115,788 research outputs found
A full Eulerian finite difference approach for solving fluid-structure coupling problems
A new simulation method for solving fluid-structure coupling problems has
been developed. All the basic equations are numerically solved on a fixed
Cartesian grid using a finite difference scheme. A volume-of-fluid formulation
(Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely
used for multiphase flow simulations, is applied to describing the
multi-component geometry. The temporal change in the solid deformation is
described in the Eulerian frame by updating a left Cauchy-Green deformation
tensor, which is used to express constitutive equations for nonlinear
Mooney-Rivlin materials. In this paper, various verifications and validations
of the present full Eulerian method, which solves the fluid and solid motions
on a fixed grid, are demonstrated, and the numerical accuracy involved in the
fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy
Cryptography: Mathematical Advancements on Cyber Security
The origin of cryptography, the study of encoding and decoding messages, dates back to ancient times around 1900 BC. The ancient Egyptians enlisted the use of basic encryption techniques to conceal personal information. Eventually, the realm of cryptography grew to include the concealment of more important information, and cryptography quickly became the backbone of cyber security. Many companies today use encryption to protect online data, and the government even uses encryption to conceal confidential information. Mathematics played a huge role in advancing the methods of cryptography. By looking at the math behind the most basic methods to the newest methods of cryptography, one can learn how cryptography has advanced and will continue to advance
On The S-Matrix of Ising Field Theory in Two Dimensions
We explore the analytic structure of the non-perturbative S-matrix in
arguably the simplest family of massive non-integrable quantum field theories:
the Ising field theory (IFT) in two dimensions, which may be viewed as the
Ising CFT deformed by its two relevant operators, or equivalently, the scaling
limit of the Ising model in a magnetic field. Our strategy is that of collider
physics: we employ Hamiltonian truncation method (TFFSA) to extract the
scattering phase of the lightest particles in the elastic regime, and combine
it with S-matrix bootstrap methods based on unitarity and analyticity
assumptions to determine the analytic continuation of the 2 to 2 S-matrix
element to the complex s-plane. Focusing primarily on the "high temperature"
regime in which the IFT interpolates between that of a weakly coupled massive
fermion and the E8 affine Toda theory, we will numerically determine 3-particle
amplitudes, follow the evolution of poles and certain resonances of the
S-matrix, and exclude the possibility of unknown wide resonances up to
reasonably high energies.Comment: typos corrected, references added, additional comparison with
perturbation theory added. 35 pages, 21 figure
Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
The localization properties of eigenfunctions for two interacting particles
in the one-dimensional Anderson model are studied for system sizes up to
sites corresponding to a Hilbert space of dimension
using the Green function Arnoldi method. The eigenfunction structure is
illustrated in position, momentum and energy representation, the latter
corresponding to an expansion in non-interacting product eigenfunctions.
Different types of localization lengths are computed for parameter ranges in
system size, disorder and interaction strengths inaccessible until now. We
confirm that one-parameter scaling theory can be successfully applied provided
that the condition of being significantly larger than the one-particle
localization length is verified. The enhancement effect of the
two-particle localization length behaving as is clearly
confirmed for a certain quite large interval of optimal interactions strengths.
Further new results for the interaction dependence in a very large interval, an
energy value outside the band center, and different interaction ranges are
obtained.Comment: 26 pages, 19 png and pdf figures, high quality gif files for panels
of figures 1-4 are available at
http://www.quantware.ups-tlse.fr/QWLIB/tipdisorder1d, final published version
with minor corrections/revisions, addition of Journal reference and DO
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