Related papers: Disclinations in limiting Landau-de Gennes theory
Energy minimizers to a MEMS model with an insulating layer are shown to converge in its reinforced limit to the minimizer of the limiting model as the thickness of the layer tends to zero. The proof relies on the identification of the…
As a sequel to our previous analysis in [9] arXiv:2202.09411 on the Gross-Pitaevskii equation on the product space $\mathbb{R} \times \mathbb{T}$, we construct a branch of finite energy travelling waves as minimizers of the Ginzburg-Landau…
The planar bistable device [Tsakonas \textit{et al., Appl. Phys. Lett.}, 2007, {\textbf{90}}, 111913] is known to have two distinct classes of stable equilibria: the diagonal and rotated solutions. We model this device within the…
We study minimizers $\boldsymbol{m}\colon \mathbb R^2\to\mathbb S^2$ of the energy functional \begin{align*} E_\sigma(\boldsymbol{m}) = \int_{\mathbb R^2} \bigg(\frac 12 |\nabla\boldsymbol{m}|^2 +\sigma^2 \boldsymbol{ m} \cdot \nabla…
We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface $M$. More specifically, we show that for every energy larger than the maximal energy of a constant orbit…
The spatial distribution of electric current under magnetic field and the resultant orbital magnetism have been studied for two-dimensional electrons under a harmonic confining potential $V(\vecvar{r})=m \omega_0^2 r^2/2$ in various regimes…
Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken…
We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ and mildly repulsive at the origin; moreover, if the minimizer is global, then its…
The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of…
The high temperature limit of a system of two D-0 branes is investigated. The partition function can be expressed as a power series in $\beta$ (inverse temperature). The leading term in the high temperature expression of the partition…
We study two minimization questions: the nature of curves $\gamma \subset \mathbb{H}$ which minimize the Loewner energy among all curves from 0 to a fixed $z_0 \in \mathbb{H}$, and the nature of $\gamma$ which minimize the Loewner energy…
Starting from the quasi one-dimensional kinetic energy of the d_{yz} and d_{zx} bands we derive a bosonized description of the correlated electron system in Sr_2RuO_4. At intermediate coupling the magnetic correlations have a quasi…
The heat capacity of low-dimensional spin systems is studied using theoretical and numerical techniques. Keeping only two energy states, the system is mapped onto the two -level-system (TLS) model. Using the low temperature Lanczos method,…
In this paper, we study the relaxed energy for biharmonic maps from a $m$-dimensional domain into spheres. By an approximation method, we prove the existence of a minimizer of the relaxed energy of the Hessian energy, and that the minimizer…
We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the…
We prove a $\Gamma$-convergence result for a class of Ginzburg-Landau type functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is a closed and $(k-2)$-connected submanifold of $\mathbb{R}^m$, in arbitrary dimension. This…
In this paper, we build up a min-max theory for minimal surfaces using sweepouts of surfaces of genus $g\geq 2$. We develop a direct variational methods similar to the proof of the famous Plateau problem by J. Douglas and T. Rado. As a…
The magnetization for electrons on a two-dimensional sphere, under a spherically symmetrical normal magnetic field has been studied in the large field limit. This allows us to use an Euclidean approximation for low energies electron states…
We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass…
A low energy bound in a class of chiral solitonic field theories related the infrared physics of the SU(N) Yang-Mills theory is established.