Scattering of X-ray Ultrashort Pulses by Complex Polyatomic Structures

The scattering of X-ray ultrashort pulses (USPs) is an important aspect of the diffraction analysis of matter using modern USP sources. The theoretical basis, which considers the specifics of the interaction of ultrashort pulses with complex polyatomic structures, is currently not well developed. In general, research is focused on the specifics of the interaction of ultrashort pulses with simple systems—these are atoms and simple molecules. In this work, a theory of scattering of X-ray ultrashort pulses by complex polyatomic structures is developed, considering the specifics of the interaction of ultrashort pulses with such a substance. The obtained expressions have a rather simple analytical form, which allows them to be used in diffraction analysis. As an example, it is shown that the obtained expressions can be used to study the structures of deoxyribonucleic (DNA) and ribonucleic (RNA) acids.

A Simple Free Energy for the Isotropic-Nematic Phase Transition of Rods

A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant deviation of the predicted binodals. The new free energy proposed here is based upon a rationalized correction to the orientational and packing entropies when using the Gaussian ODF. In combination with Parsons-Lee theory or scaled particle theory, it enables describing the isotropic-nematic phase coexistence concentrations of rods accurately using the simple Gaussian ODF for a wide range of aspect ratios.

Thermodynamics of firms' growth

The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1 155 142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing ‘free’ creation and/or destruction of firms. For medium and smaller firm sizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.

Active earth thrust by backfills subject to a line surcharge

The current analytical solution for the thrust computation when a line of vertical surcharge acts on the backfill behind a wall assumes the soils to be simultaneously elastic, for calculating part of the thrust, and in the active state of failure, for calculating the remaining part of the thrust. This paper gives a coherent analytical solution based on Coulomb's approach. The position of the active thrust is also given in a simple analytical form and compared with the approximate solution of Terzaghi.Key words: active earth force, cantilever walls, lateral pressure, active condition.

Propagation of electromagnetic waves in inhomogeneous plasmas

The reflection and transmission coefficients for an electromagnetic beam propagating in an inhomogeneous plasma are calculated analytically using the Magnus approximation in different physical configurations. The theoretical predictions for such coefficients are expressed in simple analytical form, and are compared with the exact results obtained by numerical solution of the wave propagation equations, using the Berreman 4 × 4 matrix method. It is shown that the theoretical approach is able to reproduce the correct results for reflection and transmission coefficients over a wide range of physical parameters. The accuracy of the theoretical analysis, at different orders of approximation, is also discussed.

On the transient Leveque's problem with an application in electrochemistry

The electrochemically induced unsteady mass transfer to a uniform shear flow from a local wall electrode subjected to a step change in electrochemical potential is studied. Due to neglecting the streamwise diffusion, the problem has two solutions which however differ only insignificantly. The resulting transient characteristics of current densities have a simple analytical form suitable for an efficient data treatment.

Theory of Shock-Wave Ionization upon High-Velocity Impact of Micrometeorites

The relevant processes in shock wave ionization of a solid Fe micrometeorite impinging on a W target are analyzed. The internal energy behind the shock wave in shown to depend on impact velocity w, target and meteorite density in a simple analytical form. For low impact velocities (w<7 km sec-1) the ions generated by the shock are mostly due to surface ionization. For high impact velocities [w>20 km sec-1) the number of ions can satisfactorily be explained by isentropic expansion of the shocked material to a particle density of n ≈ 1020 cm-3 whereupon the rate processes in the expanding ion cloudlet govern the residual ionization. In velocity regions where laboratory measurements can be carried out, the agreement between theory and experiment confirms the assumptions made.

A Note on the Adler?Adler Resonance Formalism

Over restricted energy ranges, the Adler?Adler method. of parameterizing resonance cross sections is in general the exact result of inverting the channel matrix. This provides a simple analytical form for the cross section which can be used in reactor physics calculations.

Neutral eigensolutions of the stability equation for stratified shear flow

Many of the known analytic solutions of the equation for neutral disturbances to a stably stratified, inviscid, parallel shear flow are shown to belong to a wider family of solutions when a transformation to the hypergeometric differential equation is possible. Two particular cases in which the transformation can be made are examined in some detail and the solutions are expressed in a simple analytical form. A number of novel solutions are presented as examples.