abrikosov lattices in finite domains in 1957 abrikosov published his work on periodic solutions to the linearized ginzburg landau equations abrikosov s analysis assumes periodic boundary conditions which are very different from the natural boundary conditions the minimizer of the ginzburg landau energy functional should satisfy in the present work we prove that the global minimizer of the fully non linear functional can be approximated in every rectangular subset of the domain by one of the periodic solution to the linearized ginzburg landau equations in the plane furthermore we prove that the energy of this solution is close to the minimum of the energy over all abrikosov s solutions in that rectangle

magnetic wkb constructions this paper is devoted to the semiclassical magnetic laplacian until now wkb expansions for the eigenfunctions were only established in the presence of a non zero electric potential here we tackle the pure magnetic case thanks to feynman hellmann type formulas and coherent states decomposition we develop here a magnetic born oppenheimer theory exploiting the multiple scales of the problem we are led to solve an effective eikonal equation in pure magnetic cases and to obtain wkb expansions we also investigate explicit examples for which we can improve our general theorem global wkb expansions quasi optimal agmon estimates and upper bound of the tunelling effect in symmetric cases we also apply our strategy to get more accurate descriptions of the eigenvalues and eigenfunctions in a wide range of situations analyzed in the last two decades

brief estimating the domain of attraction for power systems via a group of damping reflected energy functions the well known lyapunov direct method provides precise and rigorous theoretical backgrounds for stability analysis of nonlinear systems however incorporating damping effects into accurate estimates of the domain of attraction has proved difficult which is pointed as a minor but crucial drawback this paper presents a new method to derive a group of lyapunov functions to reflect the damping effects by considering the first integral of motion obtained from the system governing equations when transfer conductances are neglected a systematical approach of converting some part of damping loss into some appropriate system energy terms is developed examples show that the proposed method remarkably improves the estimation of the region of attraction compared with the conventional approach

peak power in the 3d magnetic schrodinger equation this paper is devoted to the spectral analysis of the magnetic neumann laplacian on an infinite cone of aperture alpha when the magnetic field is constant and parallel to the revolution axis and when the aperture goes to zero we prove that the first n eigenvalues exist and admit asymptotic expansions in powers of alpha 2

dynamic gradient approaches to compute the closest unstable equilibrium point for stability region estimate and their computational limitations the reflected gradient method and the newton trajectory method are approaches to compute the closest unstable equilibrium point uep for stability region estimation we address the computational issues involved in these methods we first suggest a dynamic gradient approach as a unified and extended version of these methods then we show that computing the closest uep using the dynamic gradient approach can be infeasible

surface superconductivity in 3 dimensions we study the ginzburg landau system for a superconductor occupying a 3 dimensional bounded domain and improve the estimate of the upper critical field h c3 obtained by k lu and x pan in j diff eqns 168 2000 386 452 we also analyze the behavior of the order parameters we show that under an applied magnetic field lying below and not far from h c3 order parameters concentrate in a vicinity of a sheath of the surface that is tangential to the applied field and exponentially decay both in the normal and tangential directions away from the sheath in the l 2 sense as the applied field decreases further but keeps in between and away from h c2 and h c3 the superconducting sheath expands but does not cover the entire surface and superconductivity at the surface portion orthogonal to the applied field is always very weak this phenomenon is significantly different to the surface superconductivity on a cylinder of infinite height studied by x pan in comm math phys 228 2002 327 370 where under an axial applied field lying in between h c2 and h c3 the entire surface is in the superconducting state

implementation of diffuse reflection boundary conditions in a thermal lattice boltzmann model with flux limiters we discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice boltzmann model their accuracy is investigated in the case of couette flow by considering the slip regime the best results are recovered with versions 2 and 3 which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain version 2 is found to be more economical since it involves no interpolation procedure this version was thereafter used to investigate the temperature profile in couette flow for various values of prandtl number as well as the capability of the thermal lb model to capture the knudsen minimum in poiseuille flow

energy conserving lattice boltzmann thermal model in two dimensions a discrete velocity model is presented for lattice boltzmann thermal fluid dynamics this model is implemented and tested in two dimensions with a finite difference scheme comparison with analytical solutions shows an excellent agreement even for wide temperature differences an alternative approximate approach is then presented for traditional lattice transport schemes

the phase transitions from chiral nematic toward smectic liquid crystals a chen lubensky energy is used to investigate phase transitions from chiral nematic to smectic c and smectic a liquid crystal phases we consider a liquid crystalline material confined between two parallel plates where the dimensions of are assumed to be large relative both to the width of a smectic layer and the material s chiral pitch we take boundary conditions so that the smectic phase melts at the plates surfaces and prove the existence of energy minimizers in an admissible set consisting of order parameters psi in mathcal h 2 0 omega and molecular directors mathbf n in mathbf w 1 2 omega mathbb s 2 then under the physically observed assumption that the frank elasticity constants become large near a phase transition we establish estimates for the transition region separating phases in particular we derive analytic estimates proving that chirality lowers the transition temperature regime above which minimizers are nematic and below which minimizers are in a smectic phase

reachability analysis of nonlinear differential algebraic systems this paper presents a numerical procedure for the reachability analysis of systems with nonlinear semi explicit index 1 differential algebraic equations the procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way i e it is guaranteed that all possible trajectories of the system are enclosed thus the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them the presented approach scales favorably with the number of state variables this makes it possible to solve problems of industry relevant size as demonstrated by a transient stability analysis of the ieee 14 bus benchmark problem for power systems

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

computation of gas solid flows by finite difference boltzmann equation abstract in this paper we will discuss in detail how to use a finite difference lattice boltzmann equation model in which an external force term is involved to simulate two way coupling gas solid flows the numerical results are found to be in good agreement with analytical data and some other numerical results

direct methods for studying dynamics of large scale electric power systems a survey this paper attempts to give a unified overview of how direct methods solve the transient stability problem of large scale power systems two distinct methodologies are considered and discussed the first concerns application of the direct lyapunov method to the conventional transient stability analysis both scalar and vector lyapunov approaches are envisaged and their respective merits and potentialities are compared particular attention is also paid to the estimation of practical stability domains aiming to overcome the usual conservativeness of the lyapunov criterion the second methodology focuses on the derivation of stability indices intended for on line monitoring contingency evaluation and security control the present achievements and future trends are explored and tentatively assessed

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

lattice boltzmann models based on half range gauss hermite quadratures we discuss general features of thermal lattice boltzmann models based on half range gauss quadratures specialising to the half range gauss hermite and gauss laguerre cases the main focus of the paper is on the construction of high order half range hermite lattice boltzmann hhlb models the performance of the hhlb models is compared with that of laguerre lattice boltzmann llb and full range hermite lattice boltzmann hlb models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density macroscopic velocity temperature and heat fluxes in the two dimensional couette flow the bhatnagar gross krook bgk collision term is used throughout the paper to reduce the computational costs of the numerical simulations we use mixed lattice boltzmann models constructed using different quadrature methods on each cartesian axis for kn 0 01 the hlb models require the least number of velocities to satisfy our convergence test when kn 0 05 the hlb models are outperformed in terms of number of velocities employed by both the llb and the hhlb models moreover we find that the hhlb models require less quadrature points than the llb models at all tested values of kn which we attribute to the maxwellian form of the weight function for the half range hermite polynomials

emergence of the triangular lattice near a flat wall the bifurcation of periodic solutions near a flat wall for applied magnetic fields which are slightly weaker than hc2 is considered for a reduced ginzburg landau model obtained in the large limit we formally demonstrate that following the bifurcation of the first mode when the applied magnetic field is further decreased there is a second bifurcation after which the solution develops continuously into the well known triangular lattice

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

two dimensional thermal model of the finite difference lattice boltzmann method with high spatial isotropy the existing lattice boltzmann method multispeed thermal models show a limited accuracy this paper proposes a two dimensional multispeed thermal model for the finite difference lattice boltzmann method fdlbm to recover correct fluid equations up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy in the fdlbm particle velocities can be selected independently from the lattice configuration therefore particle velocities of octagonal directions which have up to seventh rank isotropic tensors are adopted the proposed model was verified by two simulations the model showed excellent numerical stability in addition to strict accuracy

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

remarks on the spectrum of the neumann problem with magnetic field in the half space we consider a schrodinger operator with a constant magnetic field in a one half three dimensional space with neumann type boundary conditions it is known from the works by lu pan and helffer morame that the lower bound of its spectrum is less than b the intensity of the magnetic field provided that the magnetic field is not normal to the boundary we prove that the spectrum under b is a finite set of eigenvalues each of infinite multiplicity in the case when the angle between the magnetic field and the boundary is small we give a sharp asymptotic expansion of the number of these eigenvalues

radial solutions for the ginzburg landau equation with applied magnetic field abstract the purpose of this work is a systematic study of symmetric vortices for the ginzburg landau model of superconductivity along a cylinder with applied magnetic field parallel to its axis the ginzburg landau constant of the material and the degree d of the vortex are fixed for any given parameters r the radius of the cylinder and h the intensity of the applied magnetic field one can find a symmetric vortex a which satisfies the boundary conditions b r e i d and curl a b r he 3 it is then shown that symmetric vortices form a family depending continuously on two real parameters and c which describe the behaviour at the center of the vortex as the boundary conditions depend smoothly on those parameters one can distinguish two main connected domains of vortices the first one defined by the boundary conditions b r e i d and ra r b r is a zone of stability where remains increasing the second one defined by the boundary conditions b r e i d and ra r b r d is a zone where some instability can occur attention is focused on the smooth branch of vortices which separates those two domains it is indexed by the parameter running from some l 0 to and the limit as decreases to l corresponds to a berger and chen type vortex

stable nucleation for the ginzburg landau system with an applied magnetic field we consider the ginzburg landau system with an applied magnetic field and analyze the behavior of solutions when the domain is a cylinder of radius overline r and the applied field is parallel to the axis it is shown that there is an upper critical value overline h such that if the modulus of the applied field is greater than overline h the normal nonsuperconducting state in which the order parameter is identically zero is stable and if the modulus of the applied field is slightly below oh the normal state is unstable in addition it is shown that there is a positive lower critical value underline h leq overline h such that the normal state is unstable if the modulus of the applied field is less than underline h and stable if the modulus is slightly above underline h in the case of type ii materials for whic h the ginzburg landau constant is large it is shown that there is a discrete set of radii such that if overline r notin cal b kappa and kappa overline r is sufficiently large then for each applied field of modulus slightly less than overline h or slightly more than underline h there is precisely one small superconducting solution up to a gauge transformation which is stable moreover for this solution the complex valued order parameter is zero only on the axis of the cylinder and its winding number is proportional to the product of 2 and the cross sectional area of the cylinder in addition the solution exhibits surface superconductivity as predicted by the physicists de gennes and st james

two dimensional lattice boltzmann model for compressible flows with high mach number abstract in this paper we present an improved lattice boltzmann model for compressible navier stokes system with high mach number the model is composed of three components i the discrete velocity model by m watari and m tsutahara phys rev e 67 2003 036306 ii a modified lax wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included iii artificial viscosity the improved model is convenient to compromise the high accuracy and stability the included dispersion term can effectively reduce the numerical oscillation at discontinuity the added artificial viscosity helps the scheme to satisfy the von neumann stability condition shock tubes and shock reflections are used to validate the new scheme in our numerical tests the mach numbers are successfully increased up to 20 or higher the flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems

schrodinger operators with non degenerately vanishing magnetic fields in bounded domains we establish an asymptotic estimate of the lowest eigenvalue bf of the schrodinger operator 2 bf with a magnetic field in a bounded 2 dimensional domain where curl f vanishes non degenerately and b is a large parameter our study is based on an analysis on an eigenvalue variation problem for the sturm liouville problem using the estimate we determine the value of the upper critical field for superconductors subject to non homogeneous applied magnetic fields and localize the nucleation of superconductivity

a novel coupled lattice boltzmann model for low mach number combustion simulation abstract a novel coupled lattice boltzmann model is developed for two and three dimensional low mach number combustion simulations in which the fluid density can bear sharp changes different to the hybrid lattice boltzmann scheme o filippova d hanel a novel lattice bgk approach for low mach number combustion j comput phys 158 2000 139 this scheme is strictly pure lattice boltzmann style i e we solve the flow temperature and concentration fields using the lattice boltzmann method only different to the non coupled lattice boltzmann scheme k yamamoto x he g d doolen simulation of combustion field with lattice boltzmann method j stat phys 107 2002 367 the fluid density in this model is coupled directly with the temperature in this model the time step and the fluid particle speed can be adjusted dynamically depending on the particle characteristic temperature and the algorithm is still a simple process of hopping from one grid point to the next the same as the standard lattice boltzmann method therefore the outstanding advantages of the standard lattice boltzmann method are retained in this model besides better numerical stability excellent agreement between the present results and other numerical or experimental data shows that this scheme is an efficient numerical method for practical combustion simulations

finite difference lattice boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations abstract the current finite difference lattice boltzmann method fdlbm gives a fixed specific heat ratio because internal energy is limited to the translational freedom of the space yan et al and kataoka et al clarified the conditions for deriving models with arbitrary specific heat ratio and proposed euler models however these model applications to numerical simulations showed the weakness in the numerical stability in this paper a two dimensional fdlbm navier stokes model and a three dimensional fdlbm euler model which allow arbitrary values to be set for the specific heat ratio were proposed these models stably performed numerical simulations from subsonic to supersonic ranges

magnetic bottles in connection with superconductivity abstract motivated by the theory of superconductivity and more precisely by the problem of the onset of superconductivity in dimension two a lot of papers devoted to the analysis in a semi classical regime of the lowest eigenvalue of the schrodinger operator with magnetic field have appeared recently here we mention the works by bernoff sternberg lu pan and del pino felmer sternberg this partially recovers questions analyzed in a different context by the authors around the question of the so called magnetic bottles our aim is to analyze the former results to treat them in a more systematic way and to improve them by giving sharper estimates of the remainder in particular we improve significantly the lower bounds and as a by product we solve a conjecture proposed by bernoff sternberg concerning the localization of the ground state inside the boundary in the case with constant magnetic fields

boundary concentration for eigenvalue problems related to the onset of superconductivity we examine the asymptotic behavior of the eigenvalue h and corresponding eigenfunction associated with the variational problem in the regime h 1 here a is any vector field with curl equal to 1 the problem arises within the ginzburg landau model for superconductivity with the function h yielding the relationship between the critical temperature vs applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross section omega subset r 2 we first carry out a rigorous analysis of the associated problem on a half plane and then rigorously justify some of the formal arguments of bs obtaining an expansion for while also proving that the first eigenfunction decays to zero somewhere along the sample boundary when is not a disc for interior decay we demonstrate that the rate is exponential

three dimensional finite difference lattice boltzmann model and its application to inviscid compressible flows with shock waves abstract in this paper a three dimensional 3d finite difference lattice boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double distribution function approach in the model a density distribution function is adopted to model the flow field while a total energy distribution function is adopted to model the temperature field the discrete equilibrium density and total energy distribution functions are derived from the hermite expansions of the continuous equilibrium distribution functions the discrete velocity set is obtained by choosing the abscissae of a suitable gauss hermite quadrature with sufficient accuracy in order to capture the shock waves in compressible flows and improve the numerical accuracy and stability an implicit explicit finite difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations the model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1d to 3d the numerical results are found to be in good agreement with the analytical solutions and or other numerical results reported in the literature

the onset of superconductivity in semi infinite strips the existence of a superconducting branch bifurcating from the normal state is proved in semi infinite strips it is proved that the critical magnetic field at which bifurcation takes place or the onset field for a semi infinite strip is greater than the onset field for an infinite strip with the same width in addition we find the loci of the vortices far away from the corners and show convergence of the bifurcating modes in long rectangles to those in the semi infinite strip with the same width