arXiv subjects

Siyuan Deng

Publications and source records attributed to Siyuan Deng.

3 recordsLinked to original sources

arXiv2025

Phase engineering of 1T$'$ and 1T CrS2 and Cr2S3 by MOCVD

Layered Cr-chalcogenides compounds offer a rich range of crystal phases with different magnetic properties some of which have been predicted only but not experimentally verified. Here we demonstrate a previously unreported crystal phase of CrS2, namely the distorted octahedral (1T$'$) structure, synthesized via metal-organic chemical vapour deposition (MOCVD). We achieved the tuneable synthesis of either 1T$'$ or 1T phase CrS2. The structure were identified using polarized Raman spectroscopy, density functional perturbation theory (DFPT), as well as scanning electron diffraction (4D-STEM). 4D-STEM reveals that 1T$'$ crystals grow from an originally nucleated kinetically favoured 1T phase which then transform into the thermodynamically stable 1T$'$ phase. Magneto-optic Kerr imaging reveals that the 1T$'$ CrS2 crystals have soft ferromagnetic nature at low temperature. Our MOCVD growth of complex phases of 2D CrS2 with long-range magnetic order paves the way for the scalable synthesis of 2D magnets for ultrathin magnetic memories for logic-in-memory applications and spintronics.

cond-mat.mtrl-sci↗

arXiv2024

Contributions to the Algorithmic Foundations of Approximate Lie Symmetry Algebras of Differential Equations

Lie symmetry transformations that leave a differential equation invariant play a fundamental role in science and mathematics. Such Lie symmetry groups uniquely determine their Lie symmetry algebras. Exact differential elimination algorithms have been developed to determine the dimension and structure constants of the Lie symmetry algebra of an exact polynomially nonlinear differential equation. Directly applying these symbolic algorithms to approximate models is prone to instability since these algorithms strongly depend on the orderings of the variables involved. This motivates the need to address questions at the algorithmic foundation of approximate Lie symmetry algebras of differential equations. How do we define approximate Lie symmetry? How do we compute and apply approximate Lie symmetry algebras of differential equations? How reliable are the results? To address such questions, we define approximate Lie symmetry algebras in terms of exact Lie symmetry algebras of a nearby differential equation. Our algorithm for identifying these hidden approximate Lie symmetry algebras uses the SVD to find nearby rank-deficient systems combined with approximate geometric involutive forms of the approximate symmetry-defining systems. Our approach is local and depends on an input base point in the space of independent and dependent variables. In general, our local approach can yield many different nearby Lie symmetry algebras. We also outline a numerical approach to determining the approximate isomorphic of such Lie symmetry algebras as the local base point varies across a grid in the base space. We also provide a method for evaluating the reliability of our results. This enables the base space to be partitioned into regions where different local Lie symmetry algebras are admitted, separated by unstable transition regions.

math-ph↗

arXiv2024

Algorithmic reduction of polynomially nonlinear PDE systems to parametric ODE systems

Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the inclusion of missing integrability conditions and the statement of of existence and uniqueness theorems for local analytic solutions of such systems. Further, they are useful in obtaining systems in a form more amenable to exact and approximate solution methods. Maple's \maple{dsolve} and \maple{pdsolve} algorithms for solving PDE and ODE often automatically call such routines during applications. Indeed, even casual users of Maple's dsolve and pdsolve commands have probably unknowingly used Maple's differential-elimination algorithms. Suppose that a system of PDE has been reduced by differential-elimination to a system whose automatic existence and uniqueness algorithm has been determined to be finite-dimensional. We present an algorithm for rewriting the output as a system of parameterized ODE. Exact methods and numerical methods for solving ODE and DAE can be applied to this form.

cs.SC↗