Let Ω ⊂ Rd, d ≥ 3, be a bounded Lipschitz domain. For Laplace’s equation ∆u = 0 in Ω, we study the Dirichlet and Neumann problems with boundary data in the weighted space L2(∂Ω, ωαdσ), where ωα(Q) = |Q−Q0|α, Q0 is a fixed point on ∂Ω, and dσ denotes the surface measure on ∂Ω. We prove that there exists ε = ε(Ω) ∈ (0, 2] such that the Dirichlet problem is uniquely solvable if 1 − d < α < d − 3 +...

Spatial configurations of randomly charged polymers, known as polyampholytes (PAs), are very sensitive to the overall excess charge Q. Analytical arguments, supported by Monte Carlo simulations and exact enumeration studies, lead to the following picture: For Q < Qc ≈ q0 √ N (q0 is the elementary charge, N is the number of monomers in the polymer), the radius of gyration Rg of the polymer decre...

In this paper, we first present the THex algorithm that refines a tetrahedral mesh into a hexahedral mesh. Strategies for efficient implementation of the THex algorithm are discussed. Then we present the lowest order weak Galerkin (WG) (Q0, Q0;RT[0]) finite element method for solving the Darcy equation on general hexahedral meshes. This simple solver uses constant pressure unknowns inside hexah...

We investigate the spectrum and wave functions of q0q0 bound states for heavy fourth generation quarks (q0) that have a very small mixing with the three observed generations of standard model quarks. Such bound states come with different color, spin and flavor quantum numbers. Since the fourth generation Yukawa coupling, q0 , is large we include all perturbative corrections to the potential bet...

We use perturbative QCD to calculate the parton level cross section for the production of two jets that are far apart in rapidity, subject to a limitation on the total transverse momentum Q0 in the interjet region. We specifically address the question of how to combine the approach which sums all leading logarithms in Q/Q0 (where Q is the jet transverse momentum) with the BFKL approach, in whic...

DGLAP evolution equations may be presented in a form completely analogous to the Boltzmann equation. This provides a natural proof of the positivity of the spin-dependent parton distributions, provided the initial distributions at Q0 are also positive. In addition, the evolution to Q2 < Q0 may violate positivity, providing therefore a ’time arrow’. The positivity condition is just |∆Pij(z)| ≤ P...

We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent thermal conductivity and a convective term with a constant temperature boundary condition or a heat flux boundary condition of the type −q0/ √ t (q0 > 0) at the fixed face x = 0. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the simi...

We consider polymers formed from a (quenched) random sequence of charged monomers of opposite signs. Such polymers, known as polyampholytes (PAs), are compact when completely neutral and expanded when highly charged. We examine the transition between the two regimes by Monte Carlo simulations, and by analogies to charged drops. We find that the overall excess charge, Q, is the main determinant ...