A new exact solution and corresponding localized excitations of the ()-dimensional mKdV equation

In this Letter, we show that the new (2+1)-dimensional mKdV equation possesses Painlevé property. Then, starting from the standard truncated Laurent expansion and the direct variable separation approach, a new exact solution with two lower dimensional arbitrary functions is obtained. Some high-dimensional localized excitations of the physical quantity u are constructed. These localized excitations have abundant structures at x-axis and y-axis such as dromions, peakons, loop-solitons, compactons which depend on corresponding functions.     

Equation of State for Shock Compressed Xenon in the Ionization Regime:ab Initio Study

Quantum molecular dynamic (QMD) simulations have been applied to study the thermophysical properties of liquid xenon under dynamic compressions. The equation of state (EOS) obtained from QMD calculations are corrected according to Saha equation, and contributions from atomic ionization, which are of predominance in determining the EOS at high temperature and pressure, are considered. For the pressures below 160 GPa, the necessity in accounting for the atomic ionization has been demonstrated by the Hugoniot curve, which shows excellent agreement with previous experimental measurements, and three levels of ionization have been proved to be sufficient at this stage.     

Equation of State for Shock Compressed Xenon in the Ionization Regime: ab Initio Study

Quantum molecular dynamic (QMD) simulations have been applied to study the thermophysical properties of liquid xenon under dynamic compressions. The equation of state (EOS) obtained from QMD calculations are corrected according to Saha equation, and contributions from atomic ionization, which are of predominance in determining the EOS at high temperature and pressure, are considered. For the pressures below 160 GPa, the necessity in accounting for the atomic ionization has been demonstrated by the Hugoniot curve, which shows excellent agreement with previous experimental measurements, and three levels of ionization have been proved to be sufficient at this stage.     

Fluctuations in reaction-diffusion systems: A new exactly soluble growth model

The method of compounding moments devised by Van Kampen is used to study the spatial fluctuations in a model describing the irreversible formation of clusters. The reaction and diffusion constants in this model are chosenindependent of the cluster sizes. For a monodisperse initial distribution explicit expressions are calculated for the equal-time and two-time correlation functions of the concentrations ofm- andn-mers. For general initial conditions the fluctuations in the mass density are considered and a scaling theory is presented for the fluctuations at large times. Extensions to more general models are discussed.     

A novel lip reading algorithm by using localized ACM and HMM: Tested for digit recognition

Lip contour tracking is an integral part of lip reading application. Fast and accurate lip tracking is an important step in lip reading. This paper uses a novel active contour model for lip tracking and proposes geometrical feature extraction approach for lip reading. Effect of individual features are compared and a joint feature model is obtained by combining weighted decision obtained by a feature vector of difference in inner area, height and width of lip. Ergodic hidden markov model (HMM) is used as a classifier. For each digit Markov Model is tested for 3 states and 5 states. Videos of English digit from 0 to 9 have been recorded for recognition test. Cuave database is used for comparison along with an in-house database. While doing computation of feature vectors, only significant frames are used to reduce the computation complexity. Results of experimentations on digit utterances are given to show that the maximum recognized digit can be used for important programming command of computerized numerical control machines.     

A new formalism for the statistical dynamics of vector spin systems

The relaxational dynamics of a classical vector Heisenberg spin system is studied using the Fokker-Planck equation. To calculate the eigenvalues of the Fokker-Planck operator, a new approach is introduced. In this connection, a number space repesentation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

A new formalism for the statistical dynamics of planar spin systems

The relaxational dynamics of a classical planar Heisenberg spin system is studied using the Fokker-Planck equation. A new approach is introduced in which we attempt to directly calculate the eigenvalues of the Fokker-Planck operator. In this connection a number space representation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

A family of evolution equations with nonlinear diffusion,Verhulst growth,and global regulation: Exact time-dependent solutions

A family of evolution equations describing a power-law nonlinear diffusion process coupled with a local Verhulst-like growth dynamics, and incorporating a global regulation mechanism, is considered. These equations admit an interpretation in terms of population dynamics, and are related to the so-called conserved Fisher equation. Exact time-dependent solutions exhibiting a maximum nonextensive q$q$-entropy shape are obtained.     

Spatial fluctuations in reaction-diffusion systems: A model for exponential growth

The spatial fluctuations in an exactly soluble model for the irreversible aggregation of clusters are treated. The model is characterized byrate constants K _ij =i+j for the clustering of ani- and aj-mer, anddiffusion constants D _j =D. It is assumed thatD1 (reaction-limited aggregation). Explicit expressions for the correlation functions at equal and at different times are calculated. The equal-time correlation functions show scaling behavior in the scaling limit. The correlation length remains finite ast, and the fluctuations becomelarge at large times (tt _D ) inany dimension. The crossover timet _D , at which the mean field theory (Smoluchowski's equation) breaks down, is given byt _D InD. These exact results imply that the upper critical dimension of this model isd _c= and, hence, that there isno unique upper critical dimension in models for the irreversible aggregation of clusters.     

Equation of state for warm dense lithium: A first principles investigation

The quantum molecular dynamics based on the density functional theory has been adopted to simulate the equation of state for the shock compressed lithium. In contrary to some earlier experimental measurement and theoretical simulation,there is not any evidence of the ‘kink' in the Hugoniot curve in our accurate simulation. Throughout the shock compression process, only a simple solid-to-liquid melting behavior is demonstrated, instead of complicated solid–solid phase transitions. Moreover, the x-ray absorption near-edge spectroscopy has been predicted as a feasible way to diagnose the structural evolution of warm dense lithium in this density region.     

Photon condensation: A new paradigm for Bose–Einstein condensation

Bose–Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose–Einstein condensate (BEC) in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose–Einstein condensate. We also elaborate on the theoretical framework for atomic Bose–Einstein condensation, which includes statistical mechanics and the Gross–Pitaevskii equation. As an extension, we discuss Bose–Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck’s law in statistical mechanics. Further, a comparison is made between photon condensate and laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.     

A mathematical framework for critical transitions: Bifurcations, fast-slow systems and stochastic dynamics

Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms “critical transition” or “tipping point” have been used to describe this situation. Critical transitions have been observed in an astonishingly diverse set of applications from ecosystems and climate change to medicine and finance. The main goal of this paper is to give an overview which standard mathematical theories can be applied to critical transitions. We shall focus on early-warning signs that have been suggested to predict critical transitions and point out what mathematical theory can provide in this context. Starting from classical bifurcation theory and incorporating multiple time scale dynamics one can give a detailed analysis of local bifurcations that induce critical transitions. We suggest that the mathematical theory of fast-slow systems provides a natural definition of critical transitions. Since noise often plays a crucial role near critical transitions the next step is to consider stochastic fast-slow systems. The interplay between sample path techniques, partial differential equations and random dynamical systems is highlighted. Each viewpoint provides potential early-warning signs for critical transitions. Since increasing variance has been suggested as an early-warning sign we examine it in the context of normal forms analytically, numerically and geometrically; we also consider autocorrelation numerically. Hence we demonstrate the applicability of early-warning signs for generic models. We end with suggestions for future directions of the theory.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl₆ suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown. Based on the lecture by the author “Quasi crystals: Is Linus Pauling right” and delivered on 16 December 1985 and arranged by the Departments of Physics, Metallurgy, Materials Research Laboratory, and Instrumentation Services Unit, Indian Institute of Science, Bangalore.     

A general solution to the Schrödinger–Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation.     

A new powerful source for coherent VUV radiation: Demonstration of exponential growth and saturation at the TTF free-electron laser

We present experimental evidence that the free-electron laser at the TESLA Test Facility has reached the maximum power gain of 10⁷ in the vacuum ultraviolet (VUV) region at wavelengths between 80 and 120 nm. At saturation the FEL emits short pulses with GW peak power and a high degree of transverse coherence. The radiation pulse length can be adjusted between 30 fs and 100 fs. Radiation spectra and fluctuation properties agree with the theory of high gain, single-pass free-electron lasers starting from shot noise. Received 26 April 2002 Published online 28 June 2002     

Experimental evidence of photoinduced valence change of Fe3+ in BaTiO3 and mechanism for growth of new grating in depleted pump condition: An EPR investigation

With a view to understanding the role of photo-induced valence changes of impurities in BaTiO₃ in the phenomena of photorefraction, EPR experiments were conducted under in situ He-Ne laser illumination. These experiments gave evidence for photoinduced valence change of Fe in BaTiO₃ at room temperature. The EPR signal due to trivalent iron was found to reduce in intensity with laser illumination The kinetics of the valence change has been investigated. Under large fringe width condition, the time constant of the decay is identified as the dielectric relaxation time τ_d. The changes in line shape on laser illumination to Dysonian form, appeared most predominantly in mechanically poled crystal compared to electrically poled single domain crystals. This demonstrated the possible role of domain walls and the defects there, as source or sinks of charge carriers on photo excitation. It is observed, that there is transient growth of Fe³⁺, when the laser illumination was put on, before its decay. This was attributed to charge transfer between electrons in oxygen vacancies and Fe⁴⁺. This predicted the growth of a transient grating under depleted pump condition in a two beam coupling experiment. This was experimentally proved by following the diffracted signal of the reading beam under the depleted pump condition.