Flat Friedmann cosmologies with stiff fluid in Einstein–Cartan theory

Flat Friedmann cosmologies with stiff fluid are considered in the framework of the Einstein–Cartan theory. The version of this theory which simultaneously takes into consideration two sources of torsion, namely, a perfect fluid with the vacuum equation of state and a nonminimally coupled scalar field, is studied. It is demonstrated that, for bouncing models, phantom cosmologies with and without a Big Rip singularity are possible. Singular expanding models are presented where the early stages are dominated by a scalar-torsion field which behaves as an ultrastiff fluid, while the late stages are dominated by a perfect fluid which causes a de Sitter asymptotic. Some cosmological consequences of two sources of torsion are discussed.     

Exact solution for a nonstatic cylindrically symmetric perfect fluid distribution in Einstein–Cartan theory

We consider a nonstatic, spin-polarized cylindrically symmetric perfect fluid distribution in the Einstein-Cartan theory and obtain the field equations. These field equations are solved using the Ray–Smalley energy-momentum tensor.     

Exact inflation in Einstein–Gauss–Bonnet gravity

We study cosmological inflation in the Einstein gravity model with the additionally included Gauss–Bonnet term nonminimally coupled to a scalar field. We prove that inflationary solutions of exponential and power-law types are allowable, and we found few examples of them. We also propose a method for construction of exact inflationary solutions for a single scalar field with a given scale factor and Gauss–Bonnet coupling term in a spatially flat Friedmann–Robertson–Walker Universe on the basis of connection with standard inflation and using special assumptions. With one special anzatz we presented the set of equations in a form that allows for generation of exact solutions (at least in quadratures) of a wide class by setting the scale factor.     

Numerical exploration of vortex matter in Bose–Einstein condensates

We describe a finite element numerical approach to the full Hartree-Fock-Bogoliubov treatment of a vortex lattice in a rapidly rotating Bose–Einstein condensate. We study the system in the regime of high thermal or significant quantum fluctuations where we are presented with a very large nonlinear unsymmetric eigenvalue problem which is indefinite and which possesses low-lying excitations clustered arbitrarily close to zero, a problem that requires state-of-the-art numerical techniques.     

Efficient continuation methods for spin-1 Bose–Einstein condensates in a magnetic field

We study linear stability analysis for spin-1 Bose–Einstein condensates (BEC). We show that all bounded solutions of this physical system are neutrally stable. In particular, all steady-state solutions of the physical system, and the associated discrete steady-state solutions are neutrally stable. Next, we consider the physical system without the affect of magnetic field. By exploiting the physical properties of both ferromagnetic and antiferromagnetic cases, we develop efficient multi-level pseudo-arclength continuation algorithms combined with a spectral collocation method for these two cases, respectively. When the magnetic field is imposed on the physical system, an additional multi-level continuation algorithm is described for the ferromagnetic case. Extensive numerical results for spin-1 BEC in a magnetic field, and in optical lattices are reported.     

Two-temperature theory in Green–Naghdi thermoelasticity with fractional phase-lag heat transfer

Microsystem Technologies - A mathematical model of two-temperature phase-lag Green–Naghdi thermoelasticty theories based on fractional derivative heat transfer is given. The GN theories as...     

Friedmann Dynamics Recovered from Compactified Einstein–Gauss–Bonnet Cosmology

Cosmological dynamics is studied in Einstein–Gauss–Bonnet gravity with a perfect fluid source in arbitrary dimension. A systematic analysis is performed for the case that the theory does not admit maximally symmetric solutions. Considering two independent scale factors, namely, one for the 3D space and one for the extra-dimensional space, it is found that a regime exists where the scale factor of extra dimensions tends to a constant value via damped oscillations for not too negative pressure of the fluid, so that asymptotically the evolution of the (3 + 1)-dimensional Friedmann model with perfect fluid is recovered.     

Context-dependent combination of sensor information in Dempster–Shafer theory for BDI

There has been much interest in the belief–desire–intention (BDI) agent-based model for developing scalable intelligent systems, e.g. using the AgentSpeak framework. However, reasoning from sensor information in these large-scale systems remains a significant challenge. For example, agents may be faced with information from heterogeneous sources which is uncertain and incomplete, while the sources themselves may be unreliable or conflicting. In order to derive meaningful conclusions, it is important that such information be correctly modelled and combined. In this paper, we choose to model uncertain sensor information in Dempster–Shafer (DS) theory. Unfortunately, as in other uncertainty theories, simple combination strategies in DS theory are often too restrictive (losing valuable information) or too permissive (resulting in ignorance). For this reason, we investigate how a context-dependent strategy originally defined for possibility theory can be adapted to DS theory. In particular, we use the notion of largely partially maximal consistent subsets (LPMCSes) to characterise the context for when to use Dempster’s original rule of combination and for when to resort to an alternative. To guide this process, we identify existing measures of similarity and conflict for finding LPMCSes along with quality of information heuristics to ensure that LPMCSes are formed around high-quality information. We then propose an intelligent sensor model for integrating this information into the AgentSpeak framework which is responsible for applying evidence propagation to construct compatible information, for performing context-dependent combination and for deriving beliefs for revising an agent’s belief base. Finally, we present a power grid scenario inspired by a real-world case study to demonstrate our work.     

A flexible rule for evidential combination in Dempster–Shafer theory of evidence

Dempster’s combination rule in Dempster–Shafer theory of evidence is widely used to combine multiple pieces of evidence. However, when the evidence is severely conflicting, the result could be counter-intuitive. Thus, many alternative combination rules have been proposed to address this issue. Nevertheless, the existing ones sometimes behave not very well. This may be because they do not hold some essential properties. To this end, this paper firstly identifies some of the important properties. Then, following the cues from these properties, we propose a novel evidential combination rule as a remediation of Dempster’s combination rule in Dempster–Shafertheory. Our new rule is based on the concept of complete conflict (we introduced in this paper), Dempster’s combination rule, and the concept of evidence weight. Moreover, we illustrate the effectiveness of our new rule by using it to successfully resolve well-known Zadeh’s counter-example, which is against Dempster’s combination rule. Finally, we confirm the advantages of our method over the existing methods through some examples.     

Signaling to Relativistic Observers: An Einstein–Shannon–Riemann Encounter

A communication scenario is described involving a series of events triggered by a transmitter and observed by a receiver experiencing relativistic time dilation. The message selected by the transmitter is assumed to be encoded in the events’ timings and is required to be perfectly recovered by the receiver, regardless of the difference in clock rates in the two frames of reference. It is shown that the largest proportion of the space of all k-event signals that can be selected as a code ensuring error-free information transfer in this setting equals ζ(k)^?1, where ζ is the Riemann zeta function.

     

Application of Dempster–Shafer theory in condition monitoring applications: a case study

This paper is concerned with the use of Dempster–Shafer theory in `fusion' classifiers. We argue that the use of predictive accuracy for basic probability assignments can improve the overall system performance when compared to `traditional' mass assignment techniques. We demonstrate the effectiveness of this approach in a case study involving the detection of static thermostatic valve faults in a diesel engine cooling system.     

Non-ideal teleportation of tripartite entanglement: Einstein–Podolsky–Rosen versus Greenberger–Horne–Zeilinger schemes

Channels composed by Einstein–Podolsky–Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger–Horne–Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form \(c_0|000\rangle +c_1|111\rangle \). The teleportation is made through measurements in the GHZ basis, and, to obtain deterministic results, in most of the investigated scenarios, four out of the eight elements of the basis need to be unambiguously distinguished. Most importantly, we show that when both systematic errors and noise are considered, the fidelity of the teleportation protocol is higher when a GHZ channel is used in comparison with that of a channel composed by EPR pairs.     

Entanglement mean field theory: Lipkin–Meshkov–Glick Model

Entanglement mean field theory is an approximate method for dealing with many-body systems, especially for the prediction of the onset of phase transitions. While previous studies have concentrated mainly on applications of the theory on short-range interaction models, we show here that it can be efficiently applied also to systems with long-range interaction Hamiltonians. We consider the (quantum) Lipkin–Meshkov–Glick spin model, and derive the entanglement mean field theory reduced Hamiltonian. A similar recipe can be applied to obtain entanglement mean field theory reduced Hamiltonians corresponding to other long-range interaction systems. We show, in particular, that the zero temperature quantum phase transition present in the Lipkin–Meshkov–Glick model can be accurately predicted by the theory.     

Metropolis–Hastings thermal state sampling for numerical simulations of Bose–Einstein condensates

We demonstrate the application of the Metropolis–Hastings algorithm to sampling of classical thermal states of one-dimensional Bose–Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case. The presented algorithm can be easily generalized to higher dimensions and arbitrary trap geometry. For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode). The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.     

Stochastic resonance–a nonlinear control theory interpretation

Stochastic resonance (SR) is an effect that has been known (Benzi, R., Sutera, A., and Vulpiani, A. (1981 Chapeau-Blondeau, F. 1997. Input-Output Gains for Signal in Noise in Stochastic Resonance. Physics Letters A, 232: 41–48.  [Google Scholar]), ‘The Mechanism of Stochastic Resonance’, Journal of Physics, A14, L453–L457) for almost three decades and has been extensively studied in biology, statistics, signal processing and in numerous other eclectic areas (Wiesenfeld, K., and Moss, F. (1995 Xu, B, Jiang, Z-P, Wu, X and Repperger, DW. 2009. Investigation of Two-dimensional Parameter-Induced Stochastic Resonance and Applications in Nonlinear Image Processing. Journal of Physics A–Mathematical and Theoretical, 42: 145207, 1-45207, 9 [Google Scholar]), ‘Stochastic Resonance and the Benefits of Noise: From Ice Ages to Crayfish and Squids’, Nature, 373, 33–36). Herein, a nonlinear control theory analysis is conducted on how to better understand the class of systems that may exhibit the SR effect. Using nonlinear control theory methods, equilibrium points are manipulated to create the SR response (similar to shaping dynamical response in a phase plane). From this approach, a means of synthesising and designing the appropriate class of nonlinear systems is introduced. New types of nonlinear dynamics that demonstrate the SR effects are discovered, which may have utility in control theory as well as in many diverse applications. A numerical simulation illustrates some powerful attributes of these systems.     

Adaptively entropy-based weighting classifiers in combination using Dempster–Shafer theory for word sense disambiguation

In this paper we introduce an evidential reasoning based framework for weighted combination of classifiers for word sense disambiguation (WSD). Within this framework, we propose a new way of defining adaptively weights of individual classifiers based on ambiguity measures associated with their decisions with respect to each particular pattern under classification, where the ambiguity measure is defined by Shannon’s entropy. We then apply the discounting-and-combination scheme in Dempster–Shafer theory of evidence to derive a consensus decision for the classification task at hand. Experimentally, we conduct two scenarios of combining classifiers with the discussed method of weighting. In the first scenario, each individual classifier corresponds to a well-known learning algorithm and all of them use the same representation of context regarding the target word to be disambiguated, while in the second scenario the same learning algorithm applied to individual classifiers but each of them uses a distinct representation of the target word. These experimental scenarios are tested on English lexical samples of Senseval-2 and Senseval-3 resulting in an improvement in overall accuracy.     

Excited Bose–Einstein condensates: Quadrupole oscillations and dark solitons

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory arguments, we derive explicit analytical expressions for the phase, density and width of the condensate. Furthermore, it is found that the observed oscillatory dynamics of the BEC density can even reach a quasi-resonance state when the trap strength varies according to a time-periodic driving term. Finally, the dynamics of a dark soliton on top of a breathing BEC are also briefly discussed.     

A metabolism–repair theory of by-products and side-effects

The plurality of process outputs is a genericity of Nature. In this paper, Natural Law receives a new mathematical formulation founded on two axioms: ‘Everything is a set.’ and ‘Every process is a set-valued mapping.’ I present a brief introduction to the algebraic theory of set-valued mappings, which culminates in two particular morphisms: the metabolism bundle and the imminence mapping. These are relations defined on the collection of processes of a natural system, and serve to characterize material entailment and functional entailment. Generalized metabolism is material entailment of (by-)products, and generalized repair is functional entailment of (side-)effects. Metabolism–Repair networks, hence equipped with set-valued processors, expand their role from models of biological entities to generic models of all natural systems.