Data acquisition for geoinformatics cannot be done continuously, but by discrete sampling of the object or phenomenon. The sampling involves errors on the knowledge of the continuous signal due to the loss of information in the sampling procedure. In the present study, an analytical formulation of the sampling error is provided, which embodies the amplitude, phase, bias and periodicity of the sampling error. The analysis is then subsequently applied for case studies: for the GRACE and GRACE-FO monthly solutions, and for different realizations of the Hungarian Gravimetric Network.

The aim of this paper is to construct a numerical scheme for solving a class of bilateral free boundaries problem. First, using a shape functional and some regularization terms, an optimal control problem is formulated, in addition, we prove its solution existence's. The first optimality conditions and the shape gradient are computed. the proposed numerical scheme is a genetic algorithm guided conjugate gradient combined with the finite element method, at each mesh regeneration, we perform a mesh refinement in order to avoid any domain singularities. Some numerical examples are shown to demonstrate the validity of the theoretical results, and to prove the robustness of the proposed scheme.

In this article, Haar wavelet collocation technique is adapted to acquire the approximate solution of fractional KdV, Burgers' and KdV-Burgers' equations. The fractional order derivatives involved are described using the Caputo definition. In the proposed technique, the given nonlinear fractional differential equation is discretized with the help of Haar wavelet and reduced to the nonlinear system of equations, which are solved with Newton's or Broyden's method. The proposed method is semi-analytic as it involves exact integration of Caputo derivative. The proposed technique is widely applicable and robust. The technique is tested upon many test problems. The results are computed and presented in the form of maximum absolute errors which shows the accuracy, efficiency and simple applicability of the proposed method.

In this paper, we consider a one-dimensional porous thermoelastic system with microtemperatures effects and past history term acting only on the porous equation. We show that the system is well-posed in the sens of semigroup and based on the energy method we establish a general decay result for the solutions of the system under an appropriate assumptions on the kernel. Furthermore, our result depends on the stability number that was first considered in [25]. The result of this paper improves some results in the literature.

We study a certain nonlocal evolution equation generalising a model introduced to explain colour patterns on a skin of the guppy fish. We prove an existence of stationary solutions using either the bifurcation theory or the Schauder fixed point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those modelled by well-known reaction-diffusion equations.

In this paper, we investigate the numerical approximation of stochastic convection-reaction-diffusion equations using two explicit exponential integrators. The stochastic partial differential equation (SPDE) is driven by additive Wiener process. The approximation in space is done via a combination of the standard finite element method and the Galerkin projection method. Using the linear functional of the noise, we construct two accelerated numerical methods, which achieve higher convergence orders. In particular, we achieve convergence rates approximately $1$ for trace class noise and $\frac{1}{2}$ for space-time white noise. These convergences orders are obtained under less regularities assumptions on the nonlinear drift function than those used in the literature for stochastic reaction-diffusion equations. Numerical experiments to illustrate our theoretical results are provided

We consider the incremental subgradient algorithm employing dynamic step sizes for minimizing the sum of a large number of component convex functions. The dynamic step size rule was firstly introduced by Goffin and Kiwiel [Math. Program., 1999, 85(1): 207-211] for the subgradient algorithm, soon later, for the incremental subgradient algorithm by Nedic and Bertsekas in [SIAM J. Optim., 2001, 12(1): 109-138]. It was observed experimentally that the incremental approach has been very successful in solving large separable optimizations, and that the dynamic step sizes generally have better computational performance than others in the literature. In the present paper, we propose two modified dynamic step size rules for the incremental subgradient algorithm and analyse the convergence properties of them. At last, the assignment problem is considered and the incremental subgradient algorithms employing different kinds of dynamic step sizes are applied to solve the problem. The computational experiments show that the two modified ones converges dramatically faster and stabler than the corresponding one in [SIAM J. Optim., 2001, 12(1): 109-138]. Particularly, for solving large separable convex optimizations, we strongly recommend the second one (see Algorithm 3.3 in the paper) since it has interesting computational performance and is the simplest one.

We firstly discuss the unchanged quasi direction motion (UDQM) with biharmonicity condition in the Heisenberg space. We define the energy of velocity magnetic particles and some Lorentz fields. Also, we construct the new relationship between the Fermi-Walker parallel transportation and the unchanged quasi direction motion in the Heisenberg space. In other words, we obtain the applied geometric characterization for the unchanged quasi direction motion of biharmonic velocity magnetic particles in the Heisenberg space. This concept also boosts to discover some physical and geometrical characterizations belonging to the particle such as the magnetic motion, the electrical energy functional, the torque, and the Poynting vector. Finally, we obtain electrical energy with respect to its electric field and energy flux density in the radial direction.

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the obstacle.

A nonlinear oscillator arising in a micro-electro-mechanical system (MEMS) is difficult to be solved analytically due to the zero conditions. so the main objective of this work is to analyze the mathematical model of this system, and its approximate analytical solution is solved via the coupling Variational Iteration method and Laplace transform(LVIM). This method provides an efficient way to obtain the approximate nonlinear frequency and approximate solutions of MEMS. Moreover, LVIM also approximates the pull-in threshold in terms of model parameters. Finally, the results are compared with the exact one and a good result is obtained.

We consider a PDE/ODE system for two pairs of competing species and study the spatial segregation limit as the interspecific competition rate tends to infinity. We show that the limiting problem is a one-phase Stefan problem for nonlinear diffusion equations.

In this paper, we investigate the wellposedness of the non-isentropic compressible Navier-Stokes/Allen-Cahn system with the heat-conductivity proportional to a positive power of the temperature. This system describes the flow of a two-phase immiscible heat-conducting viscous compressible mixture. The phases are allowed to shrink or grow due to changes of density in the fluid and incorporates their transport with the current. We established the global existence and uniqueness of strong solutions for this system in 1-D, which means no phase separation, vacuum, shock wave, mass or heat or phase concentration will be developed in finite time, although the motion of the two-phase immiscible flow has large oscillations and the interaction between the hydrodynamic and phase-field effects is complex. Our result can be regarded as a natural generalization of the Kazhikhov-Shelukhin’s result ([Kazhikhov-Shelukhin. J. Appl. Math. Mech. 41 (1977)]) for the compressible single-phase flow with constant heat conductivity to the non-isentropic compressible immiscible two-phase flow with degenerate and nonlinear heat conductivity.

We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack. This formulation can be related to geological faults in elastic media or to irrotational incompressible flows in a half space minus an inner wall. The direct problem is well posed in an appropriate functional space. We study the related inverse problem where the jump across the crack is unknown, and more importantly, the geometry and the location of the crack are unknown. The data for the inverse problem is of Dirichlet type over a portion of the top boundary. We prove that this inverse problem is uniquely solvable under some assumptions on the geometry of the crack. The highlight of this paper is showing a stability result for this inverse problem. Assuming that the crack is planar, we show that reconstructing the plane containing the crack is Lipschitz stable despite the fact that the forcing term for the underlying PDE is unknown. This uniform stability result holds under the assumption that the forcing term is bounded above and the Dirichlet data is bounded below away from zero in appropriate norms.

Melt superheated treatment can affect the solidification structure, but the direct evidence requires strict experiments. The molecular dynamics simulation method can break the limited experimental conditions, and provide advanced prediction for research. In this study, influences of superheated temperature (Ts) on the nucleation undercooling (ΔT) of metallic melts (Ti, Co, Mg, Al, Ni, Fe, Ag) were studied by the molecular dynamics simulation. The results show that the value of ΔT increases with the rise of Ts until the maximal ΔT approaches. In the curve of ΔT vs. Ts, there is an inflexion region where the nucleus cluster was broken. Above this inflexion region, the number of nucleus clusters decreases with the rise of Ts. Based on the simulated results, a model was proposed for describing the relation of ΔT and Ts, with which the maximal undercooling for metals can be predicted.

The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings.

The developed model of diffusion-limited and diffusionless solidification of eutectic alloy describes the relation “undercooling (ΔT)–velocity(V)–interlamellar spacing (λ)” for two cases. Namely, if the lamellar velocity V is smaller than the solute diffusion speed in bulk liquid VD, VVD, the solidification is mainly controlled by kinetic and thermal undercoolings. We show an influence of model parameters on the growth kinetics of eutectic solidification. Comparison of the model predictions with experimental data obtained on Fe-B samples processed in melt-glass fluxing is given.

Continuity, in particular sequential continuity, is an important subject of investigation not only in Topology, but also in some other branches of Mathematics. Connor and Grosse-Erdmann remodeled its definition for real functions by replacing {\sf lim} with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. Then, this definition was extended to a topological group $X$ by replacing a linear functional $G$ with an arbitrary additive function defined on a subgroup of the group of all $X$-valued sequences. Also, some new theorems in generalized setting were given and some other theorems that had not been obtained for real functions were presented. In this study, we introduce neutrosophic $G$-continuity and investigate its properties in neutrosophic topological spaces.

Numerous experimental data on rapid solidification of eutectic systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but a finite growth velocity of crystals. A model considering the diffusionless growth is developed in the present work to analyze the atomic diffusion ahead of lamellar eutectic couples growing into supercooled liquid. A general solution of the model is presented from which two regimes are followed. The first presents diffusion-limited regime with the existence of eutectic decomposition if the solid-liquid interface velocity is smaller than characteristic diffusion speed in bulk liquid. The second shows suppression of eutectic decomposition under diffusionless transformation from liquid to one-phase solid if the solid-liquid interface velocity overcomes characteristic diffusion speed in bulk liquid.