Singularities in the gravitational capture of dark matter through long-range interactions

We re-examine the gravitational capture of dark matter (DM) through long-range interactions. We demonstrate that neglecting the thermal motion of target particles, which is often a good approximation for short-range capture, results in parametrically inaccurate results for long-range capture. When the particle mediating the scattering process has a mass that is small in comparison to the momentum transfer in scattering events, correctly incorporating the thermal motion of target particles results in a quadratic, rather than logarithmic, sensitivity to the mediator mass, which substantially enhances the capture rate. We quantitatively assess the impact of this finite temperature effect on the captured DM population in the Sun as a function of mediator mass. We find that capture of DM through light dark photons, as in e.g. mirror DM, can be powerfully enhanced, with self-capture attaining a geometric limit over much of parameter space. For visibly-decaying dark photons, thermal corrections are not large in the Sun, but may be important in understanding long-range DM capture in more massive bodies such as Population III stars. We additionally provide the first calculation of the long-range DM self-evaporation rate.

Micrometer Sized Hexagonal Chromium Selenide Flakes for Cryogenic Temperature Sensors

Nanoscale thermometers with high sensitivity are needed in domains which study quantum and classical effects at cryogenic temperatures. Here, we present a micrometer sized and nanometer thick chromium selenide cryogenic temperature sensor capable of measuring a large domain of cryogenic temperatures down to tenths of K. Hexagonal Cr-Se flakes were obtained by a simple physical vapor transport method and investigated using scanning electron microscopy, energy dispersive X-ray spectrometry and X-ray photoelectron spectroscopy measurements. The flakes were transferred onto Au contacts using a dry transfer method and resistivity measurements were performed in a temperature range from 7 K to 300 K. The collected data have been fitted by exponential functions. The excellent fit quality allowed for the further extrapolation of resistivity values down to tenths of K. It has been shown that the logarithmic sensitivity of the sensor computed over a large domain of cryogenic temperature is higher than the sensitivity of thermometers commonly used in industry and research. This study opens the way to produce Cr-Se sensors for classical and quantum cryogenic measurements.

On a repulsion Keller–Segel system with a logarithmic sensitivity

In this paper, we study the initial-boundary value problem of a repulsion Keller–Segel system with a logarithmic sensitivity modelling the reinforced random walk. By establishing an energy–dissipation identity, we prove the existence of classical solutions in two dimensions as well as existence of weak solutions in the three-dimensional setting. Moreover, it is shown that the weak solutions enjoy an eventual regularity property, i.e., it becomes regular after certain time T > 0. An exponential convergence rate towards the spatially homogeneous steady states is obtained as well. We adopt a new approach developed recently by the author to study the eventual regularity. The argument is based on observation of the exponential stability of constant solutions in scaling-invariant spaces together with certain dissipative property of the global solutions in the same spaces.

Global and exponential attractor of the repulsive Keller–Segel model with logarithmic sensitivity

We consider a Keller–Segel model that describes the cellular chemotactic movement away from repulsive chemical subject to logarithmic sensitivity function over a confined region in ${{\mathbb{R}}^n},\,n \le 2$ . This sensitivity function describes the empirically tested Weber–Fecher’s law of living organism’s perception of a physical stimulus. We prove that, regardless of chemotaxis strength and initial data, this repulsive system is globally well-posed and the constant solution is the global and exponential in time attractor. Our results confirm the ‘folklore’ that chemorepulsion inhibits the formation of non-trivial steady states within the logarithmic chemotaxis model, hence preventing cellular aggregation therein.

Recent results for the logarithmic Keller-Segel-Fisher/KPP System

We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. It is a 2 by 2 system describing the interaction of cells and a chemical signal. We study Cauchy problem with finite initial data, i.e., without the commonly used smallness assumption on initial perturbations around a constant ground state. We survey a sequence of recent results by the authors on the existence of global-in-time solution, long-time behavior, vanishing coefficient limit and optimal time decay rates of the solution.

Existence of a Nontrivial Steady-State Solution to a Parabolic-Parabolic Chemotaxis System with Singular Sensitivity

This paper establishes the existence of a nontrivial steady-state solution to a parabolic-parabolic coupled system with singular (or logarithmic) sensitivity and nonlinear source arising from chemotaxis. The proofs mainly rely on the maximum principle, the implicit function theorem, and the Hopf bifurcation theorem.