arXiv subjects

Peiyao Liu

Publications and source records attributed to Peiyao Liu.

5 recordsLinked to original sources

arXiv2026

Vortex-core Majorana coupling to a chiral edge in a $p_x+ip_y$ superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics

We study how vortex--edge coupling reorganizes the low-energy sector of a finite two-dimensional $p_x+ip_y$ superconducting disk as a function of the vortex--boundary separation $d$ and examine what this reorganization implies for the parity memory associated with a prescribed vortex-core Majorana wave packet, a resource relevant to Majorana-based quantum operations. Bogoliubov--de Gennes calculations reveal nonmonotonic core--edge reorganization of the lowest positive-energy finite-disk eigenstate, with particularly rapid variation near $d\simeq7\xi$, where $\xi$ is the coherence length. To separate this eigenstate reorganization from the spectral representation of a prescribed state, we rigidly translate a centered-vortex core-reference packet to each fixed vortex position, restrict it to the target disk, and project it, without intermediate normalization, onto the particle-hole-complete low-energy subspace. For $\Delta_0/E_F=0.36$ and disk radius $R=30\xi$, the resulting retained norm exceeds $0.98$ at all six sampled separations, $4.25\leq d/\xi\leq8.25$, while, depending on $d$, the spectral measure is concentrated near zero energy, fragmented over several low-energy levels, or dominated by finite-energy weight. Correspondingly, the signed parity correlator displays slow temporal variation, rapid coherent dephasing, or sign-changing oscillations, with possible finite-size recurrences at later times. Thus a large retained norm does not by itself imply spectral concentration or persistent parity memory.

cond-mat.supr-con↗

arXiv2026

From Local to Global Symmetry: Activation Dynamics in the Independent Cascade Model on Undirected Graphs

The independent cascade model is a widely used framework for simulating the spread of influence in social networks. In this model, activations propagate stochastically through the network, with each edge having a probability of transmitting activation. We study the independent cascade model on undirected graphs with symmetric influence probabilities ($p_{ij} = p_{ji}$ for all nodes $i$ and $j$). We focus on persistent activations, where activated nodes remain active indefinitely. Our main result is to demonstrate that this local symmetry in the graph structure induces a global symmetry in the activation dynamics. Specifically, the probability of node $j$ being activated within $n$ steps, starting with only node $i$ activated, equals the probability of node $i$ being activated within $n$ steps, starting with only node $j$ activated, for all $n$. We establish this result using a novel approach based on random matrices, offering a fresh perspective on the model.

math.PR↗

arXiv2026

Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media

This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface evolution is described by the Cahn-Hilliard equation. Applying the volume averaging method, we rigorously derive upscaled equations that characterize the Darcy-scale behavior of the two-phase system. The derivation yields unclosed terms originating from spatial derivations, which are subsequently closed by modeling them as functions of averaged quantities and specific transport coefficients. These coefficients are evaluated by solving localized closure problems defined on representative elementary volumes (REVs). A key contribution of this study is the formal incorporation of wetting behavior into the averaged chemical potential. We further discuss the theoretical distinctions between the proposed framework and standard empirical two-phase Darcy models. Finally, numerical simulations of the upscaled equations are performed, demonstrating the model's capability to capture essential two-phase flow characteristics in porous media.

physics.flu-dyn↗

arXiv2025

An Automated Theorem Generator with Theoretical Foundation Based on Rectangular Standard Contradiction

Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation theory and tool. Based on the concept of standard contradiction which possesses unique deductive advantages, this paper defines and proves, for the first time, a new logical structure known as rectangular standard contradiction. Centered on this structure, a complete Automated Theorem Generation (ATG) theory is put forward. Theoretical proofs clarify two core properties of rectangular standard contradiction: first, it is a standard contradiction (necessarily unsatisfiable); second, it exhibits non-redundancy (the remaining clause set becomes satisfiable after removing any clause). Leveraging these properties, this paper proves that partitioning a rectangular standard contradiction into a premise subset $A$ and negation of its complement $H$, a valid theorem $A \vdash \neg H$ can be formed, and all such theorems are logically equivalent. To implement this theory, an efficient template-based ATG algorithm is designed, and a Rectangular Automated Theorem Generator is developed. This research enables machines to transition from "verifiers" to "discoverers", opening up new avenues for fundamental research in the fields of logic and artificial intelligence.

cs.LO↗

arXiv2023

A well-balanced lattice Boltzmann model for binary fluids based on the incompressible phase-field theory

Spurious velocities arising from the imperfect offset of the undesired term at the discrete level are frequently observed in numerical simulations of equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE) method. To capture the physical equilibrium state of two-phase fluid systems and eliminate spurious velocities, a well-balanced LBE model based on the incompressible phase-field theory is developed. In this model, the equilibrium distribution function for the Cahn-Hilliard (CH) equation is designed by treating the convection term as a source to avoid the introduction of undesired terms, enabling achievement of possible discrete force balance. Furthermore, this approach allows for the attainment of a divergence-free velocity field, effectively mitigating the impact of artificial compression effects and enhancing numerical stability. Numerical tests, including a flat interface problem, a stationary droplet, and the coalescence of two droplets, demonstrate the well-balanced properties and improvements in the stability of the present model.

physics.flu-dyn↗