Related papers: On the travel time tomography problem in 3D
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to…
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…
In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic…
This paper aims to reconstruct the initial condition of a hyperbolic equation with an unknown damping coefficient. Our approach involves approximating the hyperbolic equation's solution by its truncated Fourier expansion in the time domain…
In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the…
Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh's 1916 model of natural thermal convection. Bounds for the ODE model---an extension of Lorenz's three-ODE system---are derived by…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…
The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible…
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two…
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…
Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two…
In this prelinimary version of paper, we propose to give a complete solution to the Truncated Multidimensional Trigonometric Moment Problem (TMTMP) from a system and signal processing perspective. In mathematical TMTMPs, people care about…
Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are…