X-ray beam monitoring and wavelength calibration using four-beam diffraction

Rigorous dynamical theory calculations show that four-beam diffraction (4BD) can be activated only by a unique photon energy and a unique incidence direction. Thus, 4BD may be used to precisely calibrate X-ray photon energies and beam positions. Based on the principles that the forbidden-reflection 4BD pattern, which is typically an X-shaped cross, can be generated by instant imaging using the divergent beam from a point source without rocking the crystal, a detailed real-time high-resolution beam (and source) position monitoring scheme is illustrated for monitoring two-dimensional beam positions and directions of modern synchrotron light sources, X-ray free-electron lasers and nano-focused X-ray sources.

The holographic c-theorem and infinite-dimensional Lie algebras

We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

Inevitability of the Poisson Bracket Structure of the Relativistic Constraints

The purpose of this paper is to shed some fresh light on the long-standing conceptual question of the origin of the well-known Poisson bracket structure of the constraints that govern the canonical dynamics of generally relativistic field theories, i.e. geometrodynamics. This structure has long been known to be the same for a wide class of fields that inhabit the space-time, namely those with non-differential coupling to gravity. It has also been noticed that an identical bracket structure can be derived independently of any dynamical theory, by purely geometrical considerations in Lorentzian geometry. Here we attempt to provide the missing link between the dynamics and geometry, which we understand to be the reason for this structure to be of the specific kind. We achieve this by a careful analysis of the geometrodynamical approach, which allows us to derive the structure in question and understand it as a consistency requirement for any such theory. In order to stay close to the classical literature on the subject we stick to the metric formulation of general relativity, but the reasoning should carry over to any other formulation as long as the non-metricity tensor vanishes. The discussion section is devoted to derive some interesting consequences of the presented result in the context of reconstructing the Arnowitt–Deser–Misner (ADM) framework, thus providing a precise sense to the inevitability of the Einstein’s theory under minimal assumptions.

Ocean model response to stochastically perturbed momentum fluxes

In climate model configurations, standard approaches to the representation of unresolved, or subgrid scales, via deterministic closure schemes are being challenged by stochastic approaches inspired by statistical dynamical theory. Despite gaining popularity, studies of various stochastic subgrid scale parameterizations applied to atmospheric climate and weather prediction systems have revealed a diversity of model responses, including degeneracy in the response to different forcings and compensating model errors, with little reduction in artificial damping of the small scales required for numerical stability. Due to the greater range of spatio-temporal scales involved, how to best sample subgrid fluctuations in a computationally inexpensive manner, with the aim of reduced model error and improvements to the simulated climatological state of the ocean, remains an open question. While previous studies have considered perturbations to the surface forcing or subsurface temperature tendencies, we implement an energetically consistent, simple, stochastic subgrid eddy parameterization of the momentum fluxes in regions of the three-dimensional ocean typically associated with high eddy variability. We consider the changes in the modelled energetics of low-resolution simulations in response to stochastically forced velocity tendencies whose perturbation statistics and amplitudes are calculated from an eddy resolving ocean configuration. Kinetic energy spectra from a triple-decomposition reveal a systematic redistribution from the seasonal (climatological minus mean) potential energy to preferentially generate small scale transient kinetic energy while the total energy spectra remains largely unchanged. We show that stochastic parameterization generally improves model biases, noticeably so for the simulated energetics of the Southern Oceans.

Dynamical analysis of arbitrary dark energy and coincidence problem

This paper reviews a systematic dynamical analysis on a general form of scalar field as Dark Energy (DE) with dark matter (DM) to sort out the “cosmic coincidence” problem. Here the autonomous system of differential equations is two-dimensional (2D) as well as nonlinear. So we have utilized nonlinear dynamical theory to explain various cosmological implications of this model. Nowadays, we have noted that some works are undertaking this nonlinear systems theory. Although we have seen that most of the works are simplifying the underlying nonlinear dynamical systems similar to a linear one, that can lead to flawed conclusions about the evolution of the universe. Since an important theorem, Poincare–Bendixson theorem asserts linearization of the nonlinear system and does not give “global” stability, unlike the linear one if the dimension is more than two. Anyway, our work is different from others in this regard. Here the dimension of the system is two, and we have obtained some interesting stuffs also. We have applied the above theorem of nonlinear dynamical systems and others to find the “global” stability. This theorem offers completely different stable solutions, contrary to the prediction of linear analysis. As a result, we have obtained two fixed points; one of them is a stable “attractor” (it is attracting “node” actually), and thereafter, we have analyzed the stability. To investigate the dynamical system behavior, we have drawn different figures. These figures include vector field and a new plotting strategy (explained later). These investigations suggest a way out of the coincidence problem (or, precisely speaking, what should be the mathematical form of the term “[Formula: see text]”, which indicates interaction between DE and DM to reduce coincidence). In this scenario, if the equation of state (EoS) of DE and DM obeys [Formula: see text], then coincidence problem may be avoided.

Modification of the Exterior and Interior Solution of Einstein’s G22 Field Equation for a Homogeneous Spherical Massive Bodies whose Fields Differ in Radial Size, Polar Angle, and Time.

In general theory of relativity, Einstein’s field equations relate the geometry of space-time with the distribution of matter within it. These equations were first published by Einstein in the form of a tensor equation which related the local space-time curvature with the local energy and momentum within this space-time. In this article, Einstein’s geometrical field equations interior and exterior to astrophysically real or hypothetical distribution of mass within a spherical geometry were constructed and solved for field whose gravitational potential varies with time, radial distance and polar angle. The exterior solution was obtained using power series. The metric tensors and the solution of the Einstein’s exterior field equations used in this work has only one arbitrary function f(t,r,θ) , and thus put the Einstein’s geometrical theory of gravitation on the same bases with the Newton’s dynamical theory of gravitation. The gravitational scalar potential f(t,r,θ) obtained in this research work to the order of co, c-2 , contains Newton dynamical gravitational scalar potential and post Newtonian additional terms much importance as it can be applied to the study of rotating bodies such as stars. The interior solution was obtained using weak field and slow-motion approximation. The obtained result converges to Newton’s dynamical scalar potential with additional time factor not found in the well-known Newton’s dynamical theory of gravitation which is a profound discovery with the dependency on three arbitrary functions. Our result obeyed the equivalence principle of Physics.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

XXIII Semana de la Enseñanza de La Física. 200 años del Electromagnetismo.

Evento desarrollado del 23 al 27 de noviembre de 2020, en el Proyecto Curricular de Licenciatura en Física, de la Facultad de Ciencias y Educación. Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. A comienzos de 1820 el físico danés Hans Christian Ørsted descubrió experimentalmente la relación existente entre el magnetismo y la electricidad, publicando su descubrimiento en un corto artículo titulado: Experimenta circa effectum conflictus electrici in acum magneticam. Dando origen al electromagnetismo y a una serie de trabajos de diversos científicos, que culminaron con la unificación, lograda por James Clerk Maxwell, de la electricidad, el magnetismo y la luz como diversas manifestaciones de un mismo fenómeno físico. Trabajo que fue publicado bajo el título de: A Dynamical Theory of the Electromagnetic Field. Se cumplen así 200 años de un descubrimiento que cambiaría la concepción física de la época y potenciaría un desarrollo que aún hoy día continúa.