Search results for "Applied Mathematics"
showing 10 items of 4379 documents
The planar two-body problem for spheroids and disks
2021
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…
A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior
2013
Abstract This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations …
A gradient elasticity theory for second-grade materials and higher order inertia
2012
Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …
A membrane computing simulator of trans-hierarchical antibiotic resistance evolution dynamics in nested ecological compartments (ARES)
2015
In this article, we introduce ARES (Antibiotic Resistance Evolution Simulator) a software device that simulates P-system model scenarios with five types of nested computing membranes oriented to emulate a hierarchy of eco-biological compartments, i.e. a) peripheral ecosystem; b) local environment; c) reservoir of supplies; d) animal host; and e) host's associated bacterial organisms (microbiome). Computational objects emulating molecular entities such as plasmids, antibiotic resistance genes, antimicrobials, and/or other substances can be introduced into this framework and may interact and evolve together with the membranes, according to a set of pre-established rules and specifications. AR…
The cryogenic anticoincidence detector for ATHENA-XMS: preliminary results from the new prototype
2012
ATHENA has been the re-scoped IXO mission, and one of the foreseen focal plane instrument was the X-ray Microcalorimeter Spectrometer (XMS) working in the energy range 0.3-10 keV, which was a kilo-pixel array based on TES (Transition Edge Sensor) detectors. The need of an anticoincidence (AC) detector is legitimated by the results performed with GEANT4 simulations about the impact of the non x-ray background onto XMS at L2 orbit (REQ. < 0.02 cts/cm2/s/keV). Our consortium has both developed and tested several samples, with increasing area, in order to match the large area of the XMS (64 mm2). Here we show the preliminary results from the last prototype. The results achieved in this work off…
Simple connections between generalized hypergeometric series and dilogarithms
1997
AbstractConnections between generalized hypergeometric series and dilogarithms are investigated. Some simple relations of an Appell's function and dilogarithms are found.
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams
2000
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.
New indefinite integrals from a method using Riccati equations
2018
ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...
Themes within lecturers' views on the teaching of linear algebra
2019
Author's accepted manuscript (postprint). This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology on 25/09/2019, available online: http://www.tandfonline.com/10.1080/0020739X.2019.1668976. Available from 26/09/2020. This paper reports on themes that arose in an investigation of university lecturers’ views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course? Are there tools that should/should not …
Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
2021
We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda u - \gamma (|x|^{-1} * |u|^2) u - a |u|^{p-2}u = 0 \quad \text{in} \quad \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx = c \end{equation*} for some prescribed $c>0$. Here $ u \in H^1(\mathbb{R}^3)$, $\gamma \in \mathbb{R},$ $ a \in \mathbb{R}$ and $p \in (\frac{10}{3}, 6]$. When $\gamma >0$ and $a > 0$, both in the Sobolev subcritical case $p \in (\frac{10}{3}, 6)$ and in the Sobolev critical case $p=6$, we show that there exists a $c_1>0$ such that, for any $c \in (0,c_1)$, the equation admits two solutions $u_c^+$ and $u_c^-$ which can be characterized respectively…