The club won the East Sussex League Division Two title in the 2008–09 season.

Twin towns

 * 🇫🇷 Aubers, France

Notable people

 * Jeff Beck, guitarist, lived in Wadhurst between summer 1975 and his death on 10 January 2023. His large stone country house dates to 1591.
 * William Bidlake, (1861–1938), architect, moved to Wadhurst in 1924 and practised there until his death.
 * Caroline Augusta Foley Rhys Davids, Pāli language scholar and translator
 * Davina McCall, television presenter, lived at Faircrouch House in Wadhurst until 2019.
 * Irfan Orga (1908–1970), exiled Turkish writer, lived at Spike Island, Wadhurst, 1961–1970.
 * Hans Rausing (1926–2019), billionaire inheritor of Tetra Pak, had a house and deer park at Wadhurst. Wadhurst Park continues to be owned by the Rausing family.

title: Wadhurst


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List of tunnels in the United Kingdom

This is a list of road, railway, waterway, and other tunnels in the United Kingdom.

A tunnel is an underground passageway with no defined minimum length, though it may be considered to be at least twice as long as wide. Some government bodies define a tunnel as 150 m in length or longer.

A tunnel may be for pedestrians or cyclists, for general road traffic, for motor vehicles only, for rail traffic, or for a canal. Some are aqueducts, constructed purely for carrying water—for consumption, for hydroelectric purposes or as sewers—while others carry other services such as telecommunications cables. There are even tunnels designed as wildlife crossings for European badgers and other endangered species.

The longest tunnel in the United Kingdom is the Northern line at 27800 m. This will be superseded in the 2020s by the 37,600 m Woodsmith Mine Tunnel in North Yorkshire that will transport polyhalite from North Yorkshire to a port on Teesside. Standedge Tunnel at 5029 m is the longest canal tunnel in the United Kingdom. When completed in the late 2020s, the Chiltern tunnel will be the 2nd longest mainline railway tunnel in the UK at 16040 metres.

title: List of tunnels in the United Kingdom


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Mersey (1801 ship)

 Mersey  was a ship launched at Chittagong in 1801 and wrecked in the Torres Strait, Australia, about mid-June 1804. She was the first merchantman lost in the Strait.

Mersey was built in Chittagong in 1801 and registered at Fort William, India. At the time of her loss her captain and owner was James Wilson.

Mersey, Captain Wilson, arrived at Sydney on 10 April 1804 with a cargo chiefly consisting of sugar, port and Madeira wine, cordage, and some piece goods. An advertisement on 22 April announced the sale on Monday 23 April of Mersey's cargo. The advertisement provided a rich, detailed listing of the cargo.

Philip Gidley King, governor of New South Wales, on 15 May 1804 announced that Mersey would return to India via an "hithertoo unfrequented passage to Torres Strait in the track of Captain Flinders." King had chartered Mersey to purchase 250 cows from Bengal and deliver them to Hobart, Tasmania.

Mersey left Port Jackson on 24 May 1804 for Bengal with a cargo of 1632 feet of timber. While passing through the Torres Strait, Mersey was totally wrecked. The whaler Policy brought the news on 17 November 1804 from Timor.

Only 17 crew and the captain were saved by sailing in a longboat to Timor; 56 others had perished. After refitting the longboat at Dili the survivors reached Bencoolen from where they sailed to Madras on an Acehen vessel. Captain Wilson arrived in Calcutta 20 September 1804 on board Margaret, from Madras.

title: Mersey (1801 ship)


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Brigitte Boisselier

Brigitte Boisselier (born 1956), also known as Brigitte Roehr, is a French chemist and Raëlian religious leader best known for her claim to have overseen the creation of the first human clone. A native of Champagne-Ardenne, she studied chemistry in France and the United States, earning two PhDs. From 1984 to 1997, she lived near Paris and worked as a research chemist and a sales manager for Air Liquide. She embraced Raëlism in 1992; the group was unpopular in France and her conversion led to tensions with those around her. Five years later, she joined Clonaid, a Raëlian organization that sought to clone a human. After her service as their scientific director was publicized, she lost her position with Air Liquide and focused on cloning full-time.

In late 2000, Clonaid announced that they had received a large donation to fund the cloning of a child, and that Boisselier supervised a team of scientists at a secret laboratory in the United States who would soon produce a human clone. For the next year, the project received media coverage—and regulatory suspicion—as Boisselier promised the imminent birth of a human clone. In late 2001, she announced that one had been born and that public evidence would soon be offered. This declaration received significant press coverage in the United States, and Boisselier appeared on many television programs. After a court in Florida launched a child welfare investigation, she stated that the cloned child's parents had withdrawn their offer to provide evidence of the cloning and would have no further public comment. No evidence of the cloning, or subsequent procedures reported by Clonaid, was ever offered, and the announcements were widely perceived to have been a hoax.

In 2003, impressed with her management of Clonaid and public relations skill, Raël, the founder of Raëlism, announced that Boisselier would succeed him as the group's leader upon his death. In subsequent years, she has devoted herself to lecturing about the group's doctrines and serving as their spokesperson.

Early life and education
Brigitte Boisselier was born to a Catholic family in France in 1956. She was raised on a farm in Champagne-Ardenne and became interested in science while young. She attended the University of Dijon, earning a master's degree in biochemistry and a PhD in chemistry. In the 1980s, she moved to Texas, where she received another PhD in chemistry from the University of Houston.

Boisselier returned to France in 1984 to work for Air Liquide, an industrial gas company, where she remained for 13 years. At that time, she lived in Les Loges-en-Josas and worked as a research chemist and a sales manager in Lyon. She married and had three children between the late 1970s and early 1990s.

Conversion and new career
In 1992, Boisselier converted to Raëlism, a UFO religion founded by the French journalist Claude Vorilhon, usually known as Raël, in 1973. After attending a meeting at which Raël spoke, she felt strongly that he was completely honest and joined his movement. She had left her husband, alleging violent behavior, shortly before her conversion; afterwards, owing to her involvement with Raëlism, he gained sole custody of their youngest child. Boisselier believed that religious intolerance motivated a court to transfer the child's custody. Although her faith led to tension with her parents, her eldest child converted. In the 1990s, Raëlism was seen as dangerous and viewed with disdain in France, resulting in loss of employment for prominent members. The hostility was fueled in part by public concerns about new religious movements after deaths caused by the Order of the Solar Temple in Europe during the mid-1990s.

Boisselier became the scientific director of Clonaid, an organization founded by Raël that sought to clone humans, in 1997. That year, Boisselier was interviewed by Le Monde about her role in Clonaid, and she lost her position with Air Liquide after the company learned of this. Air Liquide stated that her termination was due to her holding dual employment, and that she was strained by her Clonaid service. She filed a lawsuit against Air Liquide, arguing that she was the victim of religious discrimination. Her suit was successful: in 1999, she won a judgment of about US$30,000.

After losing her job, Boisselier moved with her middle child, a son, to Quebec, where her eldest daughter was a student. Boisselier began to travel to discuss Clonaid, eventually becoming a high-profile speaker. Around that time, she reached the rank of Bishop within Raëlism. She was one of the 25 members closest to Raël and joined the group's Order of Angels, which promoted free love and femininity. She moved to the United States and began teaching at State University of New York at Plattsburgh for a short time before moving to Hamilton College in 2000 to teach chemistry. Her association with Clonaid was publicized in the U.S. in February 2001, and she resigned her academic position that May, although she had a three-year contract. She claimed she was initially popular at Hamilton College, but felt that she was disrespected after her association with Clonaid was publicized.

Clonaid origins
Raël founded Clonaid in March 1997, shortly after the Dolly the Sheep cloning, believing that the process was important because the human species had been created by an extraterrestrial cloning project. On a practical level, Raël promoted the practice as a way to develop more desirable genetics and eventually prolong memories in new bodies. Shortly after Clonaid's launch, Boisselier began publicizing and managing its operations. In 1999, she announced that she had set up cloning laboratories and had hired a team of six scientists. She said she had limited knowledge of cloning but was skilled in selecting experts.

In August 2000, Mark Hunt, a politician from West Virginia, asked Boisselier to clone his late son, who had died as a child. Hunt paid Clonaid $500,000 and helped them rent a science laboratory from a school. Boisselier said that the laboratory would initially be used to clone cattle, before moving on to humans. She planned to use a number of Raëlian surrogates, who were willing to abort abnormal pregnancies, to bear clones; the high number of women would compensate for the low odds of a healthy child for each implantation. In September 2000, Raël and Boisselier held a press conference with several aspiring surrogate mothers of clones. At the event, Boisselier announced the construction of a cloning laboratory and vaguely described Hunt, who wished to remain anonymous. Boisselier received significant media attention as an advocate of cloning. Some commentators initially accepted her work as a legitimate attempt at cloning; Margaret Talbot of the New York Times described her as a more credible spokesperson than Raël, projecting what she described as "an air of cool, academic professionalism". Boisselier's striking physical appearance drew particular attention, and she developed an avant-garde, stylish reputation, contrary to popular images of scientists.

Announcements and media coverage
In early 2001, Boisselier promised the cloning of a human child within a year, drawing further attention to her work. A prosecutor in New York began investigating her compliance with local medical laws. Boisselier said that the Food and Drug Administration also surreptitiously investigated her, and Raël claimed that U.S. President George W. Bush was concerned about Clonaid's work. The caretaker of the laboratory that Hunt had rented grew suspicious about their work and contacted law enforcement. They spoke with the FDA, who searched the site and persuaded Boisselier to suspend her cloning work pending legal clarification. After Hunt was asked by the laboratory's caretaker to shut down the cloning operation, he broke with Boisselier and criticized her for seeking media attention. The caretaker also spoke publicly, saying that Boisselier was seldom at the laboratory. Boisselier then announced that she was moving her cloning operations overseas. Boisselier never faced any legal charges in connection with the laboratory.

In March 2001, Boisselier was invited to speak at a U.S. Congress hearing on human cloning, and at her insistence Raël was permitted to speak as well. The event garnered public attention, in large part because of Raël's unconventional appearance. On 7 August 2001, Boisselier attended a widely publicized human cloning symposium at the National Academy of Sciences in Washington, D.C., Significant media attention was given to Boisselier, who, along with Severino Antinori and Panayiotis Zavos, was one of three participants actively engaged in efforts to produce a human clone. The rest of the attendees were renowned scientists and ethicists, one of whom, Arthur Caplan, dismissed Boisselier as part of the "loony cloning element". By May 2002, Boisselier said that she had facilitated 10 to 20 pregnancies but had been thwarted by miscarriages.

Claims of success
Boisselier confidently announced at a press conference in Florida in December 2002 that Clonaid had successfully produced a live-born clone, named Eve, for an infertile couple. Canadian sociologist Susan J. Palmer notes that naming the cloned child "Eve" recalls Raël's teachings that aliens created the first humans through cloning. After the announcement, Boisselier received abundant press, but the media, particularly late-night comedy programs, criticized her glamorous appearance and mocked Raëlism. Around that time, Boisselier appeared on many U.S. network news broadcasts and on CNN. She did not provide details about the child or its family, although she was often asked to. She hired a science editor from ABC to supervise verification of the cloning. Many scientists doubted that the Raëlians could overcome the difficulties that human cloning posed, or that they would be able to produce a healthy child. Boisselier said a DNA test was forthcoming and announced that five more clones would be born later that winter. As Raël and Boisselier continued to seek media exposure, journalistic animosity towards them grew.

Bernard Siegel, an attorney from Florida, learned of the case and felt that a hearing should be held about Eve's welfare. In January 2003, he initiated legal proceedings, seeking to bring the clone's parents to court so its health could be verified. Raël and Boisselier attacked the filing as an attempt to take a child from loving parents and announced that, in protest, they would not provide DNA for testing. An arraignment occurred on 24 January and was televised live on CNN; Boisselier and Clonaid's vice president, Thomas Kaenzig, were subpoenaed in lieu of the child's parents. In courtroom testimony, the vice president of Clonaid said he knew very little about the clone, and that Boisselier controlled all the information. She did not attend the hearing, and Kaenzig provided little information, angering the judge, who threatened contempt of court charges. Boisselier attended a second hearing on 29 January, telling the court that the child was in Israel. The judge then ruled that the court had no jurisdiction. In late January, the science editor announced that he suspected the cloning announcements were a hoax. Around that time, Boisselier held a press conference at which she announced that the cloned baby's parents had cut off contact with her and would never speak to the press.

In the following years, Boisselier claimed to have facilitated the cloning of several children in a variety of countries. As of June 2004, she reported that Clonaid has successfully cloned 13 children. She did not provide evidence to verify the claims. She stated that the machine called the RMX 2010 was used in the cloning attempts, and exhibited it publicly.

After Boisselier announced that no evidence of the cloning would be provided, journalists became very skeptical of her story. While discussing Boisselier's management of Clonaid, Palmer notes that it is impossible to know why she stated that a clone was produced but then refused to provide evidence. She argues that her refusal to provide evidence may have been because she organized a hoax, did not wish to publicize the birth of an unhealthy child, or was taken advantage of by a scientist she had hired. American science journalist Steven S. Hall criticized the media for their coverage of Clonaid, believe that they were inaccurately represented as a credible group. He speculates that the coverage of Boisselier and other cloning adherents galvanized sentiment against cloning, leading to its banning in the U.S.

Later activism
In January 2003, Raël held a ceremony at which he thanked Boisselier for her service and anointed her as his successor. He praised her for spreading the message of Raëlism internationally while publicizing the cloning. In the Raëlian hierarchy, she is one level below Raël and serves as a spokesperson for the movement. As a leader, she has attempted to rehabilitate the swastika, one of the group's symbols. She maintains that it is valuable as an ancient symbol of peace, and that it has been unfairly associated with Nazi Germany.

In the mid-2000s, Boisselier often taught about the Raëlian perspective of the body and sexuality. She discussed these topics from a biological perspective, arguing that humans are essentially robots because they can be reprogrammed. Specifically, she maintained that hormones program the brain, and they provide humans with the freedom to choose from many possibilities. Raëlians emphasize sexual stimulation as a way to positively change their members, and Boisselier has stated that she sees the pursuit of femininity as a method of spiritual growth. The group highly values feminine beauty, and Raël has applauded Boisselier for maintaining her appearance, casting her as a role model.

By 2007, Boisselier had taken the name "Brigitte Roehr" and was living in Los Angeles. That year, she began leading a Raëlian project to fight female genital mutilation. She heads a Raëlian-affiliated group known as Clitoraid, which raises funds to provide restorative surgery to women with damaged clitorises. The project, which has attracted criticism of its effectiveness, aims to build a hospital in Burkina Faso where women can receive clitoral surgery.

title: Brigitte Boisselier


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Squadron

Squadron may refer to:

Military

 * Squadron (army), a military unit of cavalry, tanks, or equivalent subdivided into troops or tank companies
 * Squadron (aviation), a military unit that consists of three or four flights with a total of 12 to 24 aircraft, depending on the type of aircraft and service
 * Squadron (naval), a military unit of three to ten warships that may be part of a larger task group, task force, or a naval fleet; also an administrative unit for warships like submarines that usually operate alone

Other uses

 * Daniel Squadron (born November 9, 1979), former New York elected official
 * Squadron (TV series), a 1982 BBC television series
 * Squadron, Ellenoff, Plesent & Sheinfeld, a New York City law firm that practiced from 1970 to 2002
 * Squadron Energy, a division of the Australian company Tattarang, owned by billionaire Andrew Forrest
 * Squadron Supreme, a fictional superhero team appearing in Marvel Comics
 * Star Wars: Squadrons, a video game set in the Star Wars universe that simulates spaceship combat

title: Squadron


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Corto Maltese

Corto Maltese is a series of adventure comics named after the character Corto Maltese, an adventurous sailor. It was created by the Italian comic book creator Hugo Pratt in 1967. The comics are highly praised as some of the most artistic and literary graphic novels ever written and have been translated into numerous languages and adapted into several animated films.

The series features Corto Maltese, an enigmatic sea captain who lives in the first three decades of the 20th century. Born in Valletta on the island of Malta on 10 July 1887, the son of a sailor from Cornwall, and a gypsy from Seville.

In his adventures full of real-world references, Corto has often crossed with real historical characters like the American author Jack London and his nurse Virginia Prentiss, the American outlaw Butch Cassidy, the German World War I flying ace Red Baron, and many others.

Publication history
The character debuted in the serial Ballad of the Salty Sea, one of several Pratt stories published in the first edition of the Ivaldi Editore comics magazine Sergeant Kirk in July 1967. The story centers around smugglers and pirates in the World War I–era Pacific Islands. In 1970, Pratt moved to France and began a series of short Corto Maltese stories for the French comics magazine Pif Gadget, an arrangement lasting four years and producing many 20-page stories. In 1974 he returned to full-length stories, sending Corto to 1918 Siberia in the story Corto Maltese in Siberia, first serialised in the Italian comics magazine Linus.

In 1976, Ballad of the Salty Sea was published in book format and was awarded the prize for best foreign realistic comic album at the Angoulême International Comics Festival.

Pratt continued to produce new stories over the next two decades, many first appearing in the eponymous comics magazine Corto Maltese, until 1988 when the final story Mu, the Lost Continent was serialised, ending in June 1989.

On October 7, 2014, Italian publisher Cong, who owns the rights to Corto Maltese, announced that a new album was being made by writer Juan Díaz Canales and artist Rubén Pellejero. "Under the Midnight Sun" was released in Europe on September 30, 2015 and takes place in 1915. In September 2017, a second album, "Equatoria" set in 1911 was published. In November 2019, a third album, "All Saints Day" set in 1912–1913 was published. The fourth album by Canales and Pellejero was published in September 2022, entitled "Berlin Nocturne". It takes place in Berlin and Prague in 1924.

Character
Corto Maltese (whose name derives from the Andalusian argot and means "quick hands") is a laconic sea captain adventuring during the early 20th century (1900–1920s). A "rogue with a heart of gold", he is tolerant and sympathetic to the underdog. Born in Valletta on July 10, 1887, he is the son of a British sailor from Cornwall and an Andalusian–Romani witch and prostitute known as "La Niña de Gibraltar". As a boy growing up in the Jewish quarter of Córdoba, Maltese discovered that he had no fate line on his palm and therefore carved his own with his father's razor, determining that his fate was his to choose. Although maintaining a neutral position, Corto instinctively supports the disadvantaged and oppressed.

The character embodies the author's skepticism of national, ideological and religious assertions. Corto befriends people from all walks of life, including the murderous Russian Rasputin (no relation with the historical figure, apart from physical resemblance and some character traits), British heir Tristan Bantam, voodoo priestess Gold Mouth and Czech academic Jeremiah Steiner. He also knows and meets various real-life historical figures, including Jack London, Ernest Hemingway, Hermann Hesse, Butch Cassidy, James Joyce, Gabriele D'Annunzio, Frederick Rolfe, Joseph Conrad, Sükhbaatar, John Reed, White Russian general Roman von Ungern-Sternberg, Enver Pasha of Turkey and Sergei Semenov, modelled after Grigory Semyonov. His acquaintances treat him with great respect, as when a telephone call to Joseph Stalin frees him from arrest when he is threatened with execution on the border of Turkey and Armenia.

Corto's favourite book is Utopia by Thomas More, but he never finishes it. He also read books by London, Lugones, Stevenson, Melville and Conrad, and quotes Rimbaud.

Corto Maltese stories range from straight historical adventure to occult dream sequences. He is present when the Red Baron is shot down, helps the Jívaro in South America, and flees Fascists in Venice, but also unwittingly helps Merlin and Oberon to defend Britain and helps Tristan Bantam to visit the lost continent of Mu.

Chronologically, the first adventure, Corto Maltese: The Early Years, happens during the Russo-Japanese War. In other albums he experiences the Great War in several locations, participates in the Russian Civil War after the October Revolution, and appears during the early stages of Fascist Italy. In a separate series by Pratt, The Desert Scorpions, Corto is said to be missing in action in Spain during the Spanish Civil War.

Chronology
This is a list of the twelve original Corto Maltese novels in chronological order. French editions were published by Casterman, Italian by Edizioni Lizard, English editions by IDW's EuroComics imprint.

 * 1905 Corto Maltese: The Early Years (black and white 1981)
 * 1913–1915 The Ballad of the Salty Sea (black and white 1967–1969)
 * 1916–1917 Under the Sign of Capricorn (black and white 1971)
 * 1917 Beyond the Windy Isles (black and white 1970–1971)
 * 1917–1918 Celtic Tales (black and white 1971–1972).
 * 1918 The Ethiopian (black and white 1972–1973).
 * 1918–1920 Corto Maltese in Siberia (black and white 1974–1975).
 * 1921 Fable of Venice (black and white 1977).
 * 1921–1922 The Golden House of Samarkand (black and white 1980).
 * 1923 Tango (black and white 1985).
 * 1924 The Secret Rose (black and white 1987).
 * 1925 Mu, the Lost Continent (black and white 1988–1989).

In 2015 the series was continued by Ruben Pellejero and Juan Díaz Canales, with the following albums published thus far:
 * 1911 Equatoria (2017, black and white/color).
 * 1912–1913 All Saints Day (2019, black and white/color).
 * 1915 Under the Midnight Sun (2015, black and white/color).
 * 1924 Berlin Nocturne (2022, black and white/color).
 * TBC Fate Line (2024, black and white/color).

In 2021 a reboot series was launched by Martin Quenehen and Bastien Vivès reimagining the character for the 21st century.
 * 2021 The Black Sea (2021, black and white/color)
 * 2023 The Queen of Babylon (2023, black and white/color).

Merchandising

 * A Corto Maltese tarot deck was published by tarot publisher lo Scarabeo in 2008.

Adaptations

 * In 1975–1977, Secondo Bignardi produced semi-animated Corto Maltese stories for the RAI television programme Supergulp, fumetti in TV!.
 * A French-language animated film, Corto Maltese, la cour secrète des arcanes adapting Corto Maltese in Siberia, was released in 2002. Also in 2002, Canal + produced a series of Corto Maltese adventures for television, adapting the stories The Ballad of the Salty Sea, Under the Sign of Capricorn, Celtic Tales and The Golden House of Samarkand. Canadian animator and cartoonist Guy Delisle documented his observations of colleagues working on one of these French-language adaptations at SEK Studio in North Korea in Pyongyang.
 * On 20 September 2018, a new opera, Corto Maltese: The Ballad of the Salty Sea, based on the stories of Hugo Pratt, premiered at the Teatru Manoel in Valletta (Malta) by the Teatru Manoel Youth Opera, as part of Valletta 2018 European Capital of Culture. The production, which was commissioned and co-produced by the Valletta 2018 Foundation and Teatru Manoel, was an adaptation of The Ballad of the Salty Sea. The opera was composed by Monique Krüs with a libretto by director Corina Van Eijk, based on an original script by Tama Matheson. Stage and set designs were by Jolanda Lanslots.
 * Christophe Gans was developing a new live-action film, for release in 2020. It was an adaptation of Corto Maltese in Siberia. It starred Tom Hughes as Corto and Milla Jovovich, and was to be produced by Samuel Hadida. However, it was cancelled due to legal problems.
 * In November 2022, it was announced that Frank Miller is going to adapt the graphic novel into a six episodes hourlong TV series with StudioCanal for Canal+.

title: Corto Maltese


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Hugo Pratt

Ugo Eugenio Prat (15 June 1927 – 20 August 1995), better known as Hugo Pratt, was an Italian comic book creator who was known for combining strong storytelling with extensive historical research on works such as Corto Maltese. He was inducted into the Will Eisner Award Hall of Fame in 2005, and was awarded the 15th anniversary special Grand Prix de la ville d'Angoulême at the Angoulême Festival. In 1946 Hugo Pratt became part of the so-called Group of Venice with Fernando Carcupino, Dino Battaglia and Damiano Damiani.

Early years
Born in Rimini, Italy, to Rolando Prat and Evelina (Genero) Prat, Ugo Eugenio Prat spent much of his childhood in Venice in a very cosmopolitan family environment. His paternal grandfather Joseph was Catholic of English and Provencal origins, his maternal grandfather was of hidden Jewish descent and his grandmother was of Turkish origin. In 1937, Pratt moved with his mother to Abyssinia (Ethiopia), joining his father who had moved there following the conquest of that country by Benito Mussolini's Italy. Pratt's father, a MVSN NCO, was captured in 1941 by British troops and, in late 1942, died from disease as a prisoner of war. The same year, Hugo Pratt and his mother were interned in a prison camp at Dirédaoua, where he would buy comics from guards, and later was sent back to Italy by the Red Cross.

After the war, Pratt moved to Venice where he organized entertainment for the Allied troops. Later Pratt joined the Venice Group with other Italian cartoonists, including Alberto Ongaro, Gian Carlo Guarda  and Mario Faustinelli. Their magazine Asso di Picche, launched in 1945 as Albo Uragano, concentrated on adventure comics. The magazine scored some success and published works by young talents, including Dino Battaglia. His eponymous character Asso di Picche (Ace of Spades) was a success, mainly in Argentina, where Pratt was invited in 1949.

Argentine years
In the late 1940s he moved to Buenos Aires, where he worked for Argentine publisher Editorial Abril and met Argentine comics artists such as Alberto Breccia and Solano López. The passage to Editorial Frontera saw the publication of some of his most important early series. These included Sergeant Kirk and Ernie Pike, written by Héctor Germán Oesterheld.

Pratt taught drawing in the Escuela Panamericana de Arte directed by Enrique Lipszyc. He often travelled to South American destinations such as the Amazon and Mato Grosso. During that period he produced his first comic book as a complete author, both writing and illustrating Anna della jungla (Ann of the Jungle), which was followed by the similar Capitan Cormorant and Wheeling. The latter was completed after his return to Italy.

Return to Italy and the creation of Corto Maltese
From the summer of 1959 to the summer of 1960, Pratt lived in London where he drew a series of war comics for Fleetway Publications, with British scriptwriters. He then returned to Argentina, despite the harsh economic times there. From there, he moved again to Italy in 1962 where he started a collaboration with the children's comic book magazine Corriere dei Piccoli, for which he adapted several classics of adventure literature, including Treasure Island and Kidnapped by Robert Louis Stevenson.

In 1967, Pratt met Florenzo Ivaldi; the two created a comics magazine named after his character, Sergeant Kirk, the hero first written by Héctor Oesterheld. Pratt's most famous story, Una ballata del mare salato (A Ballad of the Salty Sea), is published in the first issue and introduced his best-known character, Corto Maltese.

Corto's series continued three years later in the French magazine Pif Gadget. Due to his rather mixed family ancestry, Pratt had learned snippets of things such as kabbalism and much history. Many of his stories are placed in real historical eras and deal with real events: the 1755 war between French and British colonists in Ticonderoga, colonial wars in Africa and both world wars, for example. Pratt did exhaustive research for factual and visual details, and some characters are real historical figures or loosely based on them, such as Corto's main friend/enemy, Rasputin. Many of the minor characters cross over into other stories in a way that places all of Pratt’s stories into the same continuum.

Pratt's main series in the second part of his career include Gli scorpioni del deserto (five stories) and Jesuit Joe. He also wrote stories for his friend and pupil Milo Manara for Tutto ricominciò con un'estate indiana and El Gaucho.

Later years
From 1970 to 1984, Pratt lived mainly in France where Corto Maltese, a psychologically very complex character resulting from the travel experiences and the endless inventive capacity of his author, became the main character of a comics series. Initially published from 1970 to 1973 by the magazine Pif Gadget, it brought him much popular and critical success. Later published in album format, this series was eventually translated into fifteen languages. From 1984–95 he lived in Switzerland, where the international success that Corto Maltese sparked continued to grow. In France, most of his pre-Corto Maltese works were published in several album editions by publishers such as Casterman, Dargaud, and Les Humanoïdes Associés. A wanderer by nature, Hugo Pratt continued to travel from Canada to Patagonia, from Africa to the Pacific area. He died of bowel cancer on 20 August 1995.

Pratt cited authors such as Robert Louis Stevenson, James Oliver Curwood, Zane Grey, Kenneth Roberts, Henry De Vere Stacpoole, Joseph Conrad, Fenimore Cooper, Herman Melville and Jack London as influences, along with cartoonists Lyman Young, Will Eisner, and especially Milton Caniff.

On Friday, 15 July 2005, at San Diego Comic-Con's 17th Annual Will Eisner Comic Industry Awards, he was one of four professionals that year inducted into the Comic Book Hall of Fame.

One of the series created by Pratt, entitled "The Scorpions of the Desert" in English, has been continued after Pratt's death. In 2005 a sixth volume in this series was released, drawn by Pierre Wazeem and entitled "Le chemin de fièvre". A seventh album was scheduled by the French publishers Casterman for release in March 2008. Casterman have also on several occasions hinted at the possible future release of a further episode in the Corto Maltese saga.

In 2015, IDW Publishing's EuroComics imprint launched the definitive English-language edition of Corto Maltese, with new translations made from Pratt's original Italian scripts.

Awards

 * 1969: per il disegnatore italiano (award for an Italian artist) at the Lucca Comics & Games, for Una ballata del mare salato
 * 1974: Prix Saint-Michel, for the best realistic story
 * 1976: Angoulême Festival, Best foreign realistic comic book, for La ballade de la mer salée
 * 1981: Angoulême Festival, Elle award
 * 1987: Angoulême Festival, Best foreign comic book, for Indian Summer
 * 1988: Angoulême Festival, 15th anniversary special Grand Prix de la ville d'Angoulême
 * 1996: Max & Moritz Prizes, Germany, Best German language comic import, for Saint-Exupéry - le dernier vol
 * 2005: inducted into the Will Eisner Award Hall of Fame

Main works

 * Asso di Picche (L'As de pique, Ace of Spades, 1945–1949)
 * El Sargento Kirk (Sergeant Kirk, 1953–1959), written by Héctor Oesterheld
 * Ticonderoga (1957–1958), written by Héctor Oesterheld
 * Ernie Pike (1957–1959), written by Héctor Oesterheld
 * Ann y Dan (Anna nella giungla, Ann of the Jungle, Ann de la jungle, 1959)
 * Capitan Cormorant (1962)
 * Wheeling (1962)
 * Corto Maltese (1967–1992)
 * Una ballata del mare salato (1967) - translated into English as Ballad of The Salt Sea (Harvill Press 1996)
 * Il segreto di Tristan Bantam (1970)
 * Corto toujours un peu plus loin - partly translated into English as The Banana Conga (1970-1971)
 * Le Celtiche (1972) - translated into English as The Celts, (Harvill Press 1996) and A Mid-Winter Morning's Dream (1971–1972)
 * Le Etiopiche (1972–1973)
 * Corte Sconta detta Arcana (1974)
 * Favola di Venezia (1976)
 * La casa dorata di Samarcanda (1980)
 * La giovinezza (1981)
 * Tango (1985)
 * Le elvetiche "Rosa Alchemica" (1987)
 * Mu (1988)
 * Gli scorpioni del deserto - Les Scorpions du Desert, The Scorpions of the Desert (1969–92)
 * Les Scorpions du désert (Episode 1, 1969–73)
 * Piccolo chalet... (1975)
 * Vanghe Dancale (1980)
 * Dry Martini Parlor (1982)
 * Brise de mer (1992)
 * L'uomo dei Caraibi (1977)
 * L'uomo del Sertao (1977)
 * L'uomo della Somalia (1979)
 * L'uomo del gran nord - Jesuit Joe (1980)
 * Tutto ricominciò con un'estate indiana (Indian Summer, 1983, with Milo Manara)
 * Cato Zulu (1984–88)
 * El Gaucho (1991), with Milo Manara
 * Saint-Exupéry - le dernier vol (1994)
 * Morgan (1995)

In cinema
Swiss director Stefano Knuchel started a trilogy of documentaries about Pratt, releasing Hugo en Afrique in 2009, followed by Hugo in Argentina in 2021. In 2022, Knuchel announced working on the third part of the trilogy, Hugo in Venice.

title: Hugo Pratt