polynomial bound on the number of scattering poles on montre que dans la diffusion par un potentiel infiniment differentiable a support compact les poles de l operateur de diffusion sont a distribution polynomiale

eigenvalues of the reference operator and semiclassical resonances we prove that the estimate of the number of the eigenvalues in intervals 0 0 and the number of the positive eigenvalues of l h in we apply this result to obtain a breit wigner approximation of the derivative of the spectral shift function near critical energy levels

a moving mesh method for the solution of the one dimensional phase field equations a moving mesh method is developed for the numerical solution of one dimensional phase change problems modelled by the phase field equations the computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the phase field in the interfacial region existence and uniqueness of the discretised equations using a moving mesh are also established numerical results are given for classical and modified stefan test problems the numerical algorithm is relatively simple and is shown to be far more efficient than fixed grid methods

on the contribution of degenerate periodic trajectories to the wave trace this paper is concerned with the wave trace z t of a selfadjoint elliptic pseudodifferential operator on a compact manifold it is devoted to the contribution of degenerate periodic trajectories of the associated hamiltonian flow to the singularities of z t given a periodic trajectory and a point on it we obtain a trace formula which relates microlocally the trace of the unitary group of a in a neighborhood of to an oscillatory integral the phase and the amplitude of which are written in terms of the poincare map of for suitable isolated but degenerate this enables us to obtain complete asymptotic expansions applying already known results about asymptotics of oscillatory integrals as an application we obtain lower bounds on the resonances close to the real axis for the laplace beltrami operator in r n n 2 for suitable compactly supported perturbations of the euclidean metric

a second order operator splitting method for allen cahn type equations with nonlinear source terms abstract allen cahn ac type equations with nonlinear source terms have been applied to a wide range of problems for example the vector valued ac equation for phase separation and the phase field equation for dendritic crystal growth in contrast to the well developed first and second order methods for the ac equation not many second order methods are suggested for the ac type equations with nonlinear source terms due to the difficulties in dealing with the nonlinear source term numerically in this paper we propose a simple and stable second order operator splitting method a core idea of the method is to decompose the original equation into three subequations with the free energy evolution term the heat evolution term and a nonlinear source term respectively it is important to combine these three subequations in proper order to achieve the second order accuracy and stability we propose a method with a half time free energy evolution solver a half time heat evolution solver a full time midpoint solver for the nonlinear source term and a half time heat evolution solver followed by a final half time free energy evolution solver we numerically demonstrate the second order accuracy of the new numerical method through the simulations of the phase separation and the dendritic crystal growth

quantitative phase field modeling of dendritic growth in two and three dimensions we report the results of quantitative phase field simulations of the dendritic crystallization of a pure melt in two and three dimensions these simulations exploit a recently developed thin interface limit of the phase field model a karma and w j rappel phys rev e 53 r3017 1996 which is given here a detailed exposition this limit makes it possible to perform efficient computations with a smaller ratio of capillary length to interface thickness and with an arbitrary interface kinetic coefficient simulations in one and two dimensions are first carried out to test the accuracy of phase field computations performed within this limit dendrite tip velocities and tip shapes are found to be in excellent quantitative agreement with exact numerical benchmarks of solvability theory obtained by a boundary integral method both with and without interface kinetics simulations in three dimensions exploit in addition to the asymptotics a methodology to calculate grid corrections due to the surface tension and kinetic anisotropies they are used to test basic aspects of dendritic growth theory that pertain to the selection of the operating state of the tip and to the three dimensional morphology of needle crystals without sidebranches for small crystalline anisotropy simulated values of ensuremath sigma are slightly larger than solvability theory predictions computed by the boundary integral method assuming an axisymmetric shape and agree relatively well with experiments for succinonitrile given the uncertainty in the measured anisotropy in contrast for large anisotropy simulated ensuremath sigma values are significantly larger than the predicted values this disagreement however does not signal a breakdown of solvability theory it is consistent with the finding that the amplitude of the mathrm cos 4 ensuremath varphi mode which measures the departure of the tip morphology from a shape of revolution increases with anisotropy this departure can therefore influence the tip selection in a way that is not accurately captured by the axisymmetric approximation for large anisotropy finally the tail shape at a distance behind the tip that is large compared to the diffusion length is described by a linear law r ensuremath sim z with a slope dr dz that is nearly equal to the ratio of the two dimensional and three dimensional steady state tip velocities furthermore the evolution of the cross section of a three dimensional needle crystal with increasing distance behind the tip is nearly identical to the evolution of a two dimensional growth shape in time in accord with the current theory of the three dimensional needle crystal shape

analysis of a three dimensional phase field model for solidification under a magnetic field effect abstract this paper presents a mathematical analysis to a three dimensional isothermal model of solidification for a binary alloy with melt convection and under a magnetic field effect the model consists of a highly non linear system of partial differential equations for the state variables the velocity field the pressure the potential function of the electrical field the phase field which represents the solid liquid phase of the alloy and the concentration the well posedness of the model is discussed moreover the existence of solutions when the diffusion coefficient of the concentration equation vanishes for some values of the phase field is investigated

phase field study of the tip operating state of a freely growing dendrite against convection using a novel parallel multigrid approach alloy dendrite growth during solidification with coupled thermal solute convection fields has been studied by phase field modeling and simulation the coupled transport equations were solved using a novel parallel multigrid numerical approach with high computational efficiency that has enabled the investigation of dendrite growth with realistic alloy values of lewis number 10 4 and prandtl number 10 2 the detailed dendrite tip shape and character were compared with widely recognized analytical approaches to show validity and shown to be highly dependent on undercooling solute concentration and lewis number in a relatively low flow velocity regime variations in the ratio of growth selection parameter with and without convection agreed well with theory

reconstruction of gaussian and log normal fields with spectral smoothness we develop a method to infer log normal random fields from measurement data affected by gaussian noise the log normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude we use the formalism of minimum gibbs free energy to derive an algorithm that uses the signal s correlation structure to regularize the reconstruction the correlation structure described by the signal s power spectrum is thereby reconstructed from the same data set we show that the minimization of the gibbs free energy corresponding to a gaussian approximation to the posterior marginalized over the power spectrum is equivalent to the empirical bayes ansatz in which the power spectrum is fixed to its maximum a posteriori value we further introduce a prior for the power spectrum that enforces spectral smoothness the appropriateness of this prior in different scenarios is discussed and its effects on the reconstruction s results are demonstrated we validate the performance of our reconstruction algorithm in a series of one and two dimensional test cases with varying degrees of non linearity and different noise levels

sharp upper bounds on the number of resonances near the real axis for trapping systems we study resonances near the real axis jimz jd o h n n 1 and the corresponding resonant states for semiclassical long range operators p h without a priori assumptions on the distribution or on the multiplicities of the resonances we show that the truncated resonant states form a family of quasimode states for p h stable under small perturbations as a consequence they form also a family of quasimode states for any suitably defined selfadjoint reference operator p h therefore those resonances are perturbed eigenvalues of p h next we show that the semiclassical wave front set of the resonant states is contained in the set of trapped directions t we construct a suitable reference operator from p h by imposing a microlocal barrier outside t to show that the counting function for those resonances admits an upper bound of weyl s type connected with the measure of t we give an example of system for which this bound is optimal and also prove similar bound in case of classical scattering by obstacle this paper is devoted to a detailed study of the behavior of the resonances and resonant states near the real axis we work mainly in the semi classical setting but most results can be easily translated into the classical one by resonances near the real axis we mean resonances in a box h d a0 b0 ci s h 0 where 0 s h d o h k k 1 such resonances may exist only for trapping geometries we accept the convention here that resonances lie in the lower half plane

complex scaling and the distribution of scattering poles the purpose of this paper is to establish sharp polynomial bounds on the number of scattering poles for a general class of compactly supported self adjoint perturbations of the laplacian in r n odd we also consider more general types of bounds that give sharper estimates in certain situations the general conclusion can be stated as follows the order of growth of the poles is the same as the order of growth of eigenvalues for corresponding compact problems from the few known cases however the exact asymptotics are expected to be different the scattering poles for compactly supported perturbations were rigorously defined by lax and phillips 13 in a more general setting they correspond to resonances the study of which has a long tradition in mathematical physics in the lax phillips theory they appear as the poles of the meromorphic continuation of the scattering matrix and coincide with the poles of the meromorphic continuation of the resolvent of the perturbed operator because of the latter characterization they can be considered as the analogue of the discrete spectral data for problems on noncompact domains the problem of estimating the counting function

phase field lattice kinetic scheme for the numerical simulation of dendritic growth a phase field lattice kinetic model is presented for the numerical simulation of the dendritic growth of a pure crystal in the presence of thermal transport a finite difference scheme for the phase field is combined with an explicit lattice kinetic scheme for the temperature field the resulting scheme is advanced in time with an adaptive time marching procedure which permits us to achieve long simulation times with larger time steps than explicit finite difference and previous kinetic methods the method is demonstrated for the case of dendritic growth of a single crystal over a wide range of stefan and capillarity numbers

three dimensional magnetotelluric modeling using difference equations theory and comparisons to integral equation solutions we have developed an algorithm for computing the magnetotelluric response of three dimensional 3 d earth models it is a difference equation algorithm that is based on the integral forms of maxwell s equations rather than the differential forms this formulation does not require approximating derivatives of earth properties or electromagnetic fields as happens when using the second order vector diffusion equation rather one must determine how averages are to be computed side boundary values for the h fields are obtained from putting two dimensional 2 d slices of the model into a larger scale 2 d model and solving for the fields at the 3 d boundary positions to solve the 3 d system of equations we propagate an impedance matrix which relates all the horizontal e fields in a layer to all the horizontal h fields in that same layer up through the earth model applying a plane wave source condition and the side boundary h field values allows us to solve for the unknown fields within the model the r

3 d electromagnetic modeling and nonlinear inversion we describe a new algorithm for 3 d electromagnetic inversion that uses global integral and local differential equations for both the forward and inverse problems the coupled integral and differential equations are discretized by the finite element method and solved on a parallel computer using domain decomposition the structure of the algorithm allows efficient solution of large 3 d inverse problems tests on both synthetic and field data show that the algorithm converges reliably and efficiently and gives high resolution conductivity images

sharp polynomial bounds on the number of scattering poles of radial potentials abstract it is shown that for scattering by a radially symmetric potential in r n n odd the number of poles in a disk of radius r satisfies an estimate n r c n r 1 n this bound is sharp as shown by the special case of potentials nonvanishing at the boundary where n r k n a n r n 1 o 1 a being the diameter of the support

scattering asymptotics for riemann surfaces in this article we prove the optimal polynomial lower bound for the number of resonances of a surface with hyperbolic ends we also give weyl asymptotics for the relative scattering phase of such a surface the proofs are based on trace formulae analogous to those of the euclidean odd dimensional scattering the main technical ingredient is a new proof of the poisson formula theorem 5 7 which is applicable in the euclidean case as well our lower bound seems to be the first example of an optimal polynomial lower bound for the number of resonances holding for a general class of higher dimensional elliptic operators with no symmetries the previous general lower bounds or asymptotics were either nonoptimal 25 58 9 one dimensional or radial 65 67 and 54 41 1 or they required some degeneracy of the

efficient thermal field computation in phase field models we solve the phase field equations in two dimensions to simulate crystal growth in the low undercooling regime the novelty is the use of a fast solver for the free space heat equation to compute the thermal field this solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient free space heat equation with a smooth source term the computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed this allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field which can result in significant computational savings in the low undercooling regime

second order phase field asymptotics for unequal conductivities we extend karma and rappel s improved asymptotic analysis of the phase field model to different diffusivities in solid and liquid we consider both second order classical asymptotics in which the interface thickness is taken much smaller than the capillary length and the new isothermal asymptotics in which the two lengths are considered comparable in the first case if the phase field model is required to be gradient flow for an entropy functional then for unequal diffusivities it is impossible to construct a phase equation with finite kinetics which converges with second order accuracy to a gibbs thomson equilibrium condition with infinitely fast kinetics in the second case some error terms are pushed to higher orders and it is easy to eliminate the remaining errors with finite phase kinetics

distribution of poles for scattering on the real line abstract the density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential in the case of a potential with finite singularities at the endpoints of the support asymptotic formulae for the poles are given while in the c 0 case an example of a potential with infinitely many scattering poles on i r is constructed the scattering amplitude of a compactly supported potential is also characterized

lattice boltzmann modeling of dendritic growth in forced and natural convection a two dimensional 2d coupled model is developed for the simulation of dendritic growth during alloy solidification in the presence of forced and natural convection instead of conventional continuum based navier stokes ns solvers the present model adopts a kinetic based lattice boltzmann method lbm which describes flow dynamics by the evolution of distribution functions of moving pseudo particles for the numerical computations of flow dynamics as well as thermal and solutal transport the dendritic growth is modeled using a solutal equilibrium approach previously proposed by zhu and stefanescu zs in which the evolution of the solid liquid interface is driven by the difference between the local equilibrium composition and the local actual liquid composition the local equilibrium composition is calculated from the local temperature and curvature the local temperature and actual liquid composition controlled by both diffusion and convection are obtained by solving the lb equations using the lattice bhatnagar gross krook lbgk scheme detailed model validation is performed by comparing the simulations with analytical predictions which demonstrates the quantitative capability of the proposed model furthermore the convective dendritic growth features predicted by the present model are compared with those obtained from the zhu stefanescu and navier stokes zs ns model in which the fluid flow is calculated using an ns solver it is found that the evolution of the solid fraction of dendritic growth calculated by both models coincides well however the present model has the significant advantages of numerical stability and computational efficiency for the simulation of dendritic growth with melt convection

a coupled ericksen allen cahn model for liquid crystal droplets abstract we present a model and discretization that couples the ericksen model of liquid crystals with variable degree of orientation to the allen cahn equations with a mass constraint the coupled system models liquid crystal droplets with anisotropic surface tension effects due to the liquid crystal molecular alignment the total energy consists of the ericksen energy phase field allen cahn energy and a weak anchoring energy that couples the liquid crystal to the diffuse interface we describe our discretization of the total energy along with a method to compute minimizers via a discrete gradient flow algorithm which has a strictly monotone energy decreasing property numerical experiments are given in three dimensions that illustrate a wide variety of droplet shapes that result from their interaction with defects

multiscale finite difference diffusion monte carlo method for simulating dendritic solidification abstract we present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field the first key feature of this method is an efficient multiscale diffusion monte carlo dmc algorithm which allows off lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid liquid interface as a result the computational cost of evolving the large scale diffusion field becomes insignificant when compared to that of calculating the interface evolution the second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface inside this layer and in the solid the diffusion equation is solved using a standard finite difference algorithm that is interfaced with the dmc algorithm using the local conservation law for the diffusing quantity here we combine this algorithm with a previously developed phase field formulation of the interface dynamics and demonstrate that it can accurately simulate three dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance

quasimodes and resonances sharp lower bounds we prove that asymptotically any cluster of quasimodes close to each other approximates at least the same number of resonances counting multiplicities as a consequence we get that the counting function of the number of resonances close to the real axis is bounded from below essentially by the counting function of the quasimodes

existence of resonances in three dimensions ifp is an elliptic self adjoint perturbation of the laplacian on 3 and the coefficients ofp decay super exponentially then we show thatp has infinitely many resonances the resonances are defined here as the poles of the meromorphic continuation of p 2 1

an implicit parallel multigrid computing scheme to solve coupled thermal solute phase field equations for dendrite evolution an implicit second order space and time discretization scheme together with a parallel multigrid method involving a strip grid domain partitioning has been developed to solve fully coupled nonlinear phase field equations involving solute and heat transport for multiple solidifying dendrites the computational algorithm has been shown to be stable and monotonously convergent and allowed time marching steps that were 3 4 orders of magnitude larger than those employed in similar explicit approaches resulting in an increase of 3 4 orders of magnitude in computing efficiency full solute and thermal coupling was achieved for metallic alloys with a realistic high lewis number of 10 4 the parallel multigrid computing scheme is shown to provide a scalable methodology that allowed the efficient use of distributed supercomputing resource to simulate the evolution of tens of complex shaped 2d dendrites in a computational domain containing tens or even hundreds of millions of grid points the simulations have provided insight into the dynamic interplay of many growing dendrites in a more realistic fully coupled thermal solute condition capturing for the first time fine scale features such as dendrite splitting

consistent lattice boltzmann schemes for the brinkman model of porous flow and infinite chapman enskog expansion we show that a consistent modeling of porous flows needs at least one free collision relaxation rate to avoid a nonlinear dependency of the numerical errors on the viscosity this condition is necessary to get the viscosity independent permeability from the stokes flow and to parametrize properly with nondimensional physical numbers the lattice boltzmann brinkman schemes the two relaxation time trt collision operator controls all coefficients of the higher order corrections in steady solutions with a specific combination of its two collision rates a possibility lacking for the bhatnagar gross krook bgk based single relaxation time schemes the analysis is based on exact recurrence equations of the evolution equation and illustrated for the exact solutions of the brinkman scheme in simply oriented parallel and diagonal channels the apparent viscosity coefficient of the trt stokes brinkman scheme in arbitrary flow is only approximated the compatibility of one dimensional arbitrarily rotated flows with the nonlinear navier stokes equilibrium is examined an explicit dependency for all coefficients on the relaxation rates is presented for the infinite steady state chapman enskog expansion

a new lagrange multiplier approach for gradient flows abstract we propose a new lagrange multiplier approach to design unconditional energy stable schemes for gradient flows the new approach leads to unconditionally energy stable schemes that are as accurate and efficient as the recently proposed sav approach shen xu and yang 2018 but enjoys two additional advantages i schemes based on the new approach dissipate the original energy as opposed to a modified energy in the recently proposed sav approach shen xu and yang 2018 and ii they do not require the nonlinear part of the free energy to be bounded from below as is required in the sav approach the price we pay for these advantages is that a nonlinear algebraic equation has to be solved to determine the lagrange multiplier we present ample numerical results to validate the new approach and as a particular example of challenging applications we consider a block copolymer bcp coupled cahn hilliard model and carry out new and nontrivial simulations which are consistent with experiment results

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

lattice boltzmann simulations of 3d crystal growth a lattice boltzmann lb scheme based on the bhatnagar gross krook bgk collision rules is developed for a phase field model of alloy solidification in order to simulate the growth of dendrites the solidification of a binary alloy is considered taking into account diffusive transport of heat and solute as well as the anisotropy of the solid liquid interfacial free energy the anisotropic terms in the phase field evolution equation the phenomenological anti trapping current introduced in the solute evolution equation to avoid spurious solute trapping and the variation of the solute diffusion coefficient between phases make it necessary to modify the equilibrium distribution functions of the lb scheme with respect to the one used in the standard method for the solution of advection diffusion equations the effects of grid anisotropy are removed by using the lattices d3q15 and d3q19 instead of d3q7 the method is validated by direct comparison of the simulation results with a numerical code that uses the finite difference method simulations are also carried out for two different anisotropy functions in order to demonstrate the capability of the method to generate various crystal shapes

high accuracy wavefront tracing traveltime calculation conventional ray tracing algorithms for first arrival calculation suffer from drawbacks such as 1 no guarantee of finding the globally minimum traveltime path when multiple paths exist 2 shadow zones and 3 trouble finding minimum traveltime paths containing refraction and or diffraction energy algorithms that trace wavefronts circumvent these problems the new wavefront tracing algorithm presented here is based on an earth model consisting of uniform velocity triangular cells with nodes placed at vertices and along cell edges nodes are places where traces of first arrival wavefronts propagation directions and arrival times are stored the algorithm works by propagating wavefronts sampled at the nodes away from the source throughout the entire model wavefronts are propagated locally as diffraction direct arrival or critically refracted energy that implicitly describe minimum time paths once the first arrival wavefront is sampled throughout the model traveltimes and raypaths from the sour

modeling the growth and interaction of multiple dendrites in solidification using a level set method abstract a level set method is presented to study the growth and interaction of multiple dendrites in solidification the method couples thermal and solute diffusion with propagation of multiple interfaces a single signed distance function is used to track the solid liquid interface with the aid of markers the value of which is the orientation angle for identification of different crystals the problem of evolving multiple crystal interfaces is reduced to two tasks 1 tracking one level set variable signed distance function and 2 determination of the marker for a newly solidified finite element nodal point tracking a single level set variable is implemented by solving the level set equation with interface velocity computed from an extended stefan equation using the marker information crystal orientation determination of the marker for a newly solidified finite element nodal point is implemented by using an algorithm modified from the fast marching technique both of these two steps are computationally efficient and the approach is suitable for incorporating effects of multiple crystals convergence and accuracy of this approach are demonstrated by using different grid spacings and comparing with results obtained from the multi phase level set method a parametric study is performed to investigate the effects of solidification speed and thermal gradient on the resulting solidification microstructure pattern numerical results of columnar to equiaxed transition cet qualitatively agree with an analytical estimation and are similar to previous numerical results obtained using a phase field method a convergence study is performed to determine the appropriate grid spacing for numerical simulation at lower surface tension cet occurs at a lower thermal gradient for a giving solidification speed secondary dendrite formation is more apparent with lower surface tension the differences and similarities between the three dimensional and two dimensional growth results are analyzed randomness in crystal orientation and required undercooling for nucleation are modeled and found to have a great effect on the microstructure pattern the efficiency of the present approach is finally demonstrated with an example that includes the growth of hundreds of crystals with consideration of randomness effects

adaptive mesh computation of polycrystalline pattern formation using a renormalization group reduction of the phase field crystal model we implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes our numerical approach uses the systematic renormalization group formulation of a phase field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field a quantity that is spatially uniform except near topological defects grain boundaries and other lattice imperfections our algorithm employs a hybrid formulation of the amplitude equations combining cartesian and polar decompositions of the complex amplitude we show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions

scattering phase asymptotics with fractal remainders for a riemannian manifold m g which is isometric to the euclidean space outside of a compact set and whose trapped set has liouville measure zero we prove weyl type asymptotics for the scattering phase with remainder depending on the classical escape rate and the maximal expansion rate for axiom a geodesic flows this gives a polynomial improvement over the known remainders we also show that the remainder can be bounded above by the number of resonances in some neighbourhoods of the real axis and provide similar asymptotics for hyperbolic quotients using the selberg zeta function

a semi analytical fourier spectral method for the allen cahn equation in recent years fourier spectral methods have been widely used as a powerful tool for solving phase field equations to improve its effectiveness many researchers have employed stabilized semi implicit fourier spectral sifs methods which allow a much larger time step than a usual explicit scheme our mathematical analysis and numerical experiments however suggest that an effective time step is smaller than a time step specified in the sifs schemes in consequence the sifs scheme is inaccurate for a considerably large time step and may lead to incorrect morphologies in phase separation processes in order to remove the time step constraint and guarantee the accuracy in time for a sufficiently large time step we present a first and a second order semi analytical fourier spectral safs methods for solving the allen cahn equation the core idea of the methods is to decompose the original equation into linear and nonlinear subequations which have closed form solutions in the fourier and physical spaces respectively both the first and the second order methods are unconditionally stable and numerical experiments demonstrate that our proposed methods are more accurate than the stabilized semi implicit fourier spectral method

crosswell electromagnetic inversion using integral and differential equations the crosswell electromagnetic em inverse problem is solved with an integral equation ie formulation using successive born approximations in the frequency domain because the inverse problem is nonlinear the predicted fields and green s functions are continually updated updating the fields and green s functions relates small changes in the predicted data to small changes in the model parameters through frechet kernels these fields and green functions are calculated with an efficient 3 d finite difference solver since the resistivity is invariant along strike the 3 d fields are integrated along strike so the 2 d kernels can be assembled at the early stages of the inversion smoothing of the electrical conductivity stabilizes the inverse solution when it is far from convergence as the solution converges this smoothing is relaxed and more effort is made to reduce the data misfit bounds on the conductivity are included in the solution to eliminate unrealistic estimates the robustness of the inver

phase field simulations of dendritic crystal growth in a forced flow convective effects on free dendritic crystal growth into a supercooled melt in two dimensions are investigated using the phase field method the phase field model incorporates both melt convection and thermal noise a multigrid method is used to solve the conservation equations for flow to fully resolve the diffuse interface region and the interactions of dendritic growth with flow both the phase field and flow equations are solved on a highly refined grid where up to 2 1 million control volumes are employed a multiple time step algorithm is developed that uses a large time step for the flow field calculations while reserving a fine time step for the phase field evolution the operating state velocity and shape of a dendrite tip in a uniform axial flow is found to be in quantitative agreement with the prediction of the oseen ivantsov transport theory if a tip radius based on a parabolic fit is used furthermore using this parabolic tip radius the ratio of the selection parameters without and with flow is shown to be close to unity which is in agreement with linearized solvability theory for the ranges of the parameters considered dendritic sidebranching in a forced flow is also quantitatively studied compared to a dendrite growing at the same supercooling in a diffusive environment convection is found to increase the amplitude and frequency of the sidebranches the phase field results for the scaled sidebranch amplitude and wavelength variations with distance from the tip are compared to linear wentzel kramers brillouin theory it is also shown that the asymmetric sidebranch growth on the upstream and downstream sides of a dendrite arm growing at an angle with respect to the flow can be explained by the differences in the mean shapes of the two sides of the arm

phase field model for three dimensional dendritic growth with fluid flow we study the effect of fluid flow on three dimensional 3d dendrite growth using a phase field model on an adaptive finite element grid in order to simulate 3d fluid flow we use an averaging method for the flow problem coupled to the phase field method and the semi implicit approximated projection method siapm we describe a parallel implementation for the algorithm using the charm fem framework and demonstrate its efficiency we introduce an improved method for extracting dendrite tip position and tip radius facilitating accurate comparison to theory we benchmark our results for 2d dendrite growth with solvability theory and previous results finding them to be in good agreement the physics of dendritic growth with fluid flow in three dimensions is very different from that in two dimensions and we discuss the origin of this behavior

sharp upper bounds on the number of the scattering poles abstract we study the scattering poles of a compactly supported black box perturbations of the laplacian in r n n odd we prove a sharp upper bound of the counting function n r modulo o r n in terms of the counting function of the reference operator in the smallest ball around the black box in the most interesting cases we prove a bound of the type n r a n r n o r n with an explicit a n we prove that this bound is sharp in a few special spherically symmetric cases where the bound turns into an asymptotic formula

a lattice boltzmann model for multiphase flows with large density ratio a lattice boltzmann model for simulating multiphase flows with large density ratios is described in this paper the method is easily implemented it does not require solving the poisson equation and does not involve the complex treatments of derivative terms the interface capturing equation is recovered without any additional terms as compared to other methods m r swift w r osborn j m yeomans lattice boltzmann simulation of liquid gas and binary fluid systems phys rev e 54 1996 5041 5052 t inamuro t ogata s tajima n konishi a lattice boltzmann method for incompressible two phase flows with large density differences j comput phys 198 2004 628 644 t lee c l lin a stable discretization of the lattice boltzmann equation for simulation of incompressible two phase flows at high density ratio j comput phys 206 2005 16 47 besides it requires less discrete velocities as a result its efficiency could be greatly improved especially in 3d applications it is validated by several cases a bubble in a stationary flow and the capillary wave the numerical surface tension obtained from the laplace law and the interface profile agrees very well with the respective analytical solution the method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods all the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios

sharp bounds on the number of scattering poles for perturbations of the laplacian sharp bounds on the numbern r of the scattering poles in the disc z r for a large class of compactly supported perturbations not necessarily selfadjoint of the laplacian in n n 3 odd are obtained in particular in the elliptic case the estimaten r cr n c is proved

efficient computation of dendritic growth with r adaptive finite element methods this paper deals with the application of a moving grid method to the solution of a phase field model for dendritic growth in two and three dimensions a mesh is found as the solution of an optimization problem that automatically includes the boundary conditions and is solved using a multi grid approach the governing equations are discretized in space by linear finite elements and a split time level scheme is used to numerically integrate in time one novel aspect of the method is the choice of a regularized monitor function the moving grid method enables us to obtain accurate numerical solutions with much less degree of freedoms it is demonstrated numerically that the tip velocity obtained by our method is in good agreement with the previously published results