Variational theory of the Ricci curvature tensor dynamics

In this letter a new Lagrangian variational principle is proved to hold for the Einstein field equations, in which the independent variational tensor field is identified with the Ricci curvature tensor $$R^{\mu \nu }$$ R μ ν rather than the metric tensor $$g_{\mu \nu }$$ g μ ν . The corresponding Lagrangian function, denoted as $$L_{R}$$ L R , is realized by a polynomial expression of the Ricci 4-scalar $$R\equiv g_{\mu \nu }R^{\mu \nu }$$ R ≡ g μ ν R μ ν and of the quadratic curvature 4-scalar $$\rho \equiv R^{\mu \nu }R_{\mu \nu }$$ ρ ≡ R μ ν R μ ν . The Lagrangian variational principle applies both to vacuum and non-vacuum cases and for its validity it demands a non-vanishing, and actually also positive, cosmological constant $$\Lambda >0$$ Λ > 0 . Then, by implementing the deDonder–Weyl formalism, the physical conditions for the existence of a manifestly-covariant Hamiltonian structure associated with such a Lagrangian formulation are investigated. As a consequence, it is proved that the Ricci tensor can obey a Hamiltonian dynamics which is consistent with the solutions predicted by the Einstein field equations.

Evaluation of Accelerometer-Derived Data in the Context of Cycling Cadence and Saddle Height Changes in Triathlon

In the multisport of triathlon cycling is the longest of the three sequential disciplines. Triathlon bicycles differ from road bicycles with steeper seat tube angles with a change to saddle height altering the seat tube angle. This study evaluated the effectiveness of a tri axial accelerometer to determine acceleration magnitudes of the trunk in outdoor cycling in two saddle positions. Interpretation of data was evaluated based on cadence changes whilst triathletes cycled in an aerodynamic position in two saddle positions. The evaluation of accelerometer derived data within a characteristic overground setting suggests a significant reduction in mediolateral acceleration of the trunk, yielding a 25.1% decrease when saddle height was altered alongside reduced rate of perceived exertion (3.9%). Minimal differences were observed in anteroposterior and longitudinal acceleration. Evaluation of sensor data revealed a polynomial expression of the subtle changes between both saddle positions. This study shows that a triaxial accelerometer has capability to continuously measure acceleration magnitude of trunk movements during an in-the-field, varied cadence cycle protocol. Accessible and practical sensor technology could be relevant for postural considerations when exploring saddle position in dynamic settings.

SELECTION OF LOCATIONS FOR GROUND BASED OPTICAL SURVEILLANCE DEVICES BASED ON THE FUZZY PROBABILITY MODEL

When choosing the location of groundbased optical surveillance devices (NOSN), the problem arises of evaluating the suitability of a particular area of terrain or choosing the best of a number of considered ones, provided that the ability to perform professional tasks with specified characteristics is quantified. A method for solving this problem is proposed by constructing a fuzzyprobability model of a generalized (integral) indicator of the quality of NOS placements based on the knowledge and experience of experts. Such an indicator is determined by a systemically confirmed set of seven linguistic variables included in the factor space for constructing a fuzzy probability model in the form of a nonlinear polynomial expression. At the same time, the dependent variablethe ability to perform the task with the specified characteristicsindirectly determines the degree of the best placement of the NOS, taking into account its astroclimate. Practical recommendations on the choice and justification of the factor space are given, the main stages of constructing a fuzzy probability model are shown, and the degree of adequacy of calculations based on it to the actual ability to perform tasks with specified characteristics, evaluated by independent experts, for the locations of NOS in various geographical regions of the Russian Federation.

Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities

The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form of the boundary value problem formulated at the microscopic level, a polynomial expression of the virtual velocity is adopted as the minimum microscopic kinematics consistent with the selected macroscopic kinematics of the strain gradient effective continuum. The effective volumetric and interfacial mesoscopic strains and stress measures for the effective substitution are obtained versus the microscopic strains and stresses. The Hill macrohomogeneity condition is successively formulated for continuous interfaces and discontinuous interfaces witnessing strong discontinuities. It highlights the expressions of the effective stress measures associated to the volumetric and interfacial behavior for both classical and higher-order effects.

Mathematical Modeling of Suspended Microbial Fuel Cells and Electron Transfer Mediator using Homotopy Perturbation Method

The theoretical model of microbial fuel cells with suspended cells and an additional electron transfer mediator is analyzed. Many biological, chemical and electrochemical reactions occur in the bulk liquid and on the surface of the electrode with the substrate (glucose), oxidized mediators and reduced mediators. The homotopy perturbation method (HPM) is used to solve the nonlinear diffusion equations in microbial fuel cells. Direct and approximate polynomial expression of a substrate (glucose), oxidized mediator and reduced mediator concentration are obtained at the mass transfer balance layer. The results of the experiment are compared with the results of the analytical and simulation and satisfactory agreement is noted.

Almost Exact Computation of Eigenvalues in Approximate Differential Problems

Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab toolbox was recently presented and here we explore its potential use and suitability for this problem. The first step is to translate the eigenvalue differential problem into an algebraic approximated eigenvalues problem. In a second step, making use of symbolic computations, we arrive at the exact polynomial expression of the determinant of the algebraic problem matrix, allowing us to get high accuracy approximations of differential eigenvalues.

ELASTO-PLASTIC PROPERTIES OF Mo-MODIFIED Ti DEDUCED FROM INDENTATION TESTS AND FINITE ELEMENT ANALYSIS

The aim of this paper is to establish an approach to quantitatively determine the elasto-plastic parameters of the Mo-modified Ti obtained by the plasma surface alloying technique. A micro-indentation test is conducted on the surface under 10[Formula: see text]N. Considering size effects, nanoindentation tests are conducted on the cross-section with two loads of 6 and 8[Formula: see text]mN. Assuming nanoindentation testing sublayers are homogeneous, finite element reverse analysis is adopted to determine their plastic parameters. According to the gradient distributions of the elasto-plastic parameters with depth in the Mo-modified Ti, two types of mathematical expressions are proposed. Compared with the polynomial expression, the linear simplified expression does not need the graded material to be sectioned and has practical utility in the surface treatment industry. The validation of the linear simplified expression is verified by the micro-indentation test and corresponding finite element forward analysis. This approach can assist in improving the surface treatment process of the Mo-modified Ti and further enhancing its load capacity and wear resistance.

Exact solutions of the sextic oscillator from the bi-confluent Heun equation

In this paper, the sextic oscillator is discussed as a potential obtained from the bi-confluent Heun equation after a suitable variable transformation. Following earlier results, the solutions of this differential equation are expressed as a series expansion of Hermite functions with shifted and scaled arguments. The expansion coefficients are obtained from a three-term recurrence relation. It is shown that this construction leads to the known quasi-exactly solvable (QES) form of the sextic oscillator when some parameters are chosen in a specific way. By forcing the termination of the recurrence relation, the Hermite functions turn into Hermite polynomials with shifted arguments, and, at the same time, a polynomial expression is obtained for one of the parameters, the roots of which supply the energy eigenvalues. With the [Formula: see text] choice the quartic potential term is canceled, leading to the reduced sextic oscillator. It was found that the expressions for the energy eigenvalues and the corresponding wave functions of this potential agree with those obtained from the QES formalism. Possible generalizations of the method are also presented.