We investigate doping of a single-layer graphene in the presence of electrolytic top gating. The interfacial phenomenon is modeled using a modified Poisson-Boltzmann equation for an aqueous solution of simple salt. We demonstrate both the sensitivity of graphene's doping levels to the salt concentration and the importance of quantum capacitance that arises due to the smallness of the Debye scre...

The goal of this paper is to reconstruct a collection of small inclusions inside a homogeneous object by applying a heat flux and measuring the induced temperature on its boundary. Taking advantage of the smallness of the inclusions, we design efficient non-iterative algorithms for locating the inclusions from boundary measurements of the temperature. We illustrate the feasibility and the viabi...

Non-zero neutrino masses and mixing angles provide at the moment the only convincing evidence 1 of physics beyond the standard model. A paradigm to understand the smallness of neutrino masses, involving some new heavy states which break lepton number, is called the seesaw mechanism 2. If the heavy particles couple to the Standard Model lepton and Higgs doublets, decoupling of them generates at ...

We find all possible relations among physical observables arising from neutrino mass matrices that describe in a natural way the currently observed pattern (θ23 and θ12 large, ∆m 2 ⊙/∆m 2 Atm and θ13 small) in terms of a minimum number of parameters. Natural here means due only to the relative smallness (vanishing) of some parameters in the relevant lagrangian, without special relations or acci...

Anthropic solutions to the cosmological constant problem require seemingly unnatural scalar field potentials with a very small slope or domain walls (branes) with a very small coupling to a four-form field. Here we introduce a class of models in which the smallness of the corresponding parameters can be attributed to a spontaneously broken discrete symmetry. We also demonstrate the equivalence ...

We consider a model for the interaction of a gas with photons. In the article [10], smooth traveling wave solutions called shock profiles have been constructed under a suitable smallness assumption between the asymptotic states. In this work, we construct piecewise smooth traveling wave solutions that connect two asymptotic states with a large jump. In particular, we give a rigorous mathematica...

Abstract Wave scattering by many (M = M(a)) small bodies, at the boundary of which an interface boundary condition is imposed, is studied. Smallness of the bodies means that ka << 1, where a is the characteristic dimension of the body and k = 2π λ is the wave number in the medium in which small bodies are embedded. Equation for the effective field is derived in the limit as a → 0, M(a)→∞, at a ...

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.

It is shown that plane wave solutions to the cubic nonlinear Schrödinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend to arbitrary negative powers of the smallness parameter. The perturbation stays small in the same Sobolev norm over such long times. The proof uses a Hamiltoni...