A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton’s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton’s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.

Self-gravitating anisotropic star using gravitational decoupling

This paper addresses a new gravitationally decoupled anisotropic solution for the compact star model via the minimal geometric deformation (MGD) approach. We consider a non-singular well-behaved gravitational potential corresponding to the radial component of the seed spacetime and embedding class I condition that determines the temporal metric function to solve the seed system completely. However, two different well-known mimic approaches such as pr = Θ1 1 and ρ = Θ0 0 have been employed to determine the deformation function which gives the solution of the second system corresponding to the extra source. In order to test the physical viability of the solution, we have checked several conditions such as regularity conditions, energy conditions, causality conditions, hydrostatic equilibrium, etc. Moreover, the stability of the solutions has been also discussed by the adiabatic index and its critical value. We find that the solutions set seems viable as far as observational data are concerned.

Dynamo seeds from Gravitational Torsional Anomalies and De Sitter Magnetized Metrics

Recently gravitational and Nieh-Yan chiral anomalies have been obtained in Riemann-Cartan spacetime Class and Quantum Gravity 38 (2021)], where electrodynamics is encoddded in the metric. In this paper we follow the path of obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized DSMM without axial anomalies is proved. Here we obtain unified theories a la Einstein and Eddington and Schroedinger, called modified de Sitter metric (MDSM) with the novel following features: (i) First we show that a pure de Sitter unmagnetized metric in T4 does not induce gravitational anomalies. Therefore this is a motivation to study modifications of De Sitter metric. What is done in the following items. (ii) Nieh-Yan torsion anomaly in (DSMM) in teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-tivial anomalies are obtained from these metrics. But torsional anomaly much used in condensed matter physics, does not vanish. From these magnetized metrics, we show that with dynamo equation with torsion gradients sources is valid from class 3 of the metrics but is torsionless sourced in second class. (iii) We show that in the gravitational anomaly of new deformed de Sitter metric one may cancell the gravitational anomaly by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. Use original de Sitter nonconformal metric . A simple deformation leads to the existence of the NY form in the case of magnetized de Sitter metric. This would be class IV of DSMM.

Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

Note on the Charged Black Hole Solutions in a Static Quantum Inspired Spacetime: Massive Gravity as Background

In this paper, we explore the black hole solutions with rainbow deformed metric in the presence of exponential form of nonlinear electrodynamics with asymptotic Reissner-Nordstrom properties. We calculate the exact solution of metric function and explore the geometrical prop- erties in the background of massive gravity. From the obtained solution, the existence of the singularity is confirmed in proper limits. Using the solutions we also investigate the thermody- namic properties of the solutions by checking the validity of the first law of thermodynamics. Continuing the thermodynamic study, we investigate the conditions under which the system is thermally stable from the heat capacity and the Gibbs free energy. We also discuss the possible phase transition and the criticality of the system. It was found that the quantum gravitational effects of gravity’s rainbow render the thermodynamic system stable in the vicinity of the singu- larity. From the equation of state it was found that after diverging at the singularity, the system evolves asymptotically into pressure-less dust as one moves away from the central singularity.

Magnetic nonsingular black holes in lovelock gravity coupled to exponential electrodynamics

The model of exponential electromagnetic field is coupled to Lovelock gravitational field in [Formula: see text]-dimensional spacetime geometry. In this context, new class of magnetically charged nonsingular or regular Lovelock black holes has been introduced. The asymptotic behavior of resulting metric function in the vicinity of [Formula: see text] is studied. The obtained asymptotic expressions in both even and odd critical dimensions show the finiteness and regularity of the solution at [Formula: see text]. The thermodynamic quantities such as Hawking temperature and specific heat capacity at constant magnetic charge corresponding to the nonsingular black hole are computed. The tunneling probability associated with Hawking radiations from these black holes is calculated as well.

The Direction of Erosion

The rate of erosion of a geomorphic surface depends on its local gradient and on the material fluxes over it. Since both quantities are functions of the shape of the catchment surface, this dependence constitutes a mathematical straitjacket, in the sense that – subject to simplifying assumptions about the erosion process, and absent variations in external forcing and erodibility – the rate of change of surface geometry is solely a function of surface geometry. Here we demonstrate how to use this geometric self-constraint to convert an erosion model into its equivalent Hamiltonian, and explore the implications of having a Hamiltonian description of the erosion process. To achieve this conversion, we recognize that the rate of erosion defines the velocity of surface motion in its orthogonal direction, and we express this rate in its reciprocal form as the surface-normal slowness. By rewriting surface tilt in terms of normal slowness components, and by deploying a substitution developed in geometric mechanics, we extract what is known as the fundamental metric function of the model phase space; its square is the Hamiltonian. Such a Hamiltonian provides several new ways of solving for the evolution of an erosion surface: here we use it to derive Hamilton's ray tracing equations, which describe both the velocity of a surface point and the rate of change of the surface-normal slowness at that point. In this context, erosion involves two distinct directions: (i) the surface-normal direction, which points subvertically downwards, and (ii) the erosion ray direction, which points upstream at a generally small angle to horizontal with a sign controlled by the scaling of erosion with slope. If the model erosion rate scales faster than linearly with gradient, the rays point obliquely upwards; but if erosion scales sublinearly with gradient, the rays point obliquely downwards. Analysis of the Hamiltonian shows that these rays carry boundary-condition information upstream, and that they are geodesics, meaning that erosion takes the path of least erosion time. This constitutes a definition of the variational principle governing landscape evolution. In contrast with previous studies of network self-organization, neither energy nor energy dissipation is invoked in this variational principle, only geometry.

Stable Morris Thorne wormholes supported by non-exotic matter

The present work is focused on the study of traversable wormholes, proposed by Morris and Thorne [Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395], using the background of modified gravity. It is performed by using the models: I. [Formula: see text], II. [Formula: see text] and III. [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are constants. The Model I belongs to the theory of [Formula: see text] gravity, Model II belongs to the theory of [Formula: see text] gravity and Model III is a combination of Models I and II. These functions have been taken into account for the exploration of wormhole solutions. The shape function, a wormhole metric function, is newly defined which satisfies the flare out condition. Further, the stability condition and energy conditions, namely null, weak and dominant energy conditions, have been examined with respect to each model.

Beyond gravitomagnetism with applications to Mercury’s perihelion advance and the bending of light

The expansion of both sides of Einstein’s field equations in the weak-field approximation, up to terms of order [Formula: see text] is derived. This new approach leads to an extended form of gravitomagnetism (GEM) properly named as Beyond Gravitomagnetism (BGEM). The metric of BGEM includes a quadratic term in the gravitoelectric potential n the time and also space metric functions in contrast with first post-Newtonian [Formula: see text]PN approximation where the quadratic term appears only in the time metric function. This nonlinear term does not appear in conventional GEM, but is essential in achieving the exact value of Mercury’s perihelion advance as we explicitly show. The new BGEM metric is also applied to the classical problem of light deflection by the Sun, but the contribution of the new nonlinear terms produce higher-order terms in this problem and can be neglected, giving the correct result obtained already in the Lense–Thirring (GEM) approximation. The BGEM approximation also provides new terms that depend on the dynamics of the system, which may bring new insights into galactic and stellar physics.

Multi-Source Co-adaptation for EEG-Based Emotion Recognition by Mining Correlation Information

Since each individual subject may present completely different encephalogram (EEG) patterns with respect to other subjects, existing subject-independent emotion classifiers trained on data sampled from cross-subjects or cross-dataset generally fail to achieve sound accuracy. In this scenario, the domain adaptation technique could be employed to address this problem, which has recently got extensive attention due to its effectiveness on cross-distribution learning. Focusing on cross-subject or cross-dataset automated emotion recognition with EEG features, we propose in this article a robust multi-source co-adaptation framework by mining diverse correlation information (MACI) among domains and features with l2,1−norm as well as correlation metric regularization. Specifically, by minimizing the statistical and semantic distribution differences between source and target domains, multiple subject-invariant classifiers can be learned together in a joint framework, which can make MACI use relevant knowledge from multiple sources by exploiting the developed correlation metric function. Comprehensive experimental evidence on DEAP and SEED datasets verifies the better performance of MACI in EEG-based emotion recognition.