Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.

Gelatin-stabilized traditional emulsions:Emulsion forms,droplets,and storage stability

Fish oils are important substances in the field of food and drug delivery.Due to their unstable double bonds,fishy taste,and poor water solubility,it is pivotal to investigate novel dosage forms for fish oils,such as encapsulated droplets.In this work,we primarily prepared gelatin-stabilized fish oil-loaded traditional emulsions and investigated their emulsion forms,droplets,and storage stability under different preparation and storage conditions.Our results showed that higher gelatin solution pH,higher storage temperature in the range of 4–37℃,and increased storage time induced the emulsion form switch from a liquid form to a redispersible gel form of the fish oil emulsion.The droplets had core-shell microstructures and a trimodal size distribution,which decreases linearly with increasing gelatin solution pH and homogenizing time,but decreases exponentially with increasing homogenizing speed.In addition,storage temperature showed a notably different effect on traditional emulsion storage.This work provides a fundamental knowledge for the formation,microstructure,and properties of gelatin-based traditional emulsions.It also provides a promising new application for fish oil-loaded emulsions in food beverages,soft candy,and other food products.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

Existence theory for Rosseland equation and its homogenized equation

The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

Velocity Calculation by Automatic Camera Calibration Based on Homogenous Fog Weather Condition

A novel algorithm for vehicle average velocity detection through automatic and dynamic camera calibration based on dark channel in homogenous fog weather condition is presented in this paper. Camera fixed in the middle of the road should be calibrated in homogenous fog weather condition, and can be used in any weather condition. Unlike other researches in velocity calculation area, our traffic model only includes road plane and vehicles in motion. Painted lines in scene image are neglected because sometimes there are no traffic lanes, especially in un-structured traffic scene. Once calibrated, scene distance will be got and can be used to calculate vehicles average velocity. Three major steps are included in our algorithm. Firstly, current video frame is recognized to discriminate current weather condition based on area search method （ASM）. If it is homogenous fog, average pixel value from top to bottom in the selected area will change in the form of edge spread function （ESF）. Secondly, traffic road surface plane will be found by generating activity map created by calculating the expected value of the absolute intensity difference between two adjacent frames. Finally, scene transmission image is got by dark channel prior theory, camera s intrinsic and extrinsic parameters are calculated based on the parameter calibration formula deduced from monocular model and scene transmission image. In this step, several key points with particular transmission value for generating necessary calculation equations on road surface are selected to calibrate the camera. Vehicles pixel coordinates are transformed to camera coordinates. Distance between vehicles and the camera will be calculated, and then average velocity for each vehicle is got. At the end of this paper, calibration results and vehicles velocity data for nine vehicles in different weather conditions are given. Comparison with other algorithms verifies the effectiveness of our algorithm.

GROUNDWATER MASS TRANSPORT AND HOMOGENEOUS EQUILIBRIUM CHEMISTRY IN THE PRESENCE OF FLUX BOUNDARY CONDITIONS

Considering a solute transport problem deseribed by some algebraic and partial differentialequations with the presence of flux boundary conditions, we reduce the problem to a fixed point oneand use a priori estimates to prove the existence and uniqueness of the global solutions.

The Initial Boundary Value Problem for Navier-Stokes Equations

By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equations in arbitrary three dimensional domain with uniformly C3 boundary, under the assumption that ‖a‖L^2(Ω)+‖f‖L^1(o,∞;L^2(Ω)) or‖▽a‖L^2(Ω)+‖f‖L^2(o,∞;L^2(Ω)) small or viscosity, large. Here a is a given initial velocity and f is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.

Numerical Study of Quantized Vortex Interaction in theGinzburg-Landau Equation on Bounded Domains

In this paper,we study numerically quantized vortex dynamics and their interaction in the two-dimensional(2D)Ginzburg-Landau equation(GLE)with a dimensionless parameter#>0 on bounded domains under either Dirichlet or homogeneous Neumann boundary condition.We begin with a reviewof the reduced dynamical laws for time evolution of quantized vortex centers in GLE and show how to solve these nonlinear ordinary differential equations numerically.Then we present efficient and accurate numerical methods for discretizing the GLE on either a rectangular or a disk domain under either Dirichlet or homogeneous Neumann boundary condition.Based on these efficient and accurate numerical methods for GLE and the reduced dynamical laws,we simulate quantized vortex interaction of GLE with different#and under different initial setups including single vortex,vortex pair,vortex dipole and vortex lattice,compare them with those obtained from the corresponding reduced dynamical laws,and identify the cases where the reduced dynamical laws agree qualitatively and/or quantitatively as well as fail to agree with those from GLE on vortex interaction.Finally,we also obtain numerically different patterns of the steady states for quantized vortex lattices under the GLE dynamics on bounded domains.