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Notes on nonsingular models of black holes Open
We discuss static spherically symmetric metrics which represent non-singular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild a…
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How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Open
The chemotaxis-Navier-Stokes system \begin{equation*} (\star )\qquad \qquad \qquad \quad \begin {cases} n_t + u\cdot \nabla n & =\ \ \Delta n - \nabla \cdot (n\chi (c)\nabla c),\\[1mm] c_t + u\cdot \nabla c & =\ \ \Delta c-nf(c), \\[1mm] u…
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Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change Open
In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Hea…
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Fractional Kirchhoff problems with critical Trudinger–Moser nonlinearity Open
This paper is concerned with the existence of solutions for a class of fractional Kirchhoff-type problems with Trudinger–Moser nonlinearity: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left( \displaystyle \iint _{{\mathbb {R}}^{2N}}\fra…
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Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption Open
This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system $\left\{ \begin{align} & {{u}_{t}}=\Delta u-\chi \nabla \cdot \left( u\nabla v \right)+\kappa u-\mu {{u}^{2}},\ \ \ \ \ \ \ x\in \ma…
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Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime Open
This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such diffus…
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Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality Open
The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety M-<= k of real mxn matrices of rank at most k. Such methods extend Riemannian optimization methods, which are successful…
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Stabilization in a chemotaxis model for tumor invasion Open
This paper deals with the chemotaxis system\[\begin{cases}u_t=\Delta u - \nabla \cdot (u\nabla v),\qquad x\in \Omega, \ t>0, \\v_t=\Delta v + wz,\qquad x\in \Omega, \ t>0, \\w_t=-wz,\qquad x\in \Omega, \ t>0, \\z_t=\Delta z - z + u, \qquad…
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Monotonicity results for fractional difference operators with discrete exponential kernels Open
We prove that if the Caputo-Fabrizio nabla fractional difference operator $({}^{\mathrm{CFR}}_{a-1}\nabla^{\alpha}y)(t)$ of order $0<\alpha\leq1$ and starting at $a-1$ is positive for $t=a,a+1,\ldots$ , then $y(t)$ is α-increasing. Convers…
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Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system Open
We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equation\begin{eqnarray*} \left\{\begin{array}{lll} n_t + u \cdot \nabla n = \Delta n - \chi\nabla\cdot(n \nabla c),&{} x\in\Omega,\ t>0,\\ c_t +…
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Non-convex Finite-Sum Optimization Via SCSG Methods Open
We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods , for the smooth nonconvex finite-sum optimization problem. Only assuming the smoothness of each component, the complexity of…
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Boundedness vs.blow-up in a two-species chemotaxis system with two chemicals Open
We consider a model for two species interacting throughchemotaxis in such a way that each species produces a signal which directs the respective motion of the other. Specifically, we shall be concerned with nonnegative solutions of the Neu…
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Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems Open
In this paper, combining the ideas of exponential integrators and discrete gradients, we propose and analyze a new structure-preserving exponential scheme for the conservative or dissipative system $\dot{y} = Q(M y + \nabla U (y))$, where …
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Global stabilization of the full attraction-repulsion Keller-Segel system Open
We are concerned with the following full Attraction-Repulsion Keller-Segel (ARKS) system\begin{document}$\left\{ {\begin{array}{*{20}{l}}{{u_t} = \Delta u - \nabla \cdot (\chi u\nabla v) + \nabla \cdot (\xi u\nabla w),}&{x \in \Omega ,t > …
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SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS Open
A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth ve…
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What are we learning from the relative orientation between density structures and the magnetic field in molecular clouds? Open
\n We investigate the conditions of ideal magnetohydrodynamic (MHD) turbulence responsible for the relative orientation between density gradients (∇ρ) and magnetic fields (B) in molecular clouds (MCs). For that purpose, we construct an exp…
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Finite-time blow-up in a degenerate chemotaxis system with flux limitation Open
This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by StartLayout 1st Row with Label left-parenthesis reverse-solidus star right-parenthesi…
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Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps Open
In this paper we study the regularity of stationary and minimizing harmonic maps $f:B_2(p)\subseteq M\to N$ between Riemannian manifolds. If $S^k(f)\equiv\{x\in M: \text{ no tangent map at $x$ is }k+1\text{-symmetric}\}$ is $k^{th}$-stratu…
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Global classical solutions of a 3D chemotaxis-Stokes system with rotation Open
This paper considers the chemotaxis-Stokes system$$\begin{cases}\displaystyle n_t+u\cdot\nabla n=\Deltan-\nabla\cdot(nS(x,n,c)\cdot\nabla c),&(x,t)\in \Omega\times (0,T),\\\displaystylec_t+u\cdot\nabla c=\Delta c-nc, &(x,t)\in\Omega\times …
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Molecular geometric phase from the exact electron-nuclear factorization Open
The Born-Oppenheimer electronic wavefunction $\\Phi_R^{BO}(r)$ picks up a\ntopological phase factor $\\pm 1$, a special case of Berry phase, when it is\ntransported around a conical intersection of two adiabatic potential energy\nsurfaces …
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The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in L1 Open
In bounded n -dimensional domains Ω , the Neumann problem for the parabolic equation $$\begin{array}{} \displaystyle u_t = \nabla \cdot \Big( A(x,t)\cdot\nabla u\Big) + \nabla \cdot \Big(b(x,t)u\Big) - f(x,t,u)+g(x,t) \end{array}$$ (*) is …
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Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness Open
We develop foundational theory for the Laplacian flow for closed G2 structures which will be essential for future study. (1). We prove Shi-type derivative estimates for the Riemann curvature tensor Rm and torsion tensor T along the flow, i…
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Early-time dynamics of gluon fields in high energy nuclear collisions Open
Nuclei colliding at very high energy create a strong, quasi-classical gluon\nfield during the initial phase of their interaction. We present an analytic\ncalculation of the initial space-time evolution of this field in the limit of\nvery h…
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Ground state solutions for Hamiltonian elliptic system with inverse square potential Open
In this paper, we study the following Hamiltonian elliptic system with gradient term and inverse square potential$ \left\{ \begin{array}{ll}-\Delta u +\vec{b}(x)\cdot \nabla u +V(x)u-\frac{\mu}{|x|^{2}}v=H_{v}(x,u,v)\\-\Delta v -\vec{b}(x)…
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Sub-sampled Newton Methods with Non-uniform Sampling Open
We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We cons…
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Global dynamics in a fully parabolic chemotaxis system with logistic source Open
In this paper, we consider a fully parabolic chemotaxis system\begin{eqnarray*}\label{1}\left\{\begin{array}{llll}u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+u-\mu u^r,\quad &x\in \Omega,\quad t>0,\\v_t=\Delta v-v+u,\quad &x\in\Omega,\quad t>0…
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Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems Open
We consider the no-flux initial-boundary value problem for Keller-Segel-type chemotaxis growth systems of the form $\begin{eqnarray*} ≤\left\{ \begin{array}{ll} u_t=Δ u -χ \nabla · (u\nabla v) + ρ u -μ u^2, & x∈Ω, \ t>0, \\ v_t=Δ v -v+u, &…
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NEW DEVELOPMENTS IN WEIGHTED n-FOLD TYPE INEQUALITIES VIA DISCRETE GENERALIZED ℏ-PROPORTIONAL FRACTIONAL OPERATORS Open
This study explores some significant consequences of discrete [Formula: see text]-proportional fractional sums [Formula: see text] having an exponential function as a nonlocal kernel. Certain novel weighted versions comprising a group of p…
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Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension Open
We develop two families of mixed finite elements on quadrilateral meshes for approximating $({\mathbf u},p)$ solving a second order elliptic equation in mixed form. Standard Raviart--Thomas (RT) and Brezzi--Douglas--Marini (BDM) elements a…
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Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity Open
This paper deals with the two-species chemotaxis-competition system $\left\{ {\begin{array}{*{20}{l}}{{u_t} = {d_1}\Delta u - \nabla \cdot (u{\chi _1}(w)\nabla w) + {\mu _1}u(1 - u - {a_1}v)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\\{{v_t…