111,529 research outputs found
A kinematically exact finite element formulation of planar elastic-plastic frames
A finite element formulation of finite deformation static analysis of plane elastic-plastic frames subjected to static loads is presented, in which the only function to be interpolated is the rotation of the centroid axis of the beam. One of the advantages of such a formulation is that the problem of the field-consistency does not arise. Exact non-linear kinematic relationships of the finite-strain beam theory are used, which assume the Bernoulli hypothesis of plane cross-sections. Finite displacements and rotations as well as finite extensional and bending strains are accounted for. The effects of shear strains and non-conservative loads are at present neglected, yet they can simply be incorporated in the formulation. Because the potential energy of internal forces does not exist with elastic-plastic material, the principle of virtual work is introduced as the basis of the finite element formulation. A generalized principle of virtual work is proposed in which the displacements, rotation, extensional and bending strains, and the Lagrangian multipliers are independent variables. By exploiting the special structure of the equations of the problem, the displacements, the strains and the multipliers are eliminated from the generalized principle of virtual work. A novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation. It is shown that (N-1)-point numerical integration must be employed in conjunction with N-node interpolation polynomials for the rotation, and the Lobatto rule is recommended. Regarding the integration over the cross-section, it is demonstrated by numerical examples that, due to discontinuous integrands, no integration order defined as `computationally efficient yet accurate enough' could be suggested. The theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples
Robin problems with a general potential and a superlinear reaction
We consider semilinear Robin problems driven by the negative Laplacian plus
an indefinite potential and with a superlinear reaction term which need not
satisfy the Ambrosetti-Rabinowitz condition. We prove existence and
multiplicity theorems (producing also an infinity of smooth solutions) using
variational tools, truncation and perturbation techniques and Morse theory
(critical groups)
Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
We study quantum chaos and spectral correlations in periodically driven
(Floquet) fermionic chains with long-range two-particle interactions, in the
presence and absence of particle number conservation () symmetry. We
analytically show that the spectral form factor precisely follows the
prediction of random matrix theory in the regime of long chains, and for
timescales that exceed the so-called Thouless/Ehrenfest time which scales with
the size as , or , in the presence, or
absence of symmetry, respectively. Using random phase assumption which
essentially requires long-range nature of interaction, we demonstrate that the
Thouless time scaling is equivalent to the behavior of the spectral gap of a
classical Markov chain, which is in the continuous-time (Trotter) limit
generated, respectively, by a gapless , or gapped , spin-1/2 chain
Hamiltonian.Comment: 6 pages, 1 figur
Knot quandle decompositions
We show that the fundamental quandle defines a functor from the oriented
tangle category to a suitably defined quandle category. Given a tangle
decomposition of a link , the fundamental quandle of may be obtained
from the fundamental quandles of tangles. We apply this result to derive a
presentation of the fundamental quandle of periodic links, composite knots and
satellite knots.Comment: 23 pages, 12 figure
Interaction instability of localization in quasiperiodic systems
Integrable models form pillars of theoretical physics because they allow for
full analytical understanding. Despite being rare, many realistic systems can
be described by models that are close to integrable. Therefore, an important
question is how small perturbations influence the behavior of solvable models.
This is particularly true for many-body interacting quantum systems where no
general theorems about their stability are known. Here, we show that no such
theorem can exist by providing an explicit example of a one-dimensional
many-body system in a quasiperiodic potential whose transport properties
discontinuously change from localization to diffusion upon switching on
interaction. This demonstrates an inherent instability of a possible many-body
localization in a quasiperiodic potential at small interactions. We also show
how the transport properties can be strongly modified by engineering potential
at only a few lattice sites.Comment: 10 pages; (v2: additional explanations, data, and references
Entanglement spreading in a minimal model of maximal many-body quantum chaos
The spreading of entanglement in out-of-equilibrium quantum systems is
currently at the centre of intense interdisciplinary research efforts involving
communities with interests ranging from holography to quantum information. Here
we provide a constructive and mathematically rigorous method to compute the
entanglement dynamics in a class of "maximally chaotic", periodically driven,
quantum spin chains. Specifically, we consider the so called "self-dual" kicked
Ising chains initialised in a class of separable states and devise a method to
compute exactly the time evolution of the entanglement entropies of finite
blocks of spins in the thermodynamic limit. Remarkably, these exact results are
obtained despite the models considered are maximally chaotic: their spectral
correlations are described by the circular orthogonal ensemble of random
matrices on all scales. Our results saturate the so called "minimal cut" bound
and are in agreement with those found in the contexts of random unitary
circuits with infinite-dimensional local Hilbert space and conformal field
theory. In particular, they agree with the expectations from both the
quasiparticle picture, which accounts for the entanglement spreading in
integrable models, and the minimal membrane picture, recently proposed to
describe the entanglement growth in generic systems. Based on a novel
"duality-based" numerical method, we argue that our results describe the
entanglement spreading from any product state at the leading order in time when
the model is non-integrable.Comment: 25 pages, 10 figures; v2 improved presentation; v3: 28 pages 11
figures, presentation improved, Section 7 rewritte
Screened Coulomb interactions of general macroions with nonzero particle volume
A semianalytical approach is developed to calculate the effective pair
potential of rigid arbitrarily shaped macroions with a nonvanishing particle
volume, valid within linear screening theory and the mean-field approximation.
The essential ingredient for this framework is a mapping of the particle to a
singular charge distribution with adjustable effective charge and shape
parameters determined by the particle surface electrostatic potential. For
charged spheres this method reproduces the well-known
Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Further exemplary benchmarks
of the method for more complicated cases, like tori, triaxial ellipsoids, and
additive torus-sphere mixtures, leads to accurate closed-form integral
expressions for all particle separations and orientations. The findings are
relevant for determining the phase behaviour of macroions with experiments and
simulations for various particle shapes.Comment: V2: 9 pages, 5 figures; Appendix: 6 pages, 5 figure
Periodic solutions for a class of evolution inclusions
We consider a periodic evolution inclusion defined on an evolution triple of
spaces. The inclusion involves also a subdifferential term. We prove existence
theorems for both the convex and the nonconvex problem, and we also produce
extremal trajectories. Moreover, we show that every solution of the convex
problem can be approximated uniformly by certain extremal trajectories (strong
relaxation). We illustrate our results by examining a nonlinear parabolic
control system
Double-phase problems with reaction of arbitrary growth
We consider a parametric nonlinear nonhomogeneous elliptic equation, driven
by the sum of two differential operators having different structure. The
associated energy functional has unbalanced growth and we do not impose any
global growth conditions to the reaction term, whose behavior is prescribed
only near the origin. Using truncation and comparison techniques and Morse
theory, we show that the problem has multiple solutions in the case of high
perturbations. We also show that if a symmetry condition is imposed to the
reaction term, then we can generate a sequence of distinct nodal solutions with
smaller and smaller energies
Impenetrable SU(N) fermions in one-dimensional lattices
We study SU(N) fermions in the limit of infinite on-site repulsion between
all species. We focus on states in which every pair of consecutive fermions
carries a different spin flavor. Since the particle order cannot be changed
(because of the infinite on-site repulsion) and contiguous fermions have a
different spin flavor, we refer to the corresponding constrained model as the
model of distinguishable quantum particles. We introduce an exact numerical
method to calculate equilibrium one-body correlations of distinguishable
quantum particles based on a mapping onto noninteracting spinless fermions. In
contrast to most many-body systems in one dimension, which usually exhibit
either power-law or exponential decay of off-diagonal one-body correlations
with distance, distinguishable quantum particles exhibit a Gaussian decay of
one-body correlations in the ground state, while finite-temperature
correlations are well described by stretched exponential decay.Comment: 13 pages, 13 figure
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