Related papers: Asymptotic behavior of critical points of an energ…
Coleman-Weinberg (CW) phenomena for the case of gravitons minimally coupled to massless scalar field is studied. The one loop effect completely vanishes if there is no self interaction term present in the matter sector. The one loop…
Let $\Omega \subset \mathbb{R}^n$ be a bounded smooth domain (open and connected) in $\mathbb{R}^n$. Given $u_0\in L^2(\Omega)$, $g\in L^\infty(\Omega)$ and $\lambda \in \mathbb{R}$, our purpose is to describe the asymptotic behavior of…
Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical…
We consider a critical quasilinear operator $-\Delta_p u +V|u|^{p-2}u$ in $\mathbb{R}^N$ perturbed by a weakly coupled potential. For $N>p$, we find the leading asymptotic of the lowest eigenvalue of such an operator in the weak coupling…
In this paper, we study that the nearly critical nonlocal problem \begin{equation*} \left\lbrace \begin{aligned} &-\Delta u=(|x|^{-{(n-2)}}\ast u^{p-\epsilon})u^{p-1-\epsilon} \quad \mbox{in}\quad \Omega, &u>0\quad…
We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…
We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a…
For the mean-field version of an important lattice-spin model due to Blume and Capel, we prove unexpected connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials…
In this paper we demonstrate that coordinate noncommutativity at short distances can show up in critical phenomena through UV-IR mixing. In the symmetric phase of the Landau-Ginsburg model, noncommutativity is shown to give rise to a…
We present the critical exponents $\nu_{L2}$, $\eta_{L2}$ and $\gamma_{L}$ for an $m$-axial Lifshitz point at second order in an $\epsilon_{L}$ expansion. We introduced a constraint involving the loop momenta along the $m$-dimensional…
We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest…
We consider Gaussian random monochromatic waves $u$ on the plane depending on a real parameter $s$ that is directly related to the regularity of its Fourier transform. Specifically, the Fourier transform of $u$ is $f\,d\sigma$, where…
In this paper we study the behaviour of critical points of the Ginzburg-Landau perturbation of the Dirichlet energy into the sphere $E_\varepsilon(u):=\int_\Sigma \frac{1}{2}|du|^2_h\ \,dvol_h…
The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to…
We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). $$ The asymptotic behavior proves to…
We study the asymptotic behavior of finite energy $\rm{SU}(2)$ monopoles, and general critical points of the $\rm{SU}(2)$ Yang--Mills--Higgs energy, on asymptotically conical $3$-manifolds with only one end. Our main results generalize…
We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation $$ -\Big(a+b\int_{\mathbb R^N}|\nabla u|^2\Big)\Delta u+ \lambda u= u^{q-1}+ u^{p-1} \quad {\rm in} \ \mathbb R^N, $$ as $\lambda\to 0$ and…
\[ \left\{ \begin{array} [c]{lll} -\left( \Delta_{p}+\Delta_{q(p)}\right) u=\lambda_{p}\left\vert u(x_{u})\right\vert ^{p-2}u(x_{u})\delta_{x_{u}} & \mathrm{in} & \Omega\\ u=0 & \mathrm{on} & \partial\Omega, \end{array} \right. \] where…
Motivated by the recent numerical results of Khalid et al., Phys. Rev. Lett., 127, 134502 (2021), we consider the large-Weissenberg-number ($W$) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The…
A new description is proposed for the low-field critical behavior of type-II superconductors. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular…