Phase-space invariants for aggregates of particles: hyperangular momenta and partitions of the classical kinetic energy

Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.     

Comparison of experimental time-of-flight spectra of the HF products from the F+H2 reaction with exact quantum mechanical calculations

High resolution HF product time-of-flight spectra measured for the reactive scattering of F atoms from n-H2(p-H2) molecules at collision energies between 69 and 81 meV are compared with exact coupled-channel quantum mechanical calculations based on the Stark-Werner ab initio ground state potential energy surface. Excellent agreement between the experimental and computed rotational distributions is found for the HF product vibrational states v'=1 and v'=2. For the v'=3 vibrational state the agreement, however, is less satisfactory, especially for the reaction with p-H2. The results for v'=1 and v'=2 confirm that the reaction dynamics for these product states is accurately described by the ground electronic state 1 (2)A' potential energy surface. The deviations for HF(v'=3, j' > or =2) are attributed to an enhancement of the reaction resulting from the 25% fraction of excited ((2)P(12)) fluorine atoms in the reactant beam.     

The special features of rotationally resolved differential cross sections of the F + H2 reaction at small scattering angles

We studied the nature and collision energy dependence of the maximum that appears in the angular distributions of the HF (v′ = 3) product of the F + H₂ (v = 0; j = 0, 1, 2) → H + HF (v′, j′) reaction at small scattering angles θ in the center-of-mass frame. This maximum and its increase as the collision energy increased were discovered in the well-known experiment described by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985). In order to determine the nature of the maximum, we performed quantum-mechanical simulation of the reaction on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol corresponding to the above-mentioned experiment and calculated the vibrationally and rotationally resolved differential cross sections dσ_v′j′/dΩ of the reaction. The maximum under consideration was found to be due to a superposition of two effects, namely, the absence of HF (v′ = 3; j′) products with large j′ because of energy restrictions and an increase in the relative amplitude of quantum-mechanical oscillations on dσ_v′j′/dΩ cross sections at small j′ and θ as v′ increased. Oscillations on dσ_3j′ /dΩ cross sections with small j′ are responsible for the maximum observed.     

Covariant derivatives of a spinor in finsler geometry

The aim of the author in the present article is to introduce covariant derivatives of a spinor into Finsler geometry and to show that such an operation is not only interesting from the purely mathematical point of view but also from the physical one since it is thus possible to extend the spinor theory of Heisenberg [1] to the Finsler space [2] (and, in particular, to the Riemann space [3]). The covariant form of the spinor theory of matter is essentially a nonlinear theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 2, pp. 43–49, February, 1973.     

Chirally symmetric equation for a massive fermion field

An attempt is made to construct an equation analogous to the Dirac equation, but which has chiral symmetry. The most natural equation of this type is a nonlinear equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 87–89, November, 1981.     

Evolution of a pair of classical ions in a cavity with elastic walls,crosspieces, and implanted charges

Using the method of classical trajectories, we have simulated the motion of a pair of oppositely charged ions in spherical and ellipsoidal cavities, including cavities that contain cylindrical “crosspieces” and positively charged “nuclei.” We supposed that each of the ions reflected off the cavity wall, crosspieces, and nuclei according to the elastic impact law. Most of attention is focused on the statistics of the events of ion recombination and those of dissociation of the corresponding molecule with an ionic bond. When nuclei are absent, recombination and dissociation events are possible only on collisions of the ions with the cavity wall or crosspieces. In the presence of nuclei, on the other hand, the major part of the events occur in time intervals between the collisions of the ions with the cavity wall, crosspieces, or nuclei.     

Structure of small hydrogen nanoclusters containing ortho-molecules

Using the quantum mechanical path integral Monte Carlo method, we simulated parahydrogen clusters (j = 0) and clusters doped with several (up to 6) orthohydrogen molecules (j = 1), with the total number of molecules ranging from 4 to 40 at temperatures of 1.5, 3, and 4.5 K. Some energy parameters (including the chemical potentials) and spatial characteristics of the clusters are found. At a temperature of 1.5 K, as the total number N of molecules in the cluster increases, the chemical potential and the rotational energy of the clusters attain local minima at the same geometrically determined values of N (the magic numbers). The ortho-molecules exhibit a larger probability (compared to the para-molecules) to reside in the central region of the cluster and a smaller probability to be located near its surface. This effect is enhanced as the number of orthohydrogen molecules in the cluster increases, the total number N of molecules grows, or the temperature is lowered.     

CONTROLLING THE 3D NANOSCALE ORGANIZATION OF BULK HETEROJUNCTION POLYMER SOLAR CELLS

In this study,the three dimensional nanoscale organization in the photoactive layers of poly(3-hexylthiophene) (P3HT) and a methanofullerene derivative (PCBM) is revealed by transmission electron tomography.After annealing treatment,either at elevated temperature or during slow solvent evaporation,nanoscale interpenetrating networks are formed with high crystalline order and favorable concentration gradients of both components through the thickness of the photoactive layer.Such a tailored morphology acco...     

Specific heats of clusters near a phase transition: Energy partitions among internal modes

This Letter proposes a way to answer the question of how energy is shared by internal degrees of freedom, when nanoaggregates are heated and undergo phase transitions. Microcanonical molecular dynamics simulations of clusters of 13 and 55 atoms are assisted by our analysis of energy partitions in terms of contributions connected with groups of degrees of freedom of the nanoaggregates. The merit of the partition is shown to be the effective decoupling of modes, demonstrating its role as an indicator of the phase transitions and its perspective use for statistical mechanical approaches by the identification of active degrees of freedom.