arXiv subjects

Qiang Tao

Publications and source records attributed to Qiang Tao.

10 recordsLinked to original sources

arXiv2026

Self-induced crystalline fluctuation spin-glass state in Mn7C3 binary compounds

Crystalline spin glasses are attractive compounds owing to their unique nature and applications. Here, we synthesised a bulk Pnma-type Mn7C3 spin glass by a high-temperature, high-pressure method. Experimental characterisation including X-ray diffraction and magnetic susceptibility measurements demonstrated that the compound has a triangular Ising-model-based structure, high freezing temperature of 37.4 K, and novel competition mechanism. Theoretical calculations and simulations revealed that the triangular Mn units are spontaneously frustrated and bridge neighbouring Mn units via polarised C atoms and messenger Mn atoms. Triangular C units each share one electron within a three-pronged electron cloud. This electron is the direct cause of frustration and competition in Mn7C3. The competition within the triangular Mn units suggests that the possible magnetic configurations are highly degenerate and that the Mn7C3 spin glass has high robustness. This work introduces a new family of spin glasses with ordered microgeometries that drive electronic structure disorder, and an application-friendly spin-glass material for use in fields like high-efficiency hardware and algorithm design in artificial intelligence.

cond-mat.mtrl-sci↗

arXiv2025

Asymptotic behavior of solutions to a singular chemotaxis system in multi-dimensions

In this paper, we investigate the optimal large-time behavior of the global solution to a singular chemotaxis system in the whole space $\mathbb{R}^d$ with $d=2,3$. Assuming that the initial data is sufficiently close to an equilibrium state, we first prove the $k$-th order spatial derivative of the global solution converges to its corresponding equilibrium at the optimal rate $(1+t)^{-(\frac{d}{4}+\frac{k}{2})}$, which improve upon the result in [37]. Then, for well-chosen initial data, we also establish lower bounds on the convergence rates, which match those of the heat equation. Our proof relies on a Cole-Hopf type transformation, delicate spectral analysis, the Fourier splitting technique, and energy methods.

math.AP↗

arXiv2023

Exact controllability to nonnegative trajectory for a chemotaxis system

This paper studies the controllability for a Keller-Segel type chemotaxis model with singular sensitivity. Based on the Hopf-Cole transformation, a nonlinear parabolic system, which has first-order couplings, and the coupling coefficients are functions that depend on both time and space variables, is derived. Then, the controllability result is proved by a new global Carleman estimate for general coupled parabolic equations allowed to contain a convective term. Also, the global existence of nonnegative solution for the chemotaxis system is discussed.

math.OC↗

arXiv2022

Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large oscillations, the initial density may allowed to contain vacuum states. Furthermore, the large-time behavior of the solution is obtained.

math.AP↗

arXiv2021

Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity

In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established under the condition that the scaling invariant quantity $ (\|ρ_0\|_\infty+1)\big[\|ρ_0\|_3+(\|ρ_0\|_\infty+1)^2(\|\sqrt{ρ_0}u_0\|_2^2+ \|\nabla d_0\|_2^2)\big] \big[\|\nabla u_0\|_2^2+(\|ρ_0\|_\infty+1)(\|\sqrt{ρ_0}E_0\|_2^2 + \|\nabla^2 d_0\|_2^2)\big]$ is sufficiently small with the smallness depending only on the parameters appeared in the system.

math.AP↗

arXiv2017

Nanotwinned diamond synthesized from multi-core onion carbon

Nano-polycrystalline diamond (NPD) and nanotwinned diamond (NtD) were successfully synthesized in multi-anvil high pressure apparatus at high pressure and high temperature (HPHT) conditions using precursors of onion carbons. We found that the choices of distinct onion carbons with hollow or multi-cored microstructures lead to the synthesis of different diamond products of NPD or NtD ones. High quality NtD with an average twin size of 6.8 nm has been synthesized whose Vickers hardness reaches as high as 180 GPa as measured by indentation hardness experiment. The existence of stacking faults other than various defects in the onion carbon is found to be crucial to form twin boundary in the product. The origin of the extraordinarily high Vickers hardness in the NtD sample is attributable to the high concentration of twin boundary. Our work gave a direct support on the argument that pursuit of nanotwinned microstructure is an effective strategy to harden materials, in good coincidence with the well-known Hall-Petch effect.

cond-mat.mtrl-sci↗

arXiv2015

Optimal Decay Rates of Classical Solutions for the Full Compressible MHD Equations

In this paper, we are concerned with optimal decay rates for higher order spatial derivatives of classical solutions to the full compressible MHD equations in three dimensional whole space. If the initial perturbation are small in $H^3$-norm and bounded in $L^q(q\in \left[1, \frac{6}{5}\right))$-norm, we apply the Fourier splitting method by Schonbek[Arch. Rational Mech. Anal. 88 (1985)] to establish optimal decay rates for the second order spatial derivatives of solutions and the third order spatial derivatives of magnetic field in $L^2$-norm. These results improve the work of Pu and Guo [Z. Angew. Math. Phys. 64 (2013) 519-538].

math.AP↗

arXiv2015

Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in $\mathbb{R}^3$

In this paper, we investigate the Cauchy problem for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the time decay rates for compressible nematic liquid crystal flows by the method of spectral analysis and energy estimates. Furthermore, we enhance the convergence rates for the higher-order spatial derivatives of density, velocity and director. Finally, the time decay rates of mixed space-time derivatives of solution are also established.

math.AP↗

arXiv2015

Strong Solution to the Density-dependent Incompressible Nematic Liquid Crystal Flows

In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows in $n(n=2$ or $3)$ dimensional bounded domain. More precisely, we obtain the local existence and uniqueness of the solutions when the viscosity coefficient of fluid depends on density. Moreover, we establish blowup criterions for the regularity of the strong solutions in dimension two and three respectively. In particular, we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration. For these results, the initial density needs not be strictly positive.

math.AP↗

arXiv2015

Asymptotic Behavior of Solution to the Incompressible Nematic Liquid Crystal Flows in R^3

In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small initial data. Furthermore, the time decay rates of velocity and director are built when the initial data belongs to $L^1(\mathbb{R}^3)$ additionally. Finally, one also constructs the time convergence rates for the mixed space-time derivatives of velocity and director.

math.AP↗