Weak field reduction in teleparallel coframe gravity: Vacuum case

We study the lambda-mu-calculus, extended with explicit substitution, and define a compositional output-based interpretation into a variant of the pi-calculus with pairing that preserves single-step explicit head reduction with respect to weak bisimilarity. We define four notions of weak equivalence for lambda-mu -- one based on weak reduction, two modelling weak head-reduction and weak explicit head reduction (all considering terms without weak head-normal form equivalent as well), and one based on weak approximation -- and show they all coincide. We will then show full abstraction results for our interpretation for the weak equivalences with respect to weak bisimilarity on processes.

We apply the BRST approach, previously developed for higher spin field theories, to gauge-invariant Lagrangian construction for antisymmetric massive and massless bosonic fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models both in massless and massive cases and the order of reducibility grows with the value of the rank of the antisymmetric field. In both cases the Lagrangians contain the sets of auxiliary fields and possess more rich gauge symmetry in comparison with standard Lagrangian formulation for the antisymmetric fields. This serves as an additional demonstration of universality of the BRST approach for Lagrangian constructions in various field models.

This paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the ‘covariant force law’, the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated ‘humanoid velocity phase space’, while autonomous Hamiltonian dynamics is formulated on the associated ‘humanoid momentum phase space’. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples.

The capacity is an important parameter in multidimensional linear attack. In this paper, we firstly explore the distribution of the key-dependent capacity. Based on the magnitude of the correlation contributions, we divide the linear approximations subspace into two sets: one set consists of the strong linear approximations, and the other set consists of the weak linear approximations. We construct two statistics using the linear approximations in the two sets, respectively. Under reasonable assumptions, both of the two statistics follow Gamma distribution. Thus, the capacity is the sum of two statistics that follow Gamma distribution. Secondly, the accuracy of the model is verified by experiments on SMALLPRESENT[4]. Our experimental results show that this model can estimate the variance of the key-dependent capacity more accurately. Thus, we obtain more precise knowledge of the data complexity of the multidimensional linear attack. We derive the upper bound of the data complexity for multidimensional linear attack. Finally, based on our theoretical results, we explore the data complexity of Cho’s multidimensional linear attack on PRESENT. Our results are the smallest data complexity for the same round attack so far.

The problem of modelling the surface of stars undergoing non-radial pulsation is reviewed. Linear-approximation expressions for the surface radius, temperature, velocity and geometry of a pulsating star are derived and discussed using both the Lagrangian (fixed-element) and Eulerian (fixed-position) formalisms. In each case, small numerical discrepancies are found between the perturbed states predicted by these alternative approaches. These discrepancies are shown to scale quadratically with the pulsation amplitude, and are therefore attributed to a transgression of the linear-approximation limits. Singled out for particular attention are the expressions for the surface geometry perturbations predicted by each formalism. Marked differences are apparent between these expressions: terms containing the horizontal fluid displacement appear explicitly in the Lagrangian result, but are absent from the corresponding Eulerian one. By examining the physical origin of these terms, it is demonstrated that the two formalisms are, in fact, perfectly consistent with regard to the geometry perturbations, and — as with all other perturbations — simply furnish alternative representations of the same physical processes. The conclusion is that either formalism is an appropriate choice when modelling the surface of a pulsating star.

\n We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by $$\\sqrt{-g}$$ (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless “dust” fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.\n

Galactic dynamics is the foundation for simulating galactic structure and for solving other problems. However, the traditional dynamic equations include some unreasonable assumptions and are therefore scientifically invalid. In this paper, by introducing the following three working assumptions, we established the galactic dynamics of high precision and convenient formalism. 1. In the research of large-scale structure, the retarded potential of the gravitational field should be taken into account, and the weak field and low velocity approximation of Einstein’s field equation should be adopted. 2. The stars in a fully developed galaxy should be zero-pressure and inviscid fluid, and the equation of motion is different from that of ordinary continuum mechanics. Stars move along geodesics. 3. The structure of the galaxy is only related to the total mass density distribution. The equation of state of dark halo is different from that of ordinary luminous interstellar matter, so their trajectories are also very different. In a galaxy, the dark halo and the ordinary matter are automatically separated. The total mass density distribution can be presupposed according to the observation data, and then it can be determined by comparing the solution of the equations with the observed data. These assumptions and treatments are supported by theory and observation. The variables of the equations of simplified galactic dynamics are separated from each other, and the equations are well-posed and can be solved according to a definite procedure. The solution explains the Tully–Fisher relation. Therefore, this simplified dynamic equation system provides a more reasonable and practical framework for the further study of galactic structure, and can solve many practical problems. In addition, it is closely related to the study of dark matter halo in galaxy.

We study the behaviour of relativistic quantum particles in the space-time generated by a moving mass current, in the weak field approximation. We solve the Dirac equation in this gravitational field and calculate the current associated with the particles. The study of the behaviour of quantum systems under the influence of curved space-times goes back to the end of the 1920s and to the beginning of the 1930s[1], when the generalization of the Schr ¨ odinger and Dirac equations to curved spaces has been discussed, motivated by the idea of constructing a theory combining quantum physics and general relativity. Along this line of research the hydrogen atom has been studied in particular curved space-times[2, 3]. These investigations showed that the energy levels of an atom placed in a gravitational field is shifted as a result of the interaction of the atom with the space-time curvature[3]-[5]. This shift in the energy of each atomic level would depend on the features of the space-time. The general theory of relativity, as a metric theory, predicts that gravitation is manifested as the curvature of space-time. Therefore, it is of interest to know how the curvature of spacetime at the position of the atom affects its spectrum. On the other hand, we know that there are situations in which particles are constrained to move in a region where the Riemann curvature tensor vanishes and even in this case they exhibit gravitational effects arising from a region of non-zero curvature from which they are excluded[6]. In a more general sense, we have the case in which particles are constrained to move in a region where the Riemann curvature tensor does not vanish but does depend on certain parameter of the metric such as the velocity or the angular momentum of the source. In this case we have effects on the system associated with parameters which do not influence the curvature of the space-time as we will see. In what follows we present the study concerning the behaviour of a relativistic particle placed in the gravitational field generated by a cylindrical distribution of matter with uniform density along the z-axis moving slowly, whose metric reads[7]

In this paper, we show that the non-Newtonian gravitational potential can be explained by a scalar-tensor model with torsion in the weak field and static state approximation. The torsional effect is the intermediate-range interaction.

We compute the neutral pion mass dependence on a magnetic field in the weak field approximation at one-loop order. The calculation is carried out within the linear sigma model coupled to quarks and using Schwinger's proper-time representation for the charged particle propagators. We find that the neutral pion mass decreases with the field strength provided the boson self-coupling magnetic field corrections are also included. The calculation should be regarded as the setting of the trend for the neutral pion mass as the magnetic field is turned on.

Many interesting control are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical to obtain analysis tools which are suitable for these systems. In this dissertation we take the first steps towards a methodical treatment of mechanical control systems. First we develop a framework for analysis of certain classes of mechanical control systems. In the Lagrangian formulation we study mechanical control systems whose Lagrangian is kinetic energy minus potential energy. We propose a new and useful definition of controllability for these and obtain a computable set of conditions for this new version of controllability. We also obtain decompositions of simple mechanical in the case when they are not controllable. In the Hamiltonian formulation we study whose control vector fields are Hamiltonian. We obtain decompositions which describe the controllable and uncontrollable dynamics. In each case, the dynamics are shown to be Hamiltonian in a suitably general sense. Next we develop intrinsic descriptions of Lagrangian and Hamiltonian mechanics in the presence of external inputs. This development is a first step towards a control theory for general Lagrangian and Hamiltonian control systems. Systems with constraints are also studied. We first give a thorough overview of variational methods including a comparison of the nonholonomic and vakonomic methods. We also give a generalised definition for a constraint and, with this more general definition, we are able to give some preliminary controllability results for constrained systems.

Gravitational interactions are generally investigated under the assumptions: (i) the Lorentz invariance (special relativity), (ii) (CPT) invariance, (iii) gauge invariance and (iv) the weak (gravitation) field approximation. Discussions are given for possible effects of P and T violating gravitational interactions as well as empirical upper limits on the degrees of such violations.

We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an $M$-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.

We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in $\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.

Under weak probe field, rotating wave and electric dipole approximations, we have derived analytic expressions for absorption and dispersion coefficients, group index and group velocity in a four-level cascade atomic medium interacting with the probe and pump laser fields. The model is applied to 85Rb atomic system to study the control of the fast and slow light propagation of the probe beam according to the intensity and frequency of the pump laser beam. With this excitation model, we find two transparent domains and thus the light group velocity is also controlled at these two frequency domains. In particular, the amplitude and the sign of the group index are easily changed by adjusting the intensity or frequency of the pump laser. That is, the probe beam propagation can be changed between fast and slow light modes by adjusting the intensity or frequency of the pump laser. Our analytical results can be useful for related experimental studies.