Related papers: A remark on Li-Xu's pathology

In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…

Let $X$ be a finite aspherical CW-complex whose fundamental group $\pi_1(X)$ possesses a subnormal series $\pi_1(X) \rhd G_m \rhd ... \rhd G_0$ with a non-trivial elementary amenable group $G_0$. We investigate the $L^2$-invariants of the…

We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative…

Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate $\phi$ dominates the inverse of the chemotactic motility function…

We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields $\phi$ whose Lagrangian is non-canonical and of the form $\mathcal{L}(X,\phi)=-V(\phi)F(X)$, with $X=\frac{1}{2} g_{\mu\nu}…

We present results of a linear stability analysis of relativistic detonation fronts, which have been considered as representing phase interfaces in cosmological first order phase transitions. After discussing general stability conditions…

Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear…

This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…

We study the motion of topological defects in 1+1 and 2+1 d relativistic $\phi^6$ model with three equal vacua in the presence of radiation. We show that even small fluctuations can trigger a chain reaction leading to vanishing of…

An analysis of adiabatic perturbations of a perfect fluid is performed to first-order about a general FLRW background using the 1+3 covariant and gauge-invariant formalism. The analog of the Mukhanov-Sasaki variable and the canonical…

We study anomalous diffusion for one-dimensional systems described by a generalized Langevin equation. We show that superdiffusion can be classified in slow superdiffusion and fast superdiffusion. For fast superdiffusion we prove that the…

This paper is devoted to the study of various aspects of projectable F(R) Horava-Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and instable flat space solution. In this case, the…

We consider a disordered asymmetric exclusion process in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. We solve the steady state…

For smooth test configurations, there always exist C^{1,1} geodesic rays in Kahler metric space parallel to the algebraic ray. The $\yen$ invariant agrees with Futaki invariant, at least under nice assumptions. Explicit examples in Toric…

We present calculations of structure functions using a renormalization scheme consistent expansion which is leading order in both ln(1/x) and \alpha_s(Q^2). There is no factorization scheme dependence, and the ``physical anomalous…

In the family grand unification models (fGUTs), we propose that gauge U(1)'s beyond the minimal GUT gauge group are family gauge symmetries. For the symmetry $L_\mu-L_\tau$, i.e. $Q_{2}-Q_{3}$ in our case, to be useful for the LHC anomaly,…

By applying the Chen-Jiang decomposition, we prove that the non-vanishing conjecture holds for an lc pair \((X, \Delta)\), where \(X\) is an irregular variety, provided it holds for lower-dimensional varieties. In the second part, we extend…

A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the large N limit. In this way we make precise and concrete the notion of a non-perturbative gauge invariant…

We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry,…

We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable…