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Within the framework of f(R)=R+αR2 gravity, we study realistic models of neutron stars, using equations of state compatible with the LIGO constraints, i.e., APR4, MPA1, SLy, and WW1. By numerically solving modified Tolman-Oppenheimer-Volkoff equations, we investigate the mass-radius relation in both metric and torsional f(R)=R+αR2 gravity models. In particular, we observe that torsion effects decrease the compactness and total mass of neutron star with respect to the general relativity predictions, therefore mimicking the effects of a repulsive massive field. The opposite occurs in the metric theory, where mass and compactness increase with α, thus inducing an excess of mass that overtakes the standard general relativity limit. We also find that the sign of α must be reversed whether one considers the metric theory (positive) or torsion (negative) to avoid blowing up solutions. This could draw an easy test to either confirm or discard one or the other theory by determining the sign of parameter α.

The aim of this paper is to understand how the shear modulus of a particulate composite, manufactured with hollow spheres surrounded by a graded interphase in a matrix, depends on the properties of the interphase zone and the inclusion wall. Considering composites with small volume fractions of the hollow inclusions and assuming isotropic phases with a radial power law behavior for the shear modulus in the inhomogeneous interphase, the boundary value problems used to determine shear modulus bounds with the Composite Sphere Assemblage method, are studied. Adopting Hashin’s approach, the shear elastic bound expressions are analytically obtained, numerically investigated and compared with results present in literature. Parametric analysis allows us to highlight the effects of a soft or stiff interphase and shows that the shear bounds are close to each other for inclusions with thin wall thickness thereby leading in some cases to a unique prediction value for the shear modulus. To this end, an analytical expression supplying the thickness of the inclusion wall that gives rise to a match of the two shear modulus bounds for assigned phase property ratio and volumetric fraction is presented.

The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual Dirac spinor. IV, V, VI are those for which the scalar and pseudo-scalar bi-linear spinor quantities are identically zero, its spinors are called singular, and they are split in further sub-classes: IV has no further restrictions, its spinors are called flag-dipole; V is the one for which the spin axial-vector vanishes, its spinors are called flagpole, and among them we find the Majorana spinor; VI is the one for which the momentum antisymmetric-tensor vanishes, its spinors are called dipole, and among them we find the Weyl spinor. In the quest for exact solutions of fully-coupled systems of spinor fields in their own gravity, we have already given examples in the case of Dirac fields and Weyl fields but never in the case of Majorana or more generally flagpole spinor fields. Flagpole spinor fields in interaction with their own gravitational field, in the case of axial symmetry, will be considered. Exact solutions of the field equations will be given., 13 pages

Heat transfer in counterflow heat exchangers is modeled by using transport and balance equations with the temperatures of cold fluid, hot fluid, and metal pipe as state variables distributed along the entire pipe length. Using such models, boundary value problems can be solved to estimate the temperatures over all the length by means of measurements taken only at the boundaries. Conditions for the stability of the estimation error given by the difference between the temperatures and their estimates are established by using a Lyapunov approach. Toward this end, a method to construct nonlinear Lyapunov functionals is addressed by relying on a polynomial diagonal structure. This stability analysis is extended in case of the presence of bounded modeling uncertainty. The theoretical findings are illustrated with numerical results, which show the effectiveness of the proposed approach.

Pool boiling is a pretty well-known benchmark of diffusive system with both practical and theoretical interest. We have investigated Neumann-boundary feedback control by combining the backstepping approach and the circle criterion. Conditions for local/global stability with nonlinear boundary conditions as input are investigated by explicitly solving the backstepping kernel equations. Simulation results are reported to illustrate the findings of the theoretical investigation and compare all the considered approaches.

The paper is focused on analytical prediction of the effective bulk and shear modulus for particulate composites reinforced with solid spherical particles surrounded by graded interphase zone. A three-dimensional elasticity problem for a single inclusion embedded in a finite matrix is studied. The graded interphase zone around the inclusion is assumed to have power law variation of the shear modulus with radial co-ordinate, with Poisson’s ratio assumed to be constant and equal to that of the matrix. Following Hashin’s approach, two boundary value problems are considered and stress and displacement fields in the interphase zone are determined. They are then used to calculate the elastic energy for the single inclusion composite under spherically symmetric state and pure shear state and derive closed-form expressions for the bulk modulus and the upper and lower bounds for the shear modulus. Numerical results for hard and soft interphase zones are presented and discussed for a range of the interphase zone thickness ratios.

We present a tetrad–affine approach to f ( Q ) gravity coupled to spinor fields of spin- 1 2 . After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind f ( Q ) = α Q n . At late time such solutions are seen to isotropize and, depending on the value of the exponent n, they can undergo an accelerated expansion of the spatial scale factors.

The paper is concerned with the quantitative characterisation of the effective coefficient of thermal expansion for a particulate composite containing spherical inclusions surrounded by an interphase zone, whose properties are graded in the radial direction. A thermo-elastic problem of uniform heating is studied for a single hollow spherical inclusion embedded in a finite matrix assuming power-law variation of the thermo-elastic properties. An exact solution of the problem is derived using hypergeometric functions. The effective coefficient of thermal expansion is determined in closed form for composites with graded interphase zone around hollow and solid inclusions, as well as for the case of void in a graded matrix. Numerical results highlighting the effect of the interphase properties on the coefficient of thermal expansion for different volume fractions of inclusions are presented and discussed.

We compare theoretical predictions with observations for a class of cosmological models in which the dark energy component is modeled as a fermionic condensate, non-minimally coupled with the gravitational field and characterized by some specific self-interaction potentials. Our analysis is based on the Markov Chain Monte Carlo Method (MCMC) and employs different data sets. It turns out that with an appropriate choice of parameters our models are fully compatible with several observed data. We combine these parameter values with phase space analysis to deduce the features of the entire cosmic history of the considered models., 29 pages, 15 figures new Revised version

An analytical solution in closed form of the advection-dispersion equation in one-dimensional contaminated soils is proposed in this paper. This is valid for non-conservative solutes with first order reaction, linear equilibrium sorption, and a time-dependent Robin boundary condition. The Robin boundary condition is expressed as a combined production-decay function representing a realistic description of the source release phenomena in time. The proposed model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines, Non Aqueous Phase Liquid pools, or radioactive decay series. The developed analytical model tends towards the known analytical solutions for particular values of the rate constants.

The goal of this work is the optimal control of level sets generated by the normal flow equation. The problem consists in finding the normal velocity that minimizes a given performance index expressed by means of a cost functional. In this perspective, a sufficient condition of optimality requiring the solution of a system of partial differential equations is derived. As in general it is difficult to solve such a system, an approximation scheme based on the extended Ritz method is proposed to find suboptimal solutions. The control law is forced to take on a fixed structure depending nonlinearly on a finite number of parameters to be suitably chosen. The selection of the parameters is accomplished by using a gradient-based technique. To this end, the adjoint equation is derived to compute the gradient of the cost functional with respect to the parameters of the control law. The effectiveness of the proposed approach is shown by means of simulations.

This work deals with the problem of modeling the effect due to an interphase zone between inclusion and matrix in particulate composites to better estimate the bulk modulus of materials with inclusions. To this end, in this paper the problem of a body containing a hollow or solid spherical inclusion subjected to a spherically symmetric loading is investigated in the framework of the elasticity theory. The interphase zone around the inclusion is modeled by considering the elastic properties varying with the radius moving away from the interface with inclusion and, asymptotically approaching the value of the homogeneous matrix. The explicit solutions are obtained in closed form by using hypergeometric functions and numerical investigations are performed to highlight the localized effects of the graded interphase in the stress transfer between inclusion and matrix. Finally, the exact solutions are used to estimate the effective bulk modulus of a material containing a dispersion of hollow or solid spherical inclusions with graded interphase zone.

In this work we study the diffusion of a toxic gas in a tunnel due to an explosion in order to realize a control system--via a wireless network of active sensors--for identification and immediate containment procedures. To this end an aspiration pump is turned on instantaneously at a distance of b meters from the explosion to mitigate the effects of the terroristic act. We exactly find the diffusion concentration in order to provide a solution useful for comparison to other models: numerical ones or models with many aspiration pumps. The model is described by the diffusion partial differential equation (PDE) with a non-homogeneous term which models the aspiration pump. A model with more suction pumps is outlined.

We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $\overline{\psi}\psi=0$ with non-vanishing bi-linear pseudo-scalar $i\overline{\psi}\gamma^5\psi\not=0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations., Comment: 12 pages

Making use of the modern techniques of non-holonomic geometry and constrained variational calculus, a revisitation of Ostrogradsky's Hamiltonian formulation of the evolution equations determined by a Lagrangian of order >= 2 in the derivatives of the configuration variables is presented., 8 pages

Junction conditions are discussed within the framework of $f(R)$-gravity with torsion. After deriving general junction conditions, the cases of coupling to a Dirac field and a spin fluid are explicitly dealt with. The main differences with respect to Einstein--Cartan--Sciama--Kibble theory $\left(f(R)=R\right)$ are outlined., Comment: 13 pages

This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrodinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.

We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime while the spinor field is a flag-dipole., 12 pages

In the last dozen years a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the Universe from measured distances, only assuming that the geometry of the can be described by the Friedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshift analysis allows us to put constraints on the cosmographic parameters up to the 5fth order, thus inducing indirect constraints on any gravity theory. Here we are interested in the so called teleparallel gravity theory, f(T). Actually we use the analytical expressions of the present day values of f(T) and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for f(T) and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts (GRB) luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC)., Comment: International Journal of Modern Physics D, 20 pages, 5 figures

The Hamiltonian formulation of the theory proposed in [1, 2] is given both in the Hamilton–De Donder and in the multimomentum Hamiltonian geometrical approaches. (3 + 3) Yang–Mills gauge theories are dealt with explicitly in order to restate them in terms of Einstein–Cartan like field theories.

A new geometrical framework for tetrad-affine formulation of gravity, pure or coupled with Yang–Mills fields, is proposed. After analyzing the geometrical properties of the new mathematical setting, field equations are deduced from a variational principle in the Poincare–Cartan formalism. A generalized Noether Theorem is stated and classical relationship between symmetries and conserved quantities are recovered in the newer scheme. Some explicit examples are given.

A gauge-independent formulation of the theory developed in J. Phys. A: Math. Gen. 36 8341 (2003) is proposed.

We construct a new geometrical framework for Yang–Mills Lagrangian field theories as an appropriate quotient space of the standard first jet-bundle and investigate the geometrical properties of the resulting mathematical setting. We deduce the field equations from a variational problem formulated through a regular Poincare–Cartan form, thus ensuring the kinematical admissibility of critical sections. We state a generalized Nother theorem and explicitly consider the case of the free Yang–Mills field.

We study orthogonal and symmetric operators in non-Archimedean Hilbert spaces in the connection with p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators in the p-adic Hilbert spaces represent physical observables. We study spectral properties of one of the most important quantum operators, namely, the operator of the position (which is represented in the p-adic Hilbert L2-space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve precisions of measurements. We study properties of orthogonal operators. It is proved that each orthogonal operator in the non-Archimedean Hilbert space is continuous. However, there exist discontinuous operators with the dense domain of definition which preserve the inner product. There also exist nonisometric orthogonal operators. We describe some classes of orthogonal isometric operators and we study some general questions of the theory of non-Archimedean Hilbert spaces (in particular, general connections between topology, norm and inner product).

Gaussian measures on infinite-dimensional p-adic spaces are defined and the corresponding L2-spaces of p-adic-valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in such spaces and the formal analogy with the usual Segal representation is discussed. It is found that the parameters of the p-adic infinite-dimensional Weyl group are defined only on some balls. In p-adic Hilbert space, representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. The Hamiltonians with singular potentials are realized as bounded symmetric operators in L2-space with respect to a p-adic Gaussian measure.

A momentum representation for p-adic quantum mechanics is constructed. It uses a Fourier transform in the -space with respect to the p-adic Lebesgue distribution and a study of its properties. The momentum representation is used to investigate the spectral properties of the p-adic momentum operator and to study the (p-adic valued) Schrodinger equation for the p-adic harmonic oscillator.

We propose a physical interpretation for a p-adic picture of reality. According to this interpretation, p-adic numbers describe measurements with a finite accuracy (at the same time, real numbers describe measurements with an infinite accuracy). We consider the representation of the position operator in a p-adic Hilbert space and study the spectrum of this operator.

In this work we show how the Poincare-Cartan form can be used to describe the symmetries of Lagrangian supersymmetric (possibly p-adic) field theories. We show that the existence of the Poincare-Cartan form in supermanifold theory is ensured only in a relevant class of Lagrangian densities. Moreover, we give an abstract characterization of supersymmetric invariance based on the Poincare-Cartan form.

We show howp-adic analysis can be used in some cases to treat divergent series in quantum mechanics. We consider examples in which the usual theory of the Schrodinger equation would give rise to an infinite expectation value of the energy operator. By usingp-adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy. We present also the main ideas to interpret a quantum mechanical state by means ofp-adic statistics.

In this paper we show how p -adic analysis can be used, in some cases, to treat divergent series in quantum mechanics. We shall consider examples in which the usual theory of Schrodinger equation would give rise to an infinite for the expectation value of the energy operator; on the contrary, by using p -adic analysis, we are able to get a convergent expansion and obtain a finite rational value for the energy.

This work is the third one of a series of articles in which the foundations of a p‐adic supermanifold field theory are proposed. In this article p‐adic super‐Lie groups are defined and their properties studied; finally, the p‐adic groups of matrices are analyzed.

In this paper the authors study a simulation model for an uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain. The authors consider an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the dispersion equation in a porous media was obtained by utilizing the Jacobi E3 Function.

We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional $f(R)$-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function $f(R)$; some $f(R)$ models do not isotropize and have no Einstein limit, so that they have no physical significance, whereas for other $f(R)$ models isotropization and Einsteinization occur, and so they are physically acceptable, suggesting that phenomenological arguments may select $f(R)$ models that are physically meaningful; the singularity problem can be avoided, due to the presence of torsion; the general conservation laws holding for $f(R)$-gravity with torsion ensure the preservation of the Hamiltonian constraint, so proving that the initial value problem is well-formulated for these models., Comment: 25 pages, 1 figure

We study a uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain in order to simulate an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the advection dispersion equation in a porous medium was obtained by utilizing the Jacobiθ3Function. The analytical solution here presented has been provided when the inlet (Dirac) and the boundary conditions (Dirichelet, Neumann, and mixed types) are fixed. The proposed solution was used to study experimental data acquired by using a noninvasive technique.

A generalization of the Cauchy-Kowalewsky theorem is obtained for nonlinear evolution equations with (1,1)-supersymmetric time. This theorem ensures the existence and uniqueness of a solution for a large class of superanalytic functions. A generalization of Cartan's technique to the supersymmetric case is also obtained, and by means of it the problem of integrating a system of partial differential equations is transformed into the problem of finding a sequence of integral supermanifolds of lower dimension by means of a succession of integrations based on the Cauchy-Kowalewsky theorem. Evolution equations with (1, 1) time are important for applications to supersymmetric quantum mechanics and field theory, namely, square roots of the Schrodinger and heat-conduction equations. We consider nonlinear generalizations of such equations.

This article is the second part of a work in which p‐adic supermanifold theory is studied; by using the algebraic approach introduced in the first part of this work, p‐adic superdifferential maps are introduced and, by restricting attention to the class of strictly differential maps, the foundation of p‐adic supermanifold theory is developed herein. In particular it is shown that the superfield expansion theorem is no longer true: a superdifferential odd variables map which is not a polynomial is constructed. Finally, tangent space and Lie derivatives are constructed, and it is shown that no complex‐valued fermion field of the p‐adic argument could exist.