Abstract This article establishes cutoff thermalization (also known as the phenomenon ) for a class of generalized Ornstein–Uhlenbeck systems $$(X^\varepsilon _t(x))_{t\geqslant 0}$$ (Xt?(x<...

We study support recovery for a $$k \times k$$ principal submatrix with elevated mean $$\lambda /N$$ , hidden in an $$N\times N$$ symmetric zero Gaussian matrix. Here >0$$ is universal constant, and we assume = N \rho $$ some constant $$\rho \in (0,1)$$ . establish that there exists $$C>0$$ such the MLE recovers proportion of if {\ge C} \sqrt{\frac{1}{\rho } \log \frac{1}{\rho }}$$ while inform...

Raman spectra of hexagonal close-packed iron (varepsilon-Fe) have been measured from 15 to 152 gigapascals by using diamond-anvil cells with ultrapure synthetic diamond anvils. The results give a Gruneisen parameter gamma(0) = 1.68 (+/-0.20) and q = 0.7 (+/-0.5). Phenomenological modeling shows that the Raman-active mode can be approximately correlated with an acoustic phonon and thus provides ...

We demonstrate a composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability &mgr;(eff)(omega) and permittivity varepsilon(eff)(omega). This structure forms a "left-handed" medium, for which it has been predicted...

We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends long-wavelength limitations conventional homogenization estimates arbitrary microstructures so that it can capture spatial dispersion well beyond quasistatic regime (w...

Abstract In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in settings queries asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model k made parallel each round, and...

We consider the stochastic heat equation $$\partial _{s}u =\frac{1}{2}\Delta u +(\beta V(s,y)-\lambda )u$$ ? s = 1 2 ? + ( ? V , y ) - ? with a smooth space-time-stationary Gaussian random field V(s, y), in dimensions $$d\ge 3$$ d ? 3 an initial condition $$u(0,x)=u_0(\varepsilon x)$$ 0 x ? and suitably chosen $$\lambda \in {\mathbb {R}}$$ ? R . It is known that, for $$\beta $$ small enough, di...

This work is devoted to studying non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in domain. In its simplest form, for each $\varepsilon>0$ fixed, we seek non-negative function $u^{\varepsilon}$ satisfying $$ \begin{cases} \left\[|\nabla u^{\varepsilon}|^p + \mathfrak{a}(x)|\nabla u^{\varepsilon}|^q \right] \De...