The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation

In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R_2^ + = \left\{ {\left( {x,y} \right):x > 0,y > 0} \right\}.$ They contain Kummer's confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain $\Omega \subset R_2^ +.$ Using the method of Green's functions, solution of this problem is found in an explicit form.Comment: 11 page

Dynamic Active Earth Pressure Against Retaining Walls

Equations of equilibrium expressed along the stress characteristics are transformed onto the Zero Extension Line (ZEL) directions. The new dynamic equilibrium equations are then applied to simple ZEL field (composed of Rankine, Goursat, and Coulomb zones) behind retaining walls. Integration of differential equilibrium equations along the assumed field boundary, thus provide the final equations for the active static (Kast) and dynamic (Kady) earth pressure coefficients, which are functions of friction and dilation angles of the soil and friction angle of the wall surface. Numerical evaluation of Kast, and Kady indicates that these coefficients are not sensitive to the wall roughness for practical values of angle of friction of backfill material between 35° and 45°. In this range, the coefficients can be approximated by: Kast=tan2(π/4 -φ/2) and Kady =tan(π/4 - ν/2)

Valley-selective energy transfer between quantum dots in atomically thin semiconductors

In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electronhole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct- gap transition by assuming that the interaction between two quantum dots is described by a Coulomb potential, which allows us to include all relevant multipole terms of the interaction. We demonstrate the structural control of the valley-selective energy transfer between quantum dots