146 research outputs found
Nonlinear Waves in Rods and Beams of Power-Law Materials
Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that propagates without change of forms in time. These waves resemble the usual kink waves except that they do not possess bounded elevations. The special solutions satisfying certain boundary and initial conditions are presented to demonstrate the nonlinear behavior of the materials. This note demonstrates the apparent distinctions between linear elastic and nonlinear plastic waves
Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems
We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences. The two-dimensional system is discretized by the local discontinuous Galerkin (LDG) method on unstructured triangular meshes associated with the piecewise linear finite element spaces, which can derive not only numerical solutions but also approximations for fluxes at the same time comparing with most of study work up to now which has derived numerical solutions only. Considering the stability requirement for the explicit scheme with strict time step restriction (Δt=O(hmin2)), the implicit integration factor (IIF) method is employed for the temporal discretization so that the time step can be relaxed as Δt=O(hmin). Moreover, the method allows us to compute element by element and avoids solving a global system of nonlinear algebraic equations as the standard implicit schemes do, which can reduce the computational cost greatly. Numerical simulations about the system with exact solution and the Brusselator model, which is a theoretical model for a type of autocatalytic chemical reaction, are conducted to confirm the expected accuracy, efficiency, and advantages of the proposed schemes
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The boundary between the Central Asian Orogenic belt and Tethyan tectonic domain deduced from Pb isotopic data
A deformable plate interacting with a non-Newtonian fluid in three dimensions
We consider a deformable plate interacting with a non-Newtonian fluid flow in three dimensions as a simple model problem for fluid-structure-interaction phenomena in life sciences (e.g., red blood cell interacting with blood flow). A power-law function is used for the constitutive equation of the non-Newtonian fluid. The lattice Boltzmann equation (the D3Q19 model) is used for modeling the fluid flow. The immersed boundary (IB) method is used for modeling the flexible plate and handling the fluid-plate interaction. The plate drag and its scaling are studied; the influences of three dimensionless parameters (power-law exponent, bending modulus, and generalized Reynolds number) are investigated
ICAR: Image-based Complementary Auto Reasoning
Scene-aware Complementary Item Retrieval (CIR) is a challenging task which
requires to generate a set of compatible items across domains. Due to the
subjectivity, it is difficult to set up a rigorous standard for both data
collection and learning objectives. To address this challenging task, we
propose a visual compatibility concept, composed of similarity (resembling in
color, geometry, texture, and etc.) and complementarity (different items like
table vs chair completing a group). Based on this notion, we propose a
compatibility learning framework, a category-aware Flexible Bidirectional
Transformer (FBT), for visual "scene-based set compatibility reasoning" with
the cross-domain visual similarity input and auto-regressive complementary item
generation. We introduce a "Flexible Bidirectional Transformer (FBT)"
consisting of an encoder with flexible masking, a category prediction arm, and
an auto-regressive visual embedding prediction arm. And the inputs for FBT are
cross-domain visual similarity invariant embeddings, making this framework
quite generalizable. Furthermore, our proposed FBT model learns the
inter-object compatibility from a large set of scene images in a
self-supervised way. Compared with the SOTA methods, this approach achieves up
to 5.3% and 9.6% in FITB score and 22.3% and 31.8% SFID improvement on fashion
and furniture, respectively
A symplectic dynamics approach to the spatial isosceles three-body problem
We study the spatial isosceles three-body problem from the perspective of
Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and
energy, the dynamics on the energy surface is equivalent to a Reeb flow on the
tight three-sphere. We find a Hopf link formed by the Euler orbit and a
symmetric brake orbit, which spans an open book decomposition whose pages are
annulus-like global surfaces of section. In the case of large mass ratios, the
Hopf link is non-resonant, forcing the existence of infinitely many periodic
orbits. The rotation number of the Euler orbit plays a fundamental role in the
existence of periodic orbits and their symmetries. We explore such symmetries
in the Hill region and show that the Euler orbit is negative hyperbolic for an
open set of parameters while it can never be positive hyperbolic. Finally, we
address convexity and determine for each parameter whether the energy surface
is strictly convex, convex, or non-convex. Dynamical consequences of this fact
are then discussed.Comment: 66 pages, 15 figure
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