相关论文: There is no pointwise consistent quasicontinuum en…
We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilisation mechanism for unstable…
The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method of linearization and fixed point. Coupling between the hyperbolic and parabolic variables is allowed in the linearization and we do…
Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
The $hp$-version of the finite element method is applied to a singularly perturbed reaction-diffusion equation posed in one- and two-dimensional domains with analytic boundary. On suitably designed \emph{Spectral Boundary Layer meshes},…
We study the optical conductivity sigma(Omega) of an electron system near a quantum-critical point with finite-wavelength ordering. sigma(Omega) vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation…
In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows from consistency and stability estimates for the numerical…
We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance…
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of…
Artificial quasicrystals are nowadays routinely manufactured, yet only two naturally occurring examples are known. We present a class of systems with the potential to be realized both artificially and in nature, in which the lowest energy…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
We present a practical implementation of an energy-based atomistic-to-continuum (a/c) coupling scheme without ghost forces, and numerical tests evaluating its accuracy relative to other types of a/c coupling schemes.
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…
We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\Omega \subset \mathbb{R}^n$. We show that the limit varifold derived from the diffused…
Anomalous CP-odd W+W-Z couplings can give rise to a forward-backward asymmetry in the Z angular distribution in the e+e- centre-of-mass frame in the process e+e- -> nu nubar Z. Of the three CP-odd couplings possible, only the imaginary part…
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the…
We consider a spatial analogue of the quantum error correction threshold. Given individual time-independent subsystems in which quantum information is coherent over sufficiently long lengths, we show how the information can be kept coherent…
We present and study a conformally coupled dark energy model, characterised by an interaction between a tachyon field $\phi$, with an inverse square potential $V (\phi)$, and the matter sector. A detailed analysis of the cosmological…
We reanalyze precision LEP data and coupling constant unification in the minimal supersymmetric $SU(5)$ model including the evolution of the gaugino masses. We derive general bounds on the primordial gaugino supersymmetry-breaking…