Generalized Foldy-Lax formulation

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the Foldy-Lax formulation. This formulation forms the basis for our numerical procedure.     

Study of diamagnetic interactions between superheated-superconducting spheres: a numerical approach

In order to simulate a superheated-superconducting detector being constructed for particle physics purposes, we study a bidimensional lattice of small superconducting spheres placed in an external magnetic field. We propose a model for the diamagnetic interactions among the spheres and solve it using numerical Monte-Carlo techniques. New phenomena are found and the ensuing results are analyzed. A qualitative explanation is proposed.     

Reversible thermal gelation in soft spheres

Upon heating, concentrated solutions of star polymers and block copolymer micelles in a good solvent, representing soft spheres, undergo a reversible gelation. This phenomenon is attributed to the formation of clusters causing a partial dynamic arrest of the swollen interpenetrating spheres at high temperatures. A phase diagram analogous to that of sterically stabilized colloids is proposed.     

On the thermodynamics of hard spheres near a soft repulsive wall

We extend the variational method based on the Gibbs-Bogolioubov inequality to the case of fluids against a wall. We investigate the influence of the softness of the wall on the free energy of the system. For small packing fraction we consider a density expansion. The variational results are compared with the exact ones which are given by a direct expansion of the free energy. A comparison between variational and perturbation methods has been done for small packing fraction and also for a case corresponding to the liquid state. The accuracy of the present extension of the variational method to a surface phenomena is found as good as in the bulk fluid. A very simple expression is given for the change on surface tension when we go from the perfect hard wall to soft repulsive wall.     

Long range interactions between micro spheres and alloy surfaces in water changed by ion implantation

Ion implantation was adopted to change the surface potentials of samples made of aluminum bronze. The interactions between the SiO₂ particles and the sample surfaces in water were changed from attractive to repulsive. According to the surface element integration method, this interaction was simulated and the electrostatic double layer force was considered to be the dominated factor. This long range repulsive interaction was proved to have effect on preventing micro particles approaching the alloy surface by the fluorescent particles adhesion experiment, and the technology of ion implantation may have potential applications in adhesion resistance and abrasion reduction for alloys running in water.     

Convex-envelope formulation for separable many-particle interactions

The exact result for the free energy per particle in systems described by a hamiltonian of the type NP(V_N), where NV_N denotes a set of short-range operators, is reformulated in terms of a convex-envelope construction. A comparison is given with results obtained for classical systems with interactions of the so-called Kac-type.     

The effects of interactions between photon and the quark-gluon plasma on production of soft dileptons

We investigate the effects of interactions of the intermediate photons with the quark-gluon plasma on dilepton productions. The singular behaviour at the photon mass shell in the case of free photon is removed by the interactions. Instead, we find double resonance peaks near the photon mass shell due to the transverse and longitudinal modes. The effects of interactions further away fromM ²=0 is negligible and the photons effectively propagate as free particles in the plasma. The result of resummation is the enhancement of dilepton production rate, except in an extremely narrow region around each resonance peak, where its effect is to reduce the peak. The net result is more dilepton pairs come out of the plasma than in the one loop case. Both enhancement and reduction are partly due to Landau damping. Whereas the former is true over most range of the energy-momentum of the photon and is particularly prominent in region close to but not too close to the resonance peaks, the latter is effectively only true at the peaks.     

Diamagnetic interactions of superheated-superconducting spheres in a bidimensional lattice

In order to simulate a Superheated-Superconducting detector which is under construction for Particle Physics purposes, we study a bidimensional lattice of small superconducting spheres placed in an external magnetic field. We propose a model to study the diamagnetic interactions among the spheres and solve it using numerical Monte-Carlo techniques. New phenomena are found and the ensuing results are analyzed. Finally it is proposed a qualitative explanation. Received: 9 October 1998     

Variable dislocation widths in colloidal crystals of soft thermosensitive spheres

We report on detailed measurements of the core structure of Shockley partial dislocations in colloidal crystals. In crystalline arrays of micrometer sized thermosensitive particles, the interactions between the colloidal building blocks were tuned by changing the temperature. Individual dislocation cores were observed in a confocal microscope and their behavior as a function of temperature was studied. The obtained results qualitatively agree with the Peierls theory and are promising for further studies in which both Peierls stress and dislocation core width are measured simultaneously.     

Hydrodynamic interaction between two spheres

We evaluate the hydrodynamic interaction tensors for two spheres of unequal size and for general mixed slip-stick boundary conditions. A method of reflections leads to a series expansion for the diffusion tensors in powers of the inverse distance l^?1 between sphere centers and explicit results are derived through terms of order l^?7. It turns out that the series expansion for the diffusion tensors converges much more rapidly than that for the friction tensors.     

Generalized connection forms in the unification of gauge interactions

Within a differential-geometrical framework, the notion of a generalized connection form on a principal fibre bundle is applied to a generalized model for the unification of two (or more) gauge interactions. An example with gauge groups SU(2) and U(1) is considered.     

Symmetric harmonic maps between spheres

Necessary and sufficient conditions for the existence of symmetric harmonic maps between spheres are established.     

Generalized coherent state for soft gluon emission

By using a recursive soft insertion technique, many gluon emission amplitudes are computed to all orders in α_s and leading infrared accuracy. The resulting correlation structure is systematically exponentiated to yield a generalized coherent state operator which satisfies an integral equation where virtual corrections occur as a Sudakov matrix for many parton states. Infrared cancellations for physical quantities, including Drell-Yan processes, are derived on the basis of the unitarity relation for the coherent state. By further assuming strong ordering in emission angles, all known results on coherent effects and multiplicity distributions are easily recovered.     

Generalized quaternion formulation of relativistic quantum theory in curved space

A survey is presented of the essential principles for formulating relativistic wave equations in curved spacetime. The approach is relatively simple and avoids much of the philosophical debate about covariance principles, which is also indicated. Hypercomplex numbers provide a natural language for covariance symmetry and the two important kinds of covariant derivative.     

Generalized Dirac-Pauli equations in the Weinberg-Salam theory of electroweak interactions

M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 65–68, June, 1992.     

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r ^-n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.     

Heterogeneous crystallization of hard and soft spheres near flat and curved walls

Crystallization represents a long-standing problem in statistical physics and is of great relevance for many practical and industrial applications. It often occurs in the presence of container walls or impurities, which are usually unavoidable or might even be desirable to facilitate crystallization by exploiting heterogeneous nucleation. Heterogeneous nucleation relies on a seed. Here we discuss the role of the seed and concentrate on a very generic situation, namely crystallization of hard and soft colloidal spheres in the presence of flat or curved hard walls. Curvature serves as a simple means to introduce a tunable mismatch between the seed-induced crystal lattice and the thermodynamically-favoured lattice. The mismatch induces distortions and elastic stress, which accumulate while the crystallite grows. This has an important consequence: once the crystallite reaches a critical size, it detaches from the seed allowing it to relax. The relaxed crystal continues to grow in the bulk, but crystallization ceases before reaching the seed, which now represents an impurity. Therefore, while seeds favour nucleation, any mismatch, like the seed curvature or an incommensurate structure, induces unfavourable distortions and can lead to the detachment of the crystallite. An additional mechanism to relax distortions is available to soft spheres, which can exploit their interaction potential and possibly deform. The different multi-step processes have been investigated by confocal microscopy, which provides particle-level information, and compared to computer simulations and theoretical results.