On nonlinear boundary value problem corresponding to N-dimensional inverse spectral problem

We establish a relationship between an inverse optimization spectral problem for the N-dimensional Schrödinger equation $?\mathrm{\Delta }?+q(x)?=\lambda ?$ and a solution of the nonlinear boundary value problem $?\mathrm{\Delta }u+q(x)u=\lambda u?u^{\gamma ?1},u>0,u{|}_{?\mathrm{\Omega }}=0$. Using this relationship, we find an exact solution for the inverse optimization spectral problem, investigate its stability and obtain new results on the existence and uniqueness of the solution for the nonlinear boundary value problem.     

Full Analytic Spectrum of Generalized Jaynes-Cummings Hamiltonians

Theoretical and Mathematical Physics - We develop an analytic formalism using basic quantum mechanics techniques to successfully solve the multiphoton Jaynes–Cummings and the generalized...     

Novel parameter estimation techniques for a multi-term fractional dynamical epidemic model of dengue fever

Numerical Algorithms - An inverse problem to identify parameters for the single-term (and multi-term) fractional-order system of an outbreak of dengue fever is considered. Firstly, we propose a...     

Solid-State NMR Spectroscopy: A Powerful Technique to Directly Study Small Gas Molecules Adsorbed in Metal–Organic Frameworks

Metal–organic frameworks (MOFs) have shown great potential in gas separation and storage, and the design of MOFs for these purposes is an on-going field of research. Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is a valuable technique for characterizing these functional materials. It can provide a wide range of structural and motional insights that are complementary to and/or difficult to access with alternative methods. In this Concept article, the recent advances made in SSNMR investigations of small gas molecules (i.e., carbon dioxide, carbon monoxide, hydrogen gas and light hydrocarbons) adsorbed in MOFs are discussed. These studies demonstrate the breadth of information that can be obtained by SSNMR spectroscopy, such as the number and location of guest adsorption sites, host–guest binding strengths and guest mobility. The knowledge acquired from these experiments yields a powerful tool for progress in MOF development.     

Flamelet structure in turbulent premixed swirling oxy-combustion of methane

Two key flame macrostructures in swirling flows have been observed in experiments of oxy-combustion (as well as air-combustion); as the equivalence ratio is raised, the flame moves from being stabilized on just the inner shear layer (Flame III) to getting stabilized on both the inner and outer shear layers (Flame IV). We report results of an LES investigation of two different inlet oxy-fuel mixtures, in a turbulent swirling flow at $\text{Re}=20,000,$ that capture these two macrostructures. Previous work on the effects of heat loss have mostly focused on its impact on macro-scale observations. In this paper, we examine how heat loss impacts the flame microstructures as well for these two macrostructures. For both flames, the flamelet structure, as represented by a scatter plot of the normalized fuel concentration against the normalized temperature, depends on whether the combustor walls are adiabatic or non-adiabatic. For the adiabatic case, the flamelets of both macrostructures behave like strained flames. When wall heat transfer is included, Flame III microstructure is more bimodal. Since this flame extends farther downstream and part of it propagates along the walls, heat transfer has a greater impact on it’s microstructure. These results show that heat loss impacts not just the macro properties of the flame such as its shape or interactions with the wall, but also fundamentally changes its internal structure. Scatter plots of the turbulent flames are constructed and compared to different 1D laminar flame profiles (e.g., strained or with heat loss), and comparisons suggest the important role of the wall thermal boundary conditions in the accurate simulations of combustion dynamics and interpretations of experimental data, including data reduction and scaling.     

Mathematical Modeling of Complex Oscillations of Flexible Micropolar Mesh Cylindrical Panels

Russian Physics Journal - A new mathematical model of oscillations of mesh micropolar geometrically nonlinear cylindrical panels under the action of a normal alternating distributed load has been...     

Acoustic Signals Induced in a Copper Target under Irradiation by a Low-Energy High-Current Electron Beam

Russian Physics Journal - Results of investigations of acoustic signals induced in a copper plate irradiated with a microsecond lowenergy high-current electron beam (LEHCEB) are presented. The...     

Counterion-Trapped-Molecules: From High Polarity and Enriched IR Spectra to Induced Isomerization

We report extensive computational studies of some novel intermolecular systems and their properties. Recombination of alkali-halide counterions separated by a noncovalently trapped hydrocarbon molecule is prevented by significant potential energy barriers, resulting in unusual metastable insertion complexes. These systems are extremely polar, while the inserted molecule is strongly counter-polarized, leading to significant cooperative nonadditivity effects. The compression and electric field produced by the counterions favours isomerization of the trapped molecule via a significant reduction of the barriers to bond rearrangement, in a field-induced mechanochemical process. The predicted IR intensity spectra clearly reflect (1) formation of the insertion complex, rather than simple attachment of alkali halide, and (2) isomerization of the trapped molecule, thus allowing experimental access to these events.