how colored environmental noise affects population extinction environmental noise can cause an exponential reduction in the mean time to extinction mte of an isolated population we study this effect on an example of a stochastic birth death process with rates modulated by a colored that is correlated gaussian noise a path integral formulation yields a transparent way of evaluating the mte and finding the optimal realization of the environmental noise that determines the most probable path to extinction the population size dependence of the mte changes from exponential in the absence of the environmental noise to a power law for a short correlated noise and to no dependence for long correlated noise we also establish the validity domains of the white noise limit and adiabatic limit

spectral gaps for periodic schrodinger operators with strong magnetic fields we consider schrodinger operators h h ih d a ih d a with the periodic magnetic field b da on covering spaces of compact manifolds using methods of a paper by kordyukov mathai and shubin 14 we prove that under some assumptions on b there are in arbitrarily large number of gaps in the spectrum of these operators in the semiclassical limit of the strong magnetic field h 0

error estimates for the raviart thomas interpolation under the maximum angle condition the classical error analysis for the raviart thomas interpolation on triangular elements requires the so called regularity of the elements or equivalently the minimum angle condition however in the lowest order case optimal order error estimates have been obtained in g acosta and r g duran siam j numer anal 37 2000 pp 18 36 replacing the regularity hypothesis by the maximum angle condition which was known to be sufficient to prove estimates for the standard lagrange interpolation in this paper we prove error estimates on triangular elements for the raviart thomas interpolation of any order under the maximum angle condition also we show how our arguments can be extended to the three dimensional case to obtain error estimates for tetrahedral elements under the regular vertex property introduced in g acosta and r g duran siam j numer anal 37 2000 pp 18 36

an embedded hybridized discontinuous galerkin finite element method for the stokes equations abstract we present and analyze a new embedded hybridized discontinuous galerkin finite element method for the stokes problem the method has the attractive properties of full hybridized methods namely an h div conforming velocity field pointwise satisfaction of the continuity equation and a priori error estimates for the velocity that are independent of the pressure the embedded hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees of freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers the analysis results are supported by a range of numerical examples that demonstrate rates of convergence and which show computational efficiency gains over a full hybridized formulation

extinction rates for fluctuation induced metastabilities a real space wkb approach the extinction of a single species due to demographic stochasticity is analyzed the discrete nature of the individual agents and the poissonian noise related to the birth death processes result in local extinction of a metastable population as the system hits the absorbing state the fokker planck formulation of that problem fails to capture the statistics of large deviations from the metastable state while approximations appropriate close to the absorbing state become in general invalid as the population becomes large to connect these two regimes a real space wkb method based on the master equation is presented and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state the details of the underlying microscopic process smeared out in a mean field treatment are shown to be crucial for an exact determination of the extinction exponent this general scheme is shown to reproduce the known results in the field to yield new corollaries and to fit quite precisely the numerical solutions moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

absence of singular spectrum for a perturbation of a two dimensional laplace beltrami operator with periodic electromagnetic potential let be a lattice on we consider a metric g a one form a and a real function v on all periodic we prove that the spectrum of the schrodinger operator on is absolutely continuous

isotropic hypoellipticity and trend to equilibrium for the fokker planck equation with a high degree potential we consider the fokker planck equation with a confining or anti confining potential which behaves at infinity like a possibly high degree homogeneous function hypoellipticity techniques provide the well posedness of the weak cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding witten laplacian with detailed applications

mixed normal superconducting states in the presence of strong electric currents we study the ginzburg landau equations in the presence of large electric currents that are smaller than the critical current where the normal state loses its stability for steady state solutions in the large kappa limit we prove that the superconductivity order parameter is exponentially small in a significant part of the domain and simply small in the rest of it similar results are obtained for the time dependent problem in continuation of the paper by the two first authors 3 we conclude by obtaining some weaker results albeit similar for steady state solutions in the large domain limit

on really locking free mixed finite element methods for the transient incompressible stokes equations inf sup stable mixed methods for the steady incompressible stokes equations that relax the divergence constraint are often claimed to deliver locking free discretizations however this relaxation leads to a pressure dependent contribution in the velocity error which is proportional to the inverse of the viscosity thus giving rise to a different locking phenomenon however a recently proposed modification of the right hand side alone leads to a discretization that is really locking free i e its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity in this contribution we extend this approach to the transient incompressible stokes equations where besides the right hand side also the velocity time derivative requires an improved space discretization semidiscrete and fully discrete a priori velocity and pressure error estimates are derived which show remarkable robustness properties two numerical examples illustrate the superior accura

computations of the first eigenpairs for the schrodinger operator with magnetic field this paper is devoted to computations of eigenvalues and eigenvectors for the schrodinger operator with constant magnetic field in a domain with corners as the semi classical parameter h tends to 0 the eigenvectors corresponding to the smallest eigenvalues concentrate in the corners they have a two scale structure consisting of a corner layer at scale sqrt h and an oscillatory term at scale h the high frequency oscillations make the numerical computations particularly delicate we propose a high order finite element method to overcome this difficulty relying on such a discretization we illustrate theoretical results on plane sectors squares and other straight or curved polygons we conclude by discussing convergence issues

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

low energy spectrum of toeplitz operators with a miniwell in the semiclassical limit it is well known that the first eigenvector of a toeplitz operator concentrates on the minimal set of the symbol in this paper we give a more precise criterion for concentration in the case where the minimal set of the symbol is a submanifold in the spirit of the miniwell condition of helffer sjostrand

universal constraints on the location of extrema of eigenfunctions of non local schrodinger operators abstract we derive a lower bound on the location of global extrema of eigenfunctions for a large class of non local schrodinger operators in convex domains under dirichlet exterior conditions featuring the symbol of the kinetic term the strength of the potential and the corresponding eigenvalue and involving a new universal constant we show a number of probabilistic and spectral geometric implications and derive a faber krahn type inequality for non local operators our study also extends to potentials with compact support and we establish bounds on the location of extrema relative to the boundary edge of the support or level sets around minima of the potential

multi bump solutions to a nonlinear schrodinger equation with steep magnetic wells we show the existence of multi bump solutions to a magnetic nonlinear schrodinger equation with subcritical superlinear nonlinearity i a 2u f u2 u on n under some assumptions moreover we show that the solutions are localized near every prescribed connected component of the interior of the zero set of the magnetic field b da as

maximal inequalities and riesz transform estimates on lp spaces for magnetic schrodinger operators ii the paper concerns the magnetic schrodinger operator h bf a v sum j 1 n frac 1 i frac partial partial x j a j 2 v on mathbb r n we prove some lp estimates on the riesz transforms of h and we establish some related maximal inequalities the conditions that we arrive at are essentially based on the control of the magnetic field by the electric potential

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

a gradient robust well balanced scheme for the compressible isothermal stokes problem abstract a novel notion for constructing a well balanced scheme a gradient robust scheme is introduced and a showcase application for the steady compressible isothermal stokes equations in a nearly hydrostatic situation is presented gradient robustness means that gradient fields in the momentum balance are well balanced by the discrete pressure gradient which is possible on arbitrary unstructured grids the scheme is asymptotic preserving in the sense that it reduces for low mach numbers to a recent inf sup stable and pressure robust discretization for the incompressible stokes equations the convergence of the coupled fem fvm scheme for the nonlinear isothermal stokes equations is proved by compactness arguments numerical examples illustrate the numerical analysis and show that the novel approach can lead to a dramatically increased accuracy in nearly hydrostatic low mach number flows numerical examples also suggest that a straightforward extension to barotropic situations with nonlinear equations of state is feasible

grad div stablilization for stokes equations in this paper a stabilizing augmented lagrangian technique for the stokes equations is studied the method is consistent and hence does not change the continuous solution we show that this stabilization improves the well posedness of the continuous problem for small values of the viscosity coefficient we analyze the influence of this stabilization on the accuracy of the finite element solution and on the convergence properties of the inexact uzawa method

nodal sets for groundstates of schrodinger operators with zero magnetic field in non simply connected domains we investigate nodal sets of magnetic schrodinger operators with zero magnetic field acting on a non simply connected domain in 2 for the case of circulation 1 2 of the magnetic vector potential around each hole in the region we obtain a characterisation of the nodal set and use this to obtain bounds on the multiplicity of the groundstate for the case of one hole and a fixed electric potential we show that the first eigenvalue takes its highest value for circulation 1 2

on the third critical field in ginzburg landau theory using recent results by the authors on the spectral asymptotics of the neumann laplacian with magnetic field we give precise estimates on the critical field h c 3 describing the appearance of superconductivity in superconductors of type ii furthermore we prove that the local and global definitions of this field coincide near h c 3 only a small part near the boundary points where the curvature is maximal of the sample carries superconductivity we give precise estimates on the size of this zone and decay estimates in both the normal to the boundary and parallel variables

infiniteness of zero modes for the pauli operator with singular magnetic field abstract we establish that the pauli operator describing a spin 1 2 two dimensional quantum system with a singular magnetic field has under certain conditions an infinite dimensional space of zero modes possibly both spin up and spin down moreover there is a spectral gap separating the zero eigenvalue from the rest of the spectrum in particular infiniteness takes place if the field has infinite flux which settles this previously unknown case of aharonov casher theorem

confinement deconfinement transitions for two dimensional dirac particles abstract we consider a two dimensional massless dirac operator coupled to a magnetic field b and an electric potential v growing at infinity we find a characterization of the spectrum of the resulting operator h in terms of the relation between b and v at infinity in particular we give a sharp condition for the discreteness of the spectrum of h beyond which we find dense pure point spectrum

maximal inequalities and riesz transform estimates on lp spaces for magnetic schrodinger operators i the paper concerns the magnetic schrodinger operator h a v j 1n 1i xj aj 2 v on rn under certain conditions given in terms of the reverse holder inequality on the magnetic field and the electric potential we prove some lp estimates on the riesz transforms of h and we establish some related maximal inequalities

equilibrated residual error estimator for edge elements reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem a cheap computation of such functions via equilibration is well known for scalar equations of second order we simplify and modify the equilibration such that it can be applied to the curl curl equation and edge elements the construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions for this reason raviart thomas elements are extended in the spirit of distributions

lifschitz tail in a magnetic field the nonclassical regime we obtain the lifschitz tail i e the exact low energy asymptotics of the integrated density of states ids of the two dimensional magnetic schrodinger operator with a uniform magnetic field and random poissonian impurities the single site potential is repulsive and it has a finite but nonzero range we show that the ids is a continuous function of the energy at the bottom of the spectrum this result complements the earlier nonrigorous calculations by brezin gross and itzykson which predict that the ids is discontinuous at the bottom of the spectrum for zero range dirac delta impurities at low density we also elucidate the reason behind this apparent controversy our methods involve magnetic localization techniques both in space and energy in addition to a modified version of the enlargement of obstacles method developed by a s sznitman

colonization of a territory by a stochastic population under a strong allee effect and a low immigration pressure we study the dynamics of colonization of a territory by a stochastic population at low immigration pressure we assume a sufficiently strong allee effect that introduces in deterministic theory a large critical population size for colonization at low immigration rates the average precolonization population size is small thus invalidating the wkb approximation to the master equation we circumvent this difficulty by deriving an exact zero flux solution of the master equation and matching it with an approximate nonzero flux solution of the pertinent fokker planck equation in a small region around the critical population size this procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization for a wide range of immigration rates at sufficiently high immigration rates our results agree with wkb results obtained previously at low immigration rates the results can be very different

rare event statistics in reaction diffusion systems we present an efficient method to calculate probabilities of large deviations from the typical behavior rare events in reaction diffusion systems this method is based on a semiclassical treatment of an underlying quantum hamiltonian encoding the system s evolution to this end we formulate the corresponding canonical dynamical system and investigate its phase portrait this method is presented for a number of pedagogical examples

on velocity errors due to irrotational forces in the navier stokes momentum balance this contribution studies the influence of the pressure on the velocity error in finite element discretisations of the navier stokes equations four simple benchmark problems that are all close to real world applications convey that the pressure can be comparably large and is not to be underestimated in fact the velocity error can be arbitrarily large in such situations only pressure robust mixed finite element methods whose velocity error is pressure independent can avoid this influence indeed the presented examples show that the pressure dependent component in velocity error estimates for classical mixed finite element methods is sharp in consequence classical mixed finite element methods are not able to simulate some classes of real world flows even in cases where dominant convection and turbulence do not play a role

population extinction risk in the aftermath of a catastrophic event we investigate how a catastrophic event modeled as a temporary fall of the reproduction rate increases the extinction probability of an isolated self regulated stochastic population using a variant of the verhulst logistic model as an example we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe this quantity is given by the eikonal action computed over the optimal path instanton of an effective classical hamiltonian system with a time dependent hamiltonian for a general catastrophe the eikonal equations can be solved numerically for simple models of catastrophic events analytic solutions can be obtained one such solution becomes quite simple close to the bifurcation point of the verhulst model the eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation

immigration extinction dynamics of stochastic populations how high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population become extinct is there any relation between the population size distributions with and without immigration under what conditions can one justify the simple patch occupancy models which ignore the population distribution and its dynamics in a patch and treat a patch simply as either occupied or empty we answer these questions by exactly solving a simple stochastic model obtained by adding a steady immigration to a variant of the verhulst model a prototypical model of an isolated stochastic population

extinction of metastable stochastic populations we investigate the phenomenon of extinction of a long lived self regulating stochastic population caused by intrinsic demographic noise extinction typically occurs via one of two scenarios depending on whether the absorbing state n 0 is a repelling scenario a or attracting scenario b point of the deterministic rate equation in scenario a the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n 0 in scenario b there is an intermediate repelling point n n 1 between the attracting point n 0 and another attracting point n n 2 in the vicinity of which the metastable population resides the crux of the theory is a dissipative variant of wkb wentzel kramers brillouin approximation which assumes that the typical population size in the metastable state is large starting from the master equation we calculate the quasistationary probability distribution of the population sizes and the exponentially long mean time to extinction for each of the two scenarios when necessary the wkb approximation is complemented i by a recursive solution of the quasistationary master equation at small n and ii by the van kampen system size expansion valid near the fixed points of the deterministic rate equation the theory yields both entropic barriers to extinction and pre exponential factors and holds for a general set of multistep processes when detailed balance is broken the results simplify considerably for single step processes and near the characteristic bifurcations of scenarios a and b

divergence free reconstruction operators for pressure robust stokes discretizations with continuous pressure finite elements classical inf sup stable mixed finite elements for the incompressible navier stokes equations are not pressure robust i e their velocity errors depend on the continuous pressure however a modification only in the right hand side of a stokes discretization is able to reestablish pressure robustness as shown recently for several inf sup stable stokes elements with discontinuous discrete pressures in this contribution this idea is extended to low and high order taylor hood and mini elements which have continuous discrete pressures for the modification of the right hand side a velocity reconstruction operator is constructed that maps discretely divergence free test functions to exactly divergence free ones the reconstruction is based on local h mathrm div conforming flux equilibration on vertex patches and fulfills certain orthogonality properties to provide consistency and optimal a priori error estimates numerical examples for the incompressible stokes and navier stokes equations conf

effect of reaction step size noise on the switching dynamics of stochastic populations in genetic circuits when the messenger rna lifetime is short compared to the cell cycle proteins are produced in geometrically distributed bursts which greatly affects the cellular switching dynamics between different metastable phenotypic states motivated by this scenario we study a general problem of switching or escape in stochastic populations where influx of particles occurs in groups or bursts sampled from an arbitrary distribution the fact that the step size of the influx reaction is a priori unknown and in general may fluctuate in time with a given correlation time and statistics introduces an additional nondemographic reaction step size noise into the system employing the probability generating function technique in conjunction with hamiltonian formulation we are able to map the problem in the leading order onto solving a stationary hamilton jacobi equation we show that compared to the usual case of single step influx bursty influx exponentially decreases the population s mean escape time from its long lived metastable state in particular close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst size distribution our results are demonstrated on several realistic distributions and compare well with numerical monte carlo simulations

persistence of instanton connections in chemical reactions with time dependent rates the evolution of a system of chemical reactions can be studied in the eikonal approximation by means of a hamiltonian dynamical system the fixed points of this dynamical system represent the different states in which the chemical system can be found and the connections among them represent instantons or optimal paths linking these states we study the relation between the phase portrait of the hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time we show that the topology of the phase space is robust for small time dependent perturbations in concrete examples and state general results when possible this robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time dependent situation

pinning with a variable magnetic field of the two dimensional ginzburg landau model abstract we study the ginzburg landau energy of a superconductor with a variable magnetic field and a pinning term in a bounded smooth two dimensional domain supposing that the ginzburg landau parameter and the intensity of the magnetic field are large and of the same order we determine an accurate asymptotic formula for the minimizing energy this asymptotic formula displays the influence of the pinning term also we discuss the existence of non trivial solutions and prove some asymptotics of the third critical field

landau levels on the hyperbolic plane in the presence of aharonov bohm fields abstract we consider the magnetic schrodinger operators on the poincare upper half plane with constant gaussian curvature 1 we assume the magnetic field is given by the sum of a constant field and the dirac measures placed on some lattice we give a sufficient condition for each landau level to be an infinitely degenerated eigenvalue we also prove the lowest landau level is not an eigenvalue if the above condition fails in particular the infinite degeneracy of the lowest landau level is equivalent to the infiniteness of the zero modes of the two dimensional pauli operator

estimates for the lowest eigenvalue of magnetic laplacians we prove various estimates for the first eigenvalue of the magnetic dirichlet laplacian on a bounded open simply connected domain in two dimensions when the magnetic field is constant we give lower and upper bounds in terms of geometric quantities of the domain we furthermore prove a lower bound for the first magnetic neumann eigenvalue in the case of constant magnetic field

a hybrid high order locking free method for linear elasticity on general meshes abstract we devise an arbitrary order locking free method for linear elasticity the method relies on a pure displacement primal formulation and leads to a symmetric positive definite system matrix with compact stencil the degrees of freedom are vector valued polynomials of arbitrary order k 1 on the mesh faces so that in three space dimensions the lowest order scheme only requires 9 degrees of freedom per mesh face the method can be deployed on general polyhedral meshes the key idea is to reconstruct the symmetric gradient and divergence inside each mesh cell in terms of the degrees of freedom by solving inexpensive local problems the discrete problem is assembled cell wise using these operators and a high order stabilization bilinear form locking free error estimates are derived for the energy norm and for the l 2 norm of the displacement with optimal convergence rates of order k 1 and k 2 respectively for smooth solutions on general meshes the theoretical results are confirmed numerically and the cpu cost is evaluated on both standard and polygonal meshes

grad div stabilization and subgrid pressure models for the incompressible navier stokes equations in this paper the grad div stabilization for the incompressible navier stokes finite element approximations is considered from two different viewpoints i as a variational multiscale approach for the pressure subgrid modeling and ii as a stabilization procedure of least square type some new error estimates for the linearized problem with the grad div stabilization are proved with the help of norms induced by the pressure schur complement operator we discuss the stabilization parameter choice arising in the frameworks of least square and multiscale methods and consider assumptions which allow to relate both approaches

population extinction under bursty reproduction in a time modulated environment in recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations for example nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size or environmental variability in the form of time varying reaction rates have been separately found to dramatically impact the extinction risk of isolated populations in this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation using the so called momentum space wentzel kramers brillouin wkb approach and accounting for the explicit time dependence in the reaction rates we arrive at a set of time dependent hamilton equations to this end we evaluate the population s extinction risk by finding the instanton of the time perturbed hamiltonian numerically whereas analytical expressions are presented in particular limits using various perturbation techniques we focus on two classes of time varying environments periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe all our theoretical results are tested against numerical monte carlo simulations with time dependent rates and also against a numerical solution of the corresponding time dependent hamilton equations

semiclassical asymptotics and gaps in the spectra of periodic schrodinger operators with magnetic wells we show that under some very weak assumption of effective variation for the magnetic field a periodic schrodinger operator with magnetic wells on a noncompact riemannian mani fold m such that h 1 m r 0 equipped with a properly discon nected cocompact action of a finitely generated discrete group of isometries has an arbitrarily large number of spectral gaps in the semi classical limit

population extinction in a time modulated environment the extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment we investigate this effect using as an example a stochastic branching annihilation process with a time dependent branching rate the population extinction is treated in eikonal approximation where it is described as an instanton trajectory of a proper reaction hamiltonian the modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase we calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations the techniques include a first order theory with respect to the modulation amplitude a second order theory in the spirit of the kapitsa pendulum effect and adiabatic theory valid for low modulation frequencies

population dynamics in a changing environment random versus periodic switching environmental changes greatly influence the evolution of populations here we study the dynamics of a population of two strains one growing slightly faster than the other competing for resources in a time varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity the population dynamics is characterized by demographic noise birth and death events coupled to a varying environment we elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment importantly the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching we also determine the detailed conditions under which the fixation probability of the slow strain is maximal

population switching under a time varying environment we study the switching dynamics of a stochastic population subjected to a deterministically time varying environment our approach is demonstrated on a problem of population establishment which is important in ecology at the deterministic level the model we study gives rise to a critical population size beyond which the system experiences establishment notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations here we consider two prototypical examples of a time varying environment a temporary change in the environment and a periodically varying environment by employing a semiclassical approximation we compute within exponential accuracy the change in the establishment probability and mean establishment time of the population due to the environmental variability our analytical results are verified by using a modified gillespie algorithm which accounts for explicitly time dependent reaction rates importantly our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations

spectral asymptotics of pauli operators and orthogonal polynomials in complex domains we consider the spectrum of a two dimensional pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value the rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential a connection between these eigenvalues and orthogonal polynomials in complex domains is established

on the semi classical analysis of the ground state energy of the dirichlet pauli operator we complete and improve the results of a recent paper by ekholm kova ik and portmann in connection with a question of c guillarmou about the semiclassical expansion of the lowest eigenvalue of the pauli operator with dirichlet conditions we exhibit connections with the properties of the torsion function in mechanics the exit time of a brownian motion and the analysis of the low eigenvalues of some witten laplacian

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

analysis of zero modes for dirac operators with magnetic links abstract in this paper we provide a means to approximate dirac operators with magnetic fields supported on links in s 3 and r 3 by dirac operators with smooth magnetic fields then we proceed to prove that under certain assumptions the spectral flow of paths along these operators is the same in both the smooth and the singular case we recently characterized the spectral flow of such paths in the singular case this allows us to show the existence of new smooth compactly supported magnetic fields in r 3 for which the associated dirac operator has a non trivial kernel using clifford analysis we also obtain criteria on the magnetic link for the non existence of zero modes

spectral theory of metastability and extinction in a branching annihilation reaction we apply the spectral method recently developed by the authors to calculate the statistics of a reaction limited multistep birth death process or chemical reaction that includes as elementary steps branching a 2a and annihilation 2a 0 the spectral method employs the generating function technique in conjunction with the sturm liouville theory of linear differential operators we focus on the limit when the branching rate is much higher than the annihilation rate and obtain accurate analytical results for the complete probability distribution including large deviations of the metastable long lived state and for the extinction time statistics the analytical results are in very good agreement with numerical calculations furthermore we use this example to settle the issue of the lacking boundary condition in the spectral formulation

asymptotic of the density of states for the schrodinger operator with periodic electromagnetic potential for the schrodinger operator in l2 rn n 1 with c periodic electromagnetic potential we give an asymptotic formula of the integrate density of states of the form n an n 2 o n 2 e 2 e 0 when n 2 this estimate enables us to prove the finiteness of gaps in the spectrum

on the torsion function with robin or dirichlet boundary conditions for p2 1 1 and b2 0 1 the p torsion function with robin boundary conditions associated to an arbitrary open set r m satises for

refined a posteriori error estimation for classical and pressure robust stokes finite element methods recent works showed that pressure robust modifications of mixed finite element methods for the stokes equations outperform their standard versions in many cases this is achieved by divergence free reconstruction operators and results in pressure independent velocity error estimates which are robust with respect to small viscosities in this paper we develop a posteriori error control which reflects this robustness the main difficulty lies in the volume contribution of the standard residual based approach that includes the l 2 norm of the right hand side however the velocity is only steered by the divergence free part of this source term an efficient error estimator must approximate this divergence free part in a proper manner otherwise it can be dominated by the pressure error to overcome this difficulty a novel approach is suggested that uses arguments from the stream function and vorticity formulation of the navier stokes equations the novel error estimators only take the hbox curl of the right hand side into account and so lead to provably reliable efficient and pressure independent upper bounds in case of a pressure robust method in particular in pressure dominant situations this is also confirmed by some numerical examples with the novel pressure robust modifications of the taylor hood and mini finite element methods

pauli operator and aharonov casher theorem for measure valued magnetic fields we define the two dimensional pauli operator and identify its core for magnetic fields that are regular borel measures the magnetic field is generated by a scalar potential hence we bypass the usual a l 2 loc condition on the vector potential which does not allow to consider such singular fields we extend the aharonov casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation one of the key technical tools is a weighted l 2 estimate on a singular integral operator

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

harmonic oscillators with neumann condition on the half line this paper is devoted to the computation of the minimum theta 0 of the first eigenvalues for the neumann realization of harmonic oscillators on the half line we propose an algorithm to determine this minimum and we estimate the accuracy of these computations we also give numerical computations of constants appearing in superconductivity theory

bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function in this paper maximum principles are employed to relate solutions of certain classes of nonlinear elliptic problems to solutions of the associated torsion problem by this method a number of new isoperimetric inequalities are derived in special cases solutions of the nonlinear problems are also related to solutions of the clamped membrane problem

spectral gaps for periodic schrodinger operators with hypersurface magnetic wells analysis near the bottom we consider a periodic magnetic schrodinger operator hh depending on the semiclassical parameter h 0 on a noncompact riemannian manifold m such that h1 m r 0 endowed with a properly discontinuous cocompact isometric action of a discrete group we assume that there is no electric field and that the magnetic field has a periodic set of compact magnetic wells we suppose that the magnetic field vanishes regularly on a hypersurface s first we prove upper and lower estimates for the bottom 0 hh of the spectrum of the operator hh in l2 m then assuming the existence of non degenerate miniwells for the reduced spectral problem on s we prove the existence of an arbitrarily large number of spectral gaps for the operator hh in the region close to 0 hh as h 0 in this case we also obtain upper estimates for the eigenvalues of the one well problem

semiclassical analysis for the ground state energy of a schrodinger operator with magnetic wells abstract motivated by a recent paper by montgomery mon we give the asymptotic behavior in the semi classical sense of the ground state energy for the schrodinger operator with a magnetic field we consider the case when the locus of the minima of the intensity of the magnetic field is compact and our study is sharper when this locus is an hypersurface or a finite union of points

reducing the extinction risk of stochastic populations via nondemographic noise we consider nondemographic noise in the form of uncertainty in the reaction step size and reveal a dramatic effect this noise may have on the stability of self regulating populations employing the reaction scheme ma ka but allowing e g the product number k to be a priori unknown and sampled from a given distribution we show that such nondemographic noise can greatly reduce the population s extinction risk compared to the fixed k case our analysis is tested against numerical simulations and by using empirical data of different species we argue that certain distributions may be more evolutionary beneficial than others

on the ginzburg landau critical field in three dimensions we study the three dimensional ginzburg landau model of superconductivity several natural definitions of the third critical field h governing the transition from the superconducting state to the normal state are considered we analyze the relation between these fields and give conditions as to when they coincide an interesting part of the analysis is the study of the monotonicity of the ground state energy of the laplacian with constant magnetic field and with neumann magnetic boundary condition in a domain it is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields as a consequence of our analysis we give an affirmative answer to a conjecture by pan 2008 wiley periodicals inc