A unified theory of available potential energy

Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together with energy conservation. This raises the questions of why such constructions are required in the first place, and whether there is some general method of deriving the available potential energy for an arbitrary fluid system. By appealing to the underlying Hamiltonian structure of geophysical fluid dynamics, it becomes clear why energy conservation is not enough, and why other conservation laws such as mass conservation need to be incorporated in order to construct an invariant, known as the pseudoenergy, that is a positive‐definite functional of disturbance quantities. The available potential energy is just the non‐kinetic part of the pseudoenergy, the construction of which follows a well defined algorithm. Two notable features of the available potential energy defined thereby are first, that it is a locally defined quantity, and second, that it is inherently definable at finite amplitude (though one may of course always take the small‐amplitude limit if this is appropriate). The general theory is made concrete by systematic derivations of available potential energy in a number of different contexts. All the well known expressions are recovered, and some new expressions are obtained. The possibility of generalizing the concept of available potential energy to dynamically stable basic flows (as opposed to statically stable basic states) is also discussed.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.

Non-Hermitian multichannel theory of ultracold collisions modified by intense light fields tuned to the red of the trapping transition

We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances, In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial d wave. We apply the scheme to calculate the S matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning, We also obtain, fur this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory. [S1050-2947(98)04902-6].

Kinetic simulation of neutral∕ionized gas and electrically charged dust in the coma of comet 67P∕Churyumov-Gerasimenko

The cometary coma is a unique phenomenon in the solar system being a planetary atmosphere influenced by little or no gravity. As a comet approaches the sun, the water vapor with some fraction of other gases sublimate, generating a cloud of gas, ice and other refractory materials (rocky and organic dust) ejected from the surface of the nucleus. Sublimating gas molecules undergo frequent collisions and photochemical processes in the near‐nucleus region. Owing to its negligible gravity, comets produce a large and highly variable extensive dusty coma with a size much larger than the characteristic size of the cometary nucleus. The Rosetta spacecraft is en route to comet 67P/Churyumov‐Gerasimenko for a rendezvous, landing, and extensive orbital phase beginning in 2014. Both, interpretation of measurements and safety consideration of the spacecraft require modeling of the comet’s dusty gas environment. In this work we present results of a numerical study of multispecies gaseous and electrically charged dust environment of comet Chyuryumov‐Gerasimenko. Both, gas and dust phases of the coma are simulated kinetically. Photolytic reactions are taken into account. Parameters of the ambient plasma as well as the distribution of electric/magnetic fields are obtained from an MHD simulation [1] of the coma connected to the solar wind. Trajectories of ions and electrically charged dust grains are simulated by accounting for the Lorentz force and the nucleus gravity.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Kinetic study of the decompositions involved in the thermal degradation of commercial azodicarbonamide

The transitions and reactions involved in the thermal treatment of several commercial azodicarbonamides (ADC) in an inert atmosphere have been studied by dynamic thermogravimetry analysis (TGA), mass spectrometry and Fourier transform infrared (FTIR) spectroscopy. A pseudo-mechanistic model, involving several competitive and non-competitive reactions, has been suggested and applied to the correlation of the weight loss data. The model applied is capable of accurately representing the different processes involved, and can be of great interest in the understanding and quantification of such phenomena, including the simulation of the instantaneous amount of gases evolved in a foaming process. In addition, a brief discussion on the methodology related to the mathematical modeling of TGA data is presented, taking into account the complex thermal behaviour of the ADC.

Kinetic studies of the metathesis of 1-hexene using Re2O7/γ-Al2O3 and the synthesis and metathesis of oxazolines

The kinetics of the metathesis of 1-hexene using Re2O7/-Al_2O_3 as the catalyst were investigated under a variety of conditions. The experiments were carried out under high vacuum conditions. The product solutions were characterised by gas liquid chromatography and mass spectroscopy. The initial kinetics of the metathesis of 1-hexene showed that the reaction was first order in the weight of the catalyst and second order in the concentration of 1-hexene. A kinetic scheme which correlated the experimental data with the metallocarbene chain mechanism postulated by Herisson and Chauvin and the kinetics of the reaction was explained using a model based on the Langmuir-Hinshelwood theory. The low conversion of 1-hexene to its products is due to termination reactions which most likely occur by the decomposition of the metallocyclobutane intermediate to produce a cyclopropane derivative and an inactive centre. The optimum temperature for the metathesis of 1-hexene over Re_2O_7/-Al2O3 is 45oC and above this temperature, the rate of metathesis decreases rapidly. Co-catalysts alter the active sites for metathesis so that the catalyst is more selective to the metathesis of 1-hexene. However, the regeneration of metathesis activity is much worse for promoted catalysts than for the unpromoted. The synthesis and metathesis of 4,4-dimethyl-2-allowbreak (9-decenyl)-1,3-oxazoline and 4,4-dimethyl-2-allowbreak (3-pentenyl)-1,3-oxazoline was attempted and the products were analysed by thin layer chromatography, infra-red, 13C and 1H nmr and mass spectroscopy. Obtaining the oxazolines in a good yield with high purity was difficult and consequently metathesis of the impure products did not occur.

Plasma kinetic theory

Kinetic theory studies the macroscopic properties of large numbers of particles, starting from their (classical) equations of motion while the thermodynamics describes the equilibrium behavior of macroscopic objects in terms of concepts such as work, heat, and entropy. The phenomenological laws of thermodynamics tell us how these quantities are constrained as a system approaches its equilibrium. At the microscopic level, we know that these systems are composed of particles (atoms, particles), whose interactions and dynamics are reasonably well understood in terms of more fundamental theories. If these microscopic descriptions are complete, we should be able to account for the macroscopic behavior, i.e. derive the laws governing the macroscopic state functions in equilibrium. Kinetic theory attempts to achieve this objective. In particular, we shall try to answer the following questions [1]: How can we define equilibrium for a system of moving particles? Do all systems naturally evolve towards an equilibrium state? What is the time evolution of a system that is not quite in equilibrium?