Variation Of Potential Parameters Research Articles

Cavity-altered thermal isomerization rates and dynamical resonant localization in vibro-polaritonic chemistry

It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affects the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in the presence of a single-cavity mode of varying frequency and coupling strength. A topological analysis of the related cavity Born-Oppenheimer potential energy surface in combination with quantum mechanical and transition state theory rate calculations reveals two quantum effects, leading to decelerated reaction rates in qualitative agreement with experiments: the stiffening of quantized modes perpendicular to the reaction path at the transition state, which reduces the number of thermally accessible reaction channels, and the broadening of the barrier region, which attenuates tunneling. We find these two effects to be very robust in a fluctuating environment, causing statistical variations of potential parameters, such as the barrier height. Furthermore, by solving the time-dependent Schrödinger equation in the vibrational strong coupling regime, we identify a resonance behavior, in qualitative agreement with experimental and earlier theoretical work. The latter manifests as reduced reaction probability when the cavity frequency ωc is tuned resonant to a molecular reactant frequency. We find this effect to be based on the dynamical localization of the vibro-polaritonic wavepacket in the reactant well.

Higher-dimensional soliton generation, stability and excitations of the [formula omitted]-symmetric nonlinear Schrödinger equations

We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schrödinger equation. In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra. Also, continuous families of fundamental and higher-order solitons are produced. The fundamental states are shown to be stable, while the higher-order ones, including 1D multimodal solitons, 2D solitons, and 3D light bullets, are unstable. Further, we find that the stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells of the GS-II type, which opens the way for manipulations of optical solitons. Solitons may also be transformed into stable forms by means of adiabatic variation of potential parameters. Finally, an alternative type of n-dimensional PT-symmetric GS-II potentials is reported too. These results will be useful to further explore the higher-dimensional PT-symmetric solitons and to design the related physical experiments.

Investigation of Λ*)1405) resonant formation by using the energy spectrum of triton in stopped kaon absorption on 4He

To determine the position of quasi-bound state, the triton kinetic energy spectrum in the resonant capture of at rest in is calculated by a coupled-channel procedure. An analysis of theoretical spectra to experimental data yielded the mass and width of , respectively, and, where a possible population of and a small p-orbit capture contribution are taken into account. The calculations show that by the variation of potential parameters (range parameter, , and strength parameter,), the mass and width of are almost independent of the potential parameters.

A simulation based research on chance constrained programming in robust facility location problem

Abstract Since facility location decisions problem include long-term character and potential parameter variations, it is important to consider uncertainty in its modeling. This paper examines robust facility location problem considering supply uncertainty, in which we assume the supply of the facility in the actual operation is not equal to the supply initially established, the supply is subject to random fluctuation. The chance constraints are introduced when formulating the robust facility location model to make sure the system operate properly with a certain probability while the supply fluctuates. The chance constraints are approximated safely by using Hoeffding’s inequality and the problem is transformed to a general deterministic linear programming. Furthermore, how the facility location cost change with confidence level is investigated through a numerical example. The sensitivity analysis is conducted for important parameters of the model and we get the main factors that affect the facility location cost.

Robust Transportation Network Design Modeling with Regret Value

Based on long-term transportation network design decisions and potential parameter variations, it is important that demand uncertainty is considered in transportation modeling. In this paper, we present a novel robustness measure that combines the two objectives by minimizing the expected travel time while bounding the relative regret in each scenario facing uncertain origin-destination demand (OD demand). The concept of α-robust solution is introduced into the transportation network design problem. We propose a robust transportation network design model with regret value constraints, then design an algorithm based on the genetic algorithm to solve the problem and obtain the optimal solutions for different regret values. Finally, numerical results based on the Nguyen-Dupuis network validate the effectiveness of the algorithm. While detailed analysis on trade-offs, between the expected travel time and the maximum regret value, shows that large reductions in maximum regret do not necessarily result in a great increase in expected travel time. Meanwhile, we compared the robust model presented with the stochastic model and numerical examples demonstrate that the robust planning network is more reliable and less risky than the stochastic model if demand uncertainty is considered in modeling.

Robust Design Optimization of Flexible Backswept Wings with Structural Uncertainties

ROBUST design method, which was originally presented by Taguchi [1] to improve product quality so that structural performances were insensitive to the potential parameter variations, have been gradually applied to the designs of engineering structures [2–4]. However, the structures presented in these robust designs are relatively simple, and the aeroelastic problems that are critical in the design of modern aircraft are not primarily involved. In recent years, some efforts have been contributed to the consideration of uncertainties in aeroelastic design [5–9]; meanwhile, a few methods such as -k method [7], polynomial chaos method [9], and response surface method [10] have been developed to advance robust aeroelastic analysis and enhance aeroelastic stability. Nevertheless, the uncertainties of structural design variables in robust aeroelastic optimization are not taken into account in most studies. The objective of this research is to develop a method for robust aeroelastic optimization with structural parameter uncertainties, based on a genetic algorithm. The current work focuses on introducing the robust aeroelastic constraints into the process of optimization, and a deterministic estimate is used to account for parameter variations. Comparing with the traditional optimization method, the capability of robust method is then demonstrated by its application to the complicated structural designs of flexible composite high-aspectratio wings with various backswept angles.

Determination of Structure Candidates of Simple CrystallineAB2Systems

The potential energy surface of the fluorides and chlorides of magnesium and calcium is studied using a global optimization method (simulated annealing). Emerging configurations exhibit a structure variance very similar to that of real crystallineAB2systems. The local minima suggest new possible structure types inAB2systems. The influence of the variation of potential parameters on the resulting configurations is investigated and discussed.

Half- and full-collision VT energy transfer in the HeBr 2(B) system

The ability of model interaction potentials, inverted from spectroscopic data on the He…Br 2 (BO u +) van der Waals complex, to reproduce vibrationally inelastic He + Br 2(B) collision rates is examined. It is found that spectroscopic potentials and which quantitatively describe vibrational predissociation of the complex (or half-collision VT energy transfer) are valid for full-collision VT rate constants as well. The sensitivity of half- and full-collision rate coefficients to the variations of potential parameters is analyzed.

Trajectory modeling of organic chemiionization reactions

We have used a Monte Carlo trajectory calculation to model the chemiionization reaction, HI+B→I−+HB+. B is, in our experiments, a polyatomic amine, but the model treats it as a single atom. The reaction occurs on two potential energy surfaces, one covalent dissociating to the reactants, and one ionic corresponding to the products. Several restrictions were included in the model to account for the fact that B is really a molecule. Classical trajectories were then run at a range of energies and for several variations of potential parameters. The model showed that the reactive cross section rises rapidly as a function of translational energy and that the dynamic threshold energy is 0.38 eV higher than the minimum energy required to form the products. Product angular distributions at low energies show a peak in the forward direction but give a large amount of scattering at and behind the center of mass, in qualitative agreement with the experiments. As the energy increases, the distribution shifts to smaller angles. The Coulomb interaction in the ionic surface introduces some novel features not seen in most reactions.

Berechnung von thermodynamischen Isotopieeffekten einfacher Fluide über Quantenkorrekturen und isotopiebedingte Unterschiede in Potentialparametern

Formulae are given for thermodynamic isotope effects of simple fluids. These fluids are here treated as hard-sphere and square-well systems. A special method, the micropotential method, is used for the calculation oj classical thermodynamic functions. Quantum corrections to these functions are also given. Isotope effects due to the variation of the total mass (mass effects) are related to the estimation of quantum corrections of thermodynamic functions. Isotope effects due to the variation of potential parameters (potential effects) are calculated for methane. The potential effects of methnne are of the same order of magnitude as the corresponding mass effects.

Sensitivity analysis of differential cross sections to the intermolecular potential

This paper considers the sensitivity of both final state summed and state to state differential cross sections to the variation of parameters within a model intermolecular potential. In order to simplify the calculation of the cross sections and first order sensitivity coefficients (i.e., the partial derivative of cross sections with respect to potential parameters) attention is restricted to the scattering of an atom and rigid rotor. Furthermore, the collision dynamics are approximated by using the infinite order sudden (IOS) approximation. Particular emphasis is given to an examination of the sensitivity of angular features of the cross sections to potential parameter variations. This is facilitated by fitting the cross sections to functional forms which contain several adjustable parameters, each of which controls a particular feature. First order sensitivity coefficients are then used to derive quantitities which measure the sensitivity of a ’’feature parameter’’ with respect to the variation of a potential parameter. The first order sensitivities are also used to obtain so called derived sensitivity coefficients and, in particular, those which describe how the potential parameters are interrelated for a given set of cross section measurements. The behavior of these coefficients is examined as the angular range of the measurements is varied and as account is taken of the finite angular resolving power of molecular beam detectors. The results are used to determine the degree to which a set of differential cross section measurements is able to define various parameters of the assumed potential.

Mobility and Diffusion. II. Dependence on Experimental Variables and Interaction Potential for Alkali Ions in Rare Gases

Formulae derived in Part I are used here to calculate mobility and diffusion coefficients for K + ions in helium and in neon gases. The formulae are evaluated by inverting truncated matrices, and the effect of using successively larger matrices is investigated numerically. It is found that close agreement with the measurement .of ion mobilities can be obtained over a significant range of values of E/no .and this determines the potential parameters of an assumed 12-6-4 potential within narrow limits. Diffusion coefficients are calculated from the potential so obtained. The sensitivity of the mobility to variations in potential parameters is discussed and some observations of interest for future experiments are made.

Rotational relaxation in the Ar—N 2 system

The first ( Z (1)) and second ( Z (2)) approximations to the rotational number of the Ar—N 2 system are compared for a range of temperatures. Although Z (1) and Z (2) differ by a significant amount their difference remains nearly constant as a function of temperature. The effects of mass and potential parameter variations on the rotational relaxation time are also studied. When the mass of the incoming atom is decreased Z (2) goes through a minimum while Z (1) steadily increases.