a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

modeling microstructure evolution using gradient weighted moving finite elements microstructure evolution where grain boundaries evolve by mean curvature motion is modeled in three dimensions 3 d using gradient weighted moving finite elements gwmfe to do this we modify and extend an existing 2 d gwmfe code to create a new code grain3d which makes the 3 d microstructure modeling possible the right hand side term which drives the gwmfe motion can be viewed as surface tension forces that is as the negative gradient of the surface integral of a constant energy density mu on the triangular interfacial grid extensions to the method include equations for the motion of tetrahedra that are conformally attached to the moving piecewise linear triangular facets which represent the gwmfe discretization of the evolving grain boundaries we present some new regularization terms which control element quality as well as preventing element collapse in the simulation new capabilities for changing the mesh topology are used to keep the grid edge lengths below a maximum allowable length hmax and to mimic actual changes in the physical topology such as collapse and disappearance of individual grains validating runs are performed on some test cases that can be analytically solved including collapse of a spherical grain and the case of columnar microstructure in the spherical collapse case the gwmfe method appears to have an error in the surface area collapse rate da over dt which is cal o delta theta 2 where delta theta is a measure of the angular resolution of the mesh finally a run is presented where a true 3 d microstructure possessing triple lines and quadruple points in the interior and triple points on the exterior boundaries is evolved to a 2 d columnar microstructure and finally evolved down to a single grain

representation of lie algebra t3 and 2 variable 2 parameter bessel functions abstract in this paper we deal with the problem of framing 2 variable 2 parameter bessel functions 2v2pbf into the context of the representation q w m 0 of the 3 dimensional lie algebra t 3 further we derive generating relations and identities involving 2v2pbf furthermore we deduce some new and known relations involving various other forms of generalized bessel functions gbf and bessel functions bf as applications of these results

towards a statistical theory of texture evolution in polycrystals most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries the energetics and connectivity of the grain boundary network play a crucial role in determining the properties of a material across a wide range of scales a central problem in materials science is to develop technologies capable of producing an arrangement of grains a texture that provides for a desired set of material properties one of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening here we propose an upscaling procedure suitable for large complex systems the procedure is based on numerical experimentation combined with stochastic tools and consists of large scale numerical simulations of a system at a microscopic level statistical analysis of the microscopic data and formulation of the model based on stochastic characteristics predicted by the statistical analysis this approach promises to be valuable in establishing the effective model of microstructural evolution in realistic two and three dimensional systems to test ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one dimensional network of grain boundaries despite the simplicity of its formulation this model exhibits highly nontrivial behavior characterized by growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher dimensional simulations here we focus on the grain deletion events which are common to all coarsening systems

generating functions of multivariable generalized bessel functions and jacobi elliptic functions it is pointed out that the jacobi elliptic functions are the natural basis to get generating functions of the multivariable generalized bessel functions analytical and numerical results are given of interest for applications

magnetic interpretation in three dimensions using euler deconvolution magnetic survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using euler s homogeneity relation the method employs gradients either measured or calculated data need not be pole reduced so that remanence is not an interfering factor geologic constraints are imposed by use of a structural index model studies show that the method can locate or outline confined sources vertical pipes dikes and contacts with remarkable accuracy a field example using data from an intensively studied area of onshore britain shows that the method works well on real data from structurally complex areas and provides a series of depth labeled euler trends which mark magnetic edges notably faults with good precision

an alternate derivation of the three dimensional hilbert transform relations from first principles several techniques for determining the location geometry and strength of a source are based on a knowledge of the magnetic gradients generated by that source hood 1965 bhattacharyya 1966 and rao et al 1981 detailed three of these gradient methods for many years geophysicists have used the two dimensional 2 d hilbert transform to approximate the vertical gradient from measurements of the horizontal gradient in the magnetic field intensity nabighian 1972 stanley and green 1976 stanley 1977 mohan et al 1982 this technique is of limited applicability because of the implicit assumption that the source is a linear 2 d body oriented at right angles to the profile direction

a level set method for the evolution of faceted crystals a level set formulation for the motion of faceted interfaces is presented the evolving surface of a crystal is represented as the zero level of a phase function the crystal is identified by its orientation and facet speeds accuracy is tested on a single crystal by comparison with the exact evolution the method is extended to study the evolution of a polycrystal numerical examples in two and three dimensions are presented

theory of two index bessel functions and applications to physical problems in this article the theory of two index bessel functions is presented their generating function series expansion and integral representations are discussed their usefulness in physical problems is also discussed in the context of analysis of radiation emitted by relativistic electrons in two frequency undulators finally the theoretical analysis proving addition and multiplication theorems for two index bessel functions are completed and their modified forms are introduced

kernels with prescribed surface tension mobility for threshold dynamics schemes abstract we show how to construct a convolution kernel that has a desired anisotropic surface tension and desired anisotropic mobility to be used in threshold dynamics schemes for simulating weighted motion by mean curvature of interfaces including networks of them in both two and three dimensions moreover we discuss necessary and sufficient conditions for the positivity of the kernel which in the case of two phase flow ensures that the resulting scheme respects a comparison principle and implies convergence to the viscosity solution of the level set formulation of the flow in particular we show in a barrier type statement that the kernel cannot possibly be positive unless both the mobility and the surface tension satisfy necessary conditions in three dimensions and give a complete characterization among other results is a threshold dynamics scheme that is guaranteed to dissipate a non local approximation to the interfacial energy in the fully anisotropic multiphase setting using the new kernel construction

model for coarsening froths and foams the coarsening process of froths and foams is described statistically in two dimensions by a random neighbor model this nonlinear dynamical model contains no free parameters all rates are determined dynamically it describes normal growth agrees with experimental results throws light on old data and hopefully inspires new simulations and measurements lewis s law anat rec 38 341 1928 am j bot 30 74 1943 and some other properties can be derived analytically from the model

a geometric model for anisotropic crystal growth equilibrium crystal shapes are defined uniquely by the wulff construction the classical kinematic theory of crystal growth due mainly to frank and chernov provides a mathematically equivalent prescription for the limiting growth shape to connect these two well studied states we derive a local geometric growth model and examine the transient shape evolution of an equilibrium form containing both facets and rough regions our model is appropriate to the weakly driven growth of a two dimensional single crystal with n gonal symmetry and arbitrary closed initial shape the model links disparate kinetic processes determined by the local interfacial structure to the isotropic growth drive and reproduces the experimentally observed transition from a partly rounded equilibrium shape to a highly faceted crystal which we term global kinetic faceting we solve for the transient shape dynamics globally and locally and in the latter case present a curvature evolution equation valid for any local growth law both approaches show that during kinetic faceting rough orientations grow out of existence with decreasing curvature

diffusion generated motion using signed distance functions we describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps construction of the signed distance function i e redistancing to the interface and convolution with a suitable kernel these algorithms can be seen as variants of merriman bence and osher s threshold dynamics 25 the new algorithms proposed here preserve the computational efficiency of the original threshold dynamics algorithm however unlike threshold dynamics the new algorithms also allow attaining high accuracy on uniform grids without adaptive refinement

high precision potential field and gradient component transformations and derivative computations using cubic b splines potential field and gradient component transformations and derivative computations are necessary for many techniques of data enhancement direct interpretation and inversion we advance new unified formulas for fast interpolation differentiation and integration and propose flexible high precision algorithms to perform 3d and 2d potential field and gradient component transformations and derivative computations in the space domain using cubic b splines the spline based algorithms are applicable to uniform or nonuniform rectangular grids for the 3d case and to regular or irregular grids for the 2d case the fast fourier transform fft techniques require uniform grid spacing the spline based horizontal derivative computations can be done at any point in the computational domain whereas the fft methods use only grid points comparisons between spline and fft techniques through two gravity gradient examples and one magnetic example show that results computed with the spline technique agree better with t

diffusion generated motion for grain growth in two and three dimensions an efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed this motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials in this formulation grain boundaries are zero level sets of signed distance functions curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step a technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains hundreds of thousands of grains can be simulated using a small number of signed distance functions in this work 32 in two dimensions and 64 in three dimensions are more than sufficient using modest computational hardware

generating relations of tricomi and hermite tricomi functions using lie algebra representation abstract this paper is an attempt to stress the usefulness of the multi variable special functions in this paper we derive generating relations involving multi variable tricomi and hermite tricomi functions by using lie algebraic method further we derive certain new and known generating relations involving other forms of tricomi hermite tricomi and bessel functions as applications

a variational approach to modeling and simulation of grain growth most technologically useful materials arise as polycrystalline microstructures composed of a myriad of small crystallites called grains separated by their interfaces called grain boundaries the orientations and arrangements of the grains and their network of boundaries are implicated in many properties across wide scales for example functional properties like conductivity in microprocessors and lifetime properties like fracture toughness in structures simulation is becoming an important tool for understanding both materials properties and their processing requirements here we offer a consistent variational approach to the mesoscale simulation of these systems subject to the mullins equation of curvature driven growth in a two dimensional setting the main objective is to provide a calibration for future two dimensional and three dimensional efforts we discuss several novel features of our approach which we anticipate will render it a flexible scalable and robust tool to aid in microstructural prediction simulation results offer compelling evidence of the predictability and robustness of statistical properties of large systems such as grain size distribution and texture that are of immediate interest in materials science

unification of euler and werner deconvolution in three dimensions via the generalized hilbert transform the extended euler deconvolution algorithm is shown to be a generalization and unification of 2 d euler deconvolution and werner deconvolution after recasting the extended euler algorithm in a way that suggests a natural generalization to three dimensions we show that the 3 d extension can be realized using generalized hilbert transforms the resulting algorithm is both a generalization of extended euler deconvolution to three dimensions and a 3 d extension of werner deconvolution at a practical level the new algorithm helps stabilize the euler algorithm by providing at each point three equations rather than one we illustrate the algorithm by explicit calculation for the potential of a vertical magnetic dipole

a duality based method for generating geometric representations of polycrystals we present a method which we have termed relaxed dual complex rdc for generating geometric representations and computational models of polycrystals of arbitrary shape the rdc method combines a first topological step which defines an initial unrelaxed polycrystal geometry as the barycentric dual of an input triangulation of the solid and a second relaxation step in which the grain boundaries are relaxed by means of a gradient flow driven by grain boundary energy the rdc method applies to arbitrary solids defined by means of a triangulation and in this manner it couples seamlessly to standard solid modelling engines an additional appealing feature of the rdc method is that it generates a conforming tetrahedral mesh of the polycrystal that can be used as a basis for subsequent simulations the rdc method also affords some control over the statistical properties of the polycrystal including grain size which provides a convenient device for matching experimental statistical data the range versatility and performance of the rdc method have been demonstrated by means of selected examples

linking anisotropic sharp and diffuse surface motion laws via gradient flows we compare four surface motion laws for sharp surfaces with their diffuse interface counterparts by means of gradient flows on corresponding energy functionals the energy functionals can be defined to give the same dependence on normal direction for the energy of sharp plane surfaces as for their diffuse counterparts the anisotropy of the kinetics can be incorporated into the inner product without affecting the energy functional

diffuse interfaces with sharp corners and facets phase field models with strongly anisotropic surfaces abstract we provide the general outline of an analysis of the motion of diffuse interfaces in the order parameter phase field formulation which includes nondifferentiable and nonconvex gradient energy terms nondifferentiability leads to equilibrium and motion equations that are apparently undefined and nonconvexity leads to equations that are apparently ill posed the problem of nondifferentiability is resolved by using nonlocal variations to move entire facets or line segments with orientations having such facets or line segments in the underlying wulff shape the problem of ill posedness is resolved by using varifolds infinitesimally corrugated diffuse interfaces constructed from the edges and corners in the underlying wulff shape or equivalently by using the convexification of the gradient energy term and then reinterpreting the solutions as varifolds this is justified on a variational basis we conclude that after an initial transient level sets move by weighted mean curvature in agreement with the sharp interface limit we provide equations for tracking the shocks that develop as edges and corners in level sets

toward a three dimensional automatic interpretation of potential field data via generalized hilbert transforms fundamental relations the paper extends to three dimensions 3 d the two dimensional 2 d hilbert transform relations between potential field components for the 3 d case it is shown that the hilbert transform is composed of two parts with one part acting on the x component and one part on the y component as for the previously developed 2 d case it is shown that in 3 d the vertical and horizontal derivatives are the hilbert transforms of each other the 2 d cauchy riemann relations between a potential function and its hilbert transform are generalized for the 3 d case finally the previously developed concept of analytic signal in 2 d can be extended to 3 d as a first step toward the development of an automatic interpretation technique for potential field data

hilbert transform of gravity gradient profiles special cases of the general gravity gradient tensor in the fourier transform domain the hilbert transform has been extensively used in gravity gradient interpretation since the mid 1970s when stanley 1976 and stanley and green 1976 followed the work on the relationships between magnetic field components nabighian 1972 shuey 1972 by showing that the vertical g z z and horizontal g z x gravity gradients of a 2 d truncated plate are related by the hilbert transform butler 1983 1995 has extended the use of the hilbert transform in interpreting g z z and g z x resulting from additional geometries

interpretation of some two dimensional magnetic bodies using hilbert transforms procedures are formulated using the hilbert transform for interpreting vertical magnetic anomalies of 1 the sheets finite and infinite depth extent 2 the dike and 3 the horizontal circular cylinder the applicability of the method is tested on theoretical models the method is also applied on the well known kursk field anomaly of a sheet infinite depth extent and the field anomaly of a dike of karimnagar andhra pradesh india

relations between horizontal and vertical gradients of potential fields nabighian 1984 and nelson 1986 have both derived relations between horizontal and vertical gradients of magnetic fields or any other potential field whereby a knowledge of one enables one to calculate the other as pointed out by nelson nabighian s derivation is quite lengthy in the following i offer an alternative derivation in the wavenumber domain which is even shorter than that given by nelson

threshold dynamics for networks with arbitrary surface tensions we present and study a new algorithm for simulating the n phase mean curvature motion for an arbitrary set of isotropic surface tensions the departure point is the threshold dynamics algorithm of merriman bence and osher for the two phase case a new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of n phases for arbitrary surface tensions and arbitrary isotropic mobilities for a large class of surface tensions the algorithm is shown to be consistent in the sense that at every time step it decreases an energy functional that is an approximation in the sense of gamma convergence of the interfacial energy a broad range of numerical tests shows good convergence properties an important application is the motion of grain boundaries in polycrystalline materials it is also established that the above mentioned large class of surface tensions contains the read shockley surface tensions both in the two dimensional and three dimensional settings 2015 wiley periodicals inc

lie theoretic generating relations of hermite 2d polynomials in this paper we derive some generating relations involving hermite 2d polynomials h2dp hm n u x y of two variables with an arbitrary 2d matrix u as parameter using lie theoretic approach certain known or new generating relations for the polynomials related to h2dp are also obtained as special cases