19 papers · ranked by Valyu relevance
Michael Hayes, Giovanni Angiulli
Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Lcapy can model circuits comprised of combinations of…
Arina Oberoi
This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging, including noise reduction, data interpolation, and resolution enhancement, as…
Gertjan Bisschop
Extracting information on the selective and demographic past of populations that is contained in samples of genome sequences requires a description of the distribution of the underlying genealogies. Using the Laplace transform, this distribution can be generated with a simple recursive procedure, regardless of model…
George C. Hsiao, Tonatiuh Sánchez-Vizuet
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of…
Hamdy M. Youssef, Najat. A. Alghamdi
The use of lasers and thermal transfers on the skin is fundamental in medical and clinical treatments. In this paper, we constructed and applied bioheat transfer equations in the context of a two-temperature heat conduction model in order to discuss the three-dimensional variation in the temperature of laser-irradiated…
Ahmed E. Abouelregal, Ibrahim-Elkhalil Ahmed, Mohamed E. Nasr, Khalil M. Khalil + 2 more
'Khalil M. Khalil' 'Adam Zakria' 'Fawzy A. Mohammed'] Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore-Gibson-Thompson equation in cases where some of these…
Abinand Gopal, Lloyd N. Trefethen
Numerical algorithms based on rational functions are introduced that solve the Laplace and Helmholtz equations on 2D domains with corners quickly and accurately, despite the corner singularities.
Bastien Chaudet-Dumas, Martin J. Gander
Cross-points in domain decomposition, i.e., points where more than two subdomains meet, have received substantial attention over the past years, since domain decomposition methods often need special attention in their definition at cross-points, in particular if the transmission conditions of the domain decomposition…
Peter Lindqvist
These notes are written up after my lectures at the University of Pittsburgh in March 2014 and at Tsinghua University in May 2014. My objective is the ∞-Laplace Equation, a marvellous kin to the ordinary Laplace Equation. The ∞-Laplace Equation has delightful counterparts to the Dirichlet integral, the Mean Value…
Björn Gustafsson, Ahmed Sebbar
The Hadamard variational formula for the Green function is formulated in terms of a polarized energy-momentum tensor and a strain tensor. This is elaborated in a general setting of subdomains of a Riemannian manifold in arbitrary dimension and linked to the way the energy-momentum tensor in general field theory appears…
Lloyd N. Trefethen
At the ANZIAM conference in Hobart in February, 2018, there were several talks on the solution of Laplace problems in multiply connected domains by means of conformal mapping. It appears to be not widely known that such problems can also be solved by the elementary method of series expansions with coefficients…
U. Filobello-Nino, H. Vazquez-Leal, A. Sarmiento-Reyes, B. Benhammouda + 7 more
'B. Benhammouda' 'V. M. Jimenez-Fernandez' 'D. Pereyra-Diaz' 'A. Perez-Sesma' 'J. Cervantes-Perez' 'J. Huerta-Chua' 'J. Sanchez-Orea' 'A. D. Contreras-Hernandez'] The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear…
Authors not listed
Quadrupolar solid-state (SS) nuclear magnetic resonance (NMR) spectroscopy is an excellent tool to trace lithium (Li) ion diffusion in solid electrolytes due to its sensitivity to dynamics over timescales from nanoseconds to seconds. However, the structural and dynamical complexity of battery materials limits the…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Kathrin Knappmann, Alfred Wagner
We prove the following uniqueness result for the buckling plate. Assume there exists a smooth domain which minimizes the first buckling eigenvalue for a plate among all smooth domains of given volume. Then the domain must be a ball. The proof uses the second variation for the buckling eigenvalue and an inequality by L.…
Authors not listed
In this second part, we present the explicit analytical expression of the framework introduced in Part I. The formulation yields closed-form predictions for capillary rise and depression in cylindrical geometries and extends naturally to a wide range of configurations. It shows that the contact angle, rather than being…
Authors not listed
Alternating current voltammetry (ACV) is gaining popularity for its ability to improve the yield of electrochemical syntheses, and for its ability to improve the sensitivity of electroanalytical measurements. Chief among the analytical advantages of ACV is its ability to generate an alternating current at integer…
Robert J.H. Ross, R.E. Baker, C.A. Yates
Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these biological systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial…
Matthew J. Simpson
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction–diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such…