arXiv subjects

Lingxing Yao

Publications and source records attributed to Lingxing Yao.

3 recordsLinked to original sources

arXiv2026

A Cartesian Grid Method for Advection-Diffusion Equations with Robin Boundary Conditions on Moving Domains

We develop a Cartesian grid method for advection--diffusion equations with Robin boundary conditions on moving domains. The moving-domain problem is reformulated as an interface problem on a box, with an unknown density introduced on the moving interface to enforce the Robin condition. The bulk equation is discretized by a cell-centered finite-difference scheme on the Cartesian grid, while interface corrections are obtained from local problems in a narrow band around the interface. The resulting method requires only modest computational geometry, avoids remeshing and cut cells, and is compatible with geometric multigrid and matrix-free GMRES. The GMRES iteration count is essentially independent of the mesh size, and the computational cost scales linearly with the number of bulk degrees of freedom. For the one-dimensional scheme, first-order convergence in time and second-order convergence in space are proved. Numerical examples in one and two dimensions, including manufactured solutions and an active transport problem without an exact solution, demonstrate the accuracy and efficiency of the method.

math.NA↗

arXiv2024

Chevron patterns in an active nematic liquid crystal film in contact with Smectic A

We study a new mechanism of active matter confinement of a thin, active nematic sample consisting of microtubules, activated by Adenosine Triphosphate (ATP), placed between a slab of passive liquid crystal, the compound 8CB, and water. The 8CB slab is kept at a temperature below the phase transition value between the nematic and the smectic A phases. The smectic A molecules are horizontally aligned with an applied magnetic field, with their centers of mass arranged on equally spaced layers perpendicular to the field. The contact with the active nematic prompts flow in the smectic slab, along the direction parallel to the layers. This flow direction is transferred back to the active nematic. We set up a model of such contact flow and make predictions on the experimentally observed pattern, from the point of view of asymptotic, linear and nonlinear analyses. We examine such results within the scope of the principle of minimum energy dissipation of the flow. For analytic convenience, we consider the active nematic confined between two symmetric 8CB slabs, and show that the conclusions still hold when replacing the bottom smectic A substrate with water, as in the experimental setting.

cond-mat.soft↗

arXiv2016

Rhythmomimetic drug delivery: modeling, analysis and numerical simulation

We develop, analyse and numerically simulate a model of a prototype, glucose-driven, rhythmic drug delivery device, aimed at hormone therapies, and based on chemomechanical interaction in a polyelectrolyte gel membrane. The pH-driven interactions trigger volume phase transitions between the swollen and collapsed states of the gel.For a robust set of material parameters, we find a class of solutions of the governing system that oscillate between such states, and cause the membrane to rhythmically swell, allowing for transport of the drug, fuel and reaction products across it, and collapse, hampering all transport across it. The frequency of the oscillations can be adjusted so that it matches the natural frequency of the hormone to be released. The work is linked to extensive laboratory experimental studies of the device built by Siegel's team. The thinness of the membrane and its clamped boundary, together with the homogeneously held conditions in the experimental apparatus, justify neglecting spatial dependence on the fields of the problem. Upon identifying the forces and energy relevant to the system, and taking into account its dissipative properties, we apply Rayleigh's variational principle to obtain the governing equations. The material assumptions guarantee the monotonicity of the system and lead to the existence of a three dimensional limit cycle. By scaling and asymptotic analysis, this limit cycle is found to be related to a two-dimensional one that encodes the volume phase transitions of the model. The identification of the relevant parameter set of the model is aided by a Hopf bifurcation study of steady state solutions.

physics.chem-ph↗