Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schrödinger / Gross-Pitaevskii Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, and ...

An influence of the quantum potential on the Chern–Simons solitons leads to quantization of the statistical parameter κ = me/g, and the quantum potential strenght s = 1 − m. A new type of exponentially localized Chern–Simons solitons for the Bloch electrons near the hyperbolic energy band boundary are found.

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using the two-mode approach. Starting from Bloch states, we succeed to get analytical solutions for the TD Schrödinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well...

We consider Bloch equations which govern the evolution of the density matrix of an atom (or: a quantum system) with a discrete set of energy levels. The system is forced by a time dependent electric potential which varies on a fast scale and we address the long time evolution of the system. We show that the diagonal part of the density matrix is asymptotically solution to a linear Boltzmann equ...

Introduction: Prostate cancer (PCa) is the most prevalent malignant tumor in the male population worldwide and it is the second leading cause of cancer-related death in males. PCa is almost incurable due to the resistance of PCa to conventional treatments. Cancer stem cells (CSCs) theory suggests that a small subpopulation of cancer cells is responsible for tumor development, ...

Lightning protection design for a structure using Rolling Sphere Method is undertaken. In this case radius of the sphere is calculated using the ‘Leader Potential Concept’ for calculating striking distance. The purpose is to evaluate lightning protection performance based on the ‘Leader Potential Concept’. It is also demonstrated how low grounding resistance and bonding could be used to mitigat...

Background. The double haul is a unique feature of single-handed fly casting and is used in both fly fishing and fly casting competition. The movement behaviour during the double haul has not been investigated in previous research. Objectives. Describe the coordination of the rod and line hauling movements during distance fly casting. Methods. Elite fly casters performed distance castin...

The addition of low concentrations of the hydrotropic salt p-toluidine hydrochloride (PTHC) to solutions of the anionic surfactant sodium dodecyl sulfate (SDS) promotes the transition from spherical to rodlike micelles. NMR measurements confirm that the hydrotrope adsorbs at the micelle-water interface, thereby screening electrostatic repulsions between the surfactant headgroups. The sphere-to-...

Regulation of rod gene expression has emerged as a potential therapeutic strategy to treat retinal degenerative diseases like retinitis pigmentosa (RP). We previously reported on a small molecule modulator of the rod transcription factor Nr2e3, Photoregulin1 (PR1), that regulates the expression of photoreceptor-specific genes. Although PR1 slows the progression of retinal degeneration in models...