Search Results (399)

It is essential to establish the validity of Ohm’s law in any reference frame if we aim to implement a relativistic approach to brain dynamics based on a Lorentz covariant microscopic response relation. Here, we obtain a covariant formulation of Ohm’s law for an electromagnetic field tensor of any order derived from the emergent conductivity tensor in highly non-isotropic systems, employing the bidomain theory framework within brain tissue cells. With this, we offer a different perspective that we hope will lead to understanding the close relationship between brain dynamics and a seemingly ordinary yet profoundly crucial element: space. Full article

Since multi-view learning leverages complementary information from multiple feature sets to improve model performance, a tensor-based data fusion layer for neural networks, called Multi-View Data Tensor Fusion (MV-DTF), is used. It fuses M feature spaces ${\mathcal{X}}_1,\cdots ,{\mathcal{X}}_M$, referred to as views, in a new latent tensor space, $\mathcal{S}$, of order P and dimension $J_1\times \cdots \times J_P$, defined in the space of affine mappings composed of a multilinear map $\mathcal{T}:{\mathcal{X}}_1\times \cdots \times {\mathcal{X}}_M\to \mathcal{S}$—represented as the Einstein product between a $(P+M)$-order tensor $\mathcal{A}$ anda rank-one tensor, $\mathcal{X}={\mathrm{x}}^{\left(1\right)}\otimes \cdots \otimes {\mathrm{x}}^{\left(M\right)}$, where ${\mathrm{x}}^{\left(m\right)}\in {\mathcal{X}}_m$ is the m-th view—and a translation. Unfortunately, as the number of views increases, the number of parameters that determine the MV-DTF layer grows exponentially, and consequently, so does its computational complexity. To address this issue, we enforce low-rank constraints on certain subtensors of tensor $\mathcal{A}$ using canonical polyadic decomposition, from which M other tensors ${\mathcal{U}}^{\left(1\right)},\cdots ,{\mathcal{U}}^{\left(M\right)}$, called here Hadamard factor tensors, are obtained. We found that the Einstein product $\mathcal{A}{⊛}_M\mathcal{X}$ can be approximated using a sum of R Hadamard products of M Einstein products encoded as ${\mathcal{U}}^{\left(m\right)}{⊛}_1{\mathrm{x}}^{\left(m\right)}$, where R is related to the decomposition rank of subtensors of $\mathcal{A}$. For this relationship, the lower the rank values, the more computationally efficient the approximation. To the best of our knowledge, this relationship has not previously been reported in the literature. As a case study, we present a multitask model of vehicle traffic surveillance for occlusion detection and vehicle-size classification tasks, with a low-rank MV-DTF layer, achieving up to $92.81\%$ and $95.10\%$ in the normalized weighted Matthews correlation coefficient metric in individual tasks, representing a significant $6\%$ and $7\%$ improvement compared to the single-task single-view models. Full article

A disaffinity vector on a Riemannian manifold $(M,g)$ is a vector field whose affinity tensor vanishes. In this paper, we observe that nontrivial disaffinity functions offer obstruction to the topology of M and show that the existence of a nontrivial disaffinity function on M does not allow M to be compact. A characterization of the Euclidean space is also obtained by using nontrivial disaffinity functions. Further, we study properties of disaffinity vectors on M and prove that every Killing vector field is a disaffinity vector. Then, we prove that if the potential field $\zeta$ of a Ricci soliton $\left(M,g,\zeta ,\lambda \right)$ is a disaffinity vector, then the scalar curvature is constant. As an application, we obtain conditions under which a Ricci soliton $\left(M,g,\zeta ,\lambda \right)$ is trivial. Finally, we prove that a Yamabe soliton $\left(M,g,\xi ,\lambda \right)$ with a disaffinity potential field $\xi$ is trivial. Full article

The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman–Enskog (Ch-En) solution to the RTA. If developed to all orders, this would yield an asymptotic solution to the kinetic equation; we restrict ourselves to an approximate solution by truncating the Ch-En series to the second order. Our generalized Ch-En solution contains undetermined space-time-dependent parameters, and we derive a set of dynamical equations for them by applying the moments method. We check that these dynamical equations lead to energy–momentum conservation and positive entropy production. Finally, we compute the propagation speeds for fluctuations away from equilibrium from the linearized form of the dynamical equations. Considering relaxation times of the form $\tau ={\tau }_0{(-{\beta }_{\mu }{p}^{\mu })}^{-a}$, with $-\infty <a<2$, where ${\beta }_{\mu }=u_{\mu }/T$ is the temperature vector in the Landau frame, we show that the Anderson–Witting prescription $a=1$ yields the fastest speed in all scalar, vector and tensor sectors. This fact ought to be taken into consideration when choosing the best macroscopic description for a given physical system. Full article

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory. Full article

This paper presents the development of a hardware-in-the-loop ground testbed featuring active gravity compensation via software-in-the-loop integration, specially designed to support research in autonomous robotic removal of space debris. The testbed is designed to replicate six degrees of freedom (6DOF) motion maneuvering to accurately simulate the dynamic behaviors of free-floating robotic manipulators and free-tumbling space debris under microgravity conditions. The testbed incorporates two industrial 6DOF robotic manipulators, a three-finger robotic gripper, and a suite of sensors, including cameras, force/torque sensors, and tactile tensors. Such a setup provides a robust platform for testing and validating technologies related to autonomous tracking, capture, and post-capture stabilization within the context of active space debris removal missions. Preliminary experimental results have demonstrated advancements in motion control, computer vision, and sensor fusion. This facility is positioned to become an essential resource for the development and validation of robotic manipulators in space, offering substantial improvements to the effectiveness and reliability of autonomous capture operations in space missions. Full article

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the “Swampland” program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not. Full article

In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space $V_4$. In the case where the group of motions $G_3$ acts in a simply transitive way in the homogeneous space $V_4$, the geometry of the non-isotropic hypersurface is determined by the geometry of the transitivity space $V_3$ of the group $G_3$. In this case, the metric tensor of the space $V_3$ can be given by a nonholonomic reper consisting of three independent vectors ${\ell }_{\left(a\right)}^{\alpha }$, which define the generators of the group $G_3$ of finite transformations in the space $V_3$. The representation of the metric tensor of $V_4$ spaces by means of vector fields ${\ell }_{\left(a\right)}^{\alpha }$ has a great physical meaning and makes it possible to substantially simplify the equations of mathematical physics in such spaces. Therefore, the Petrov classification should be complemented by the classification of vector fields ${\ell }_{\left(a\right)}^{\alpha }$ connected to Killing vector fields. For homogeneous spaces, this problem has been largely solved. A complete solution of this problem is presented in the present paper, where I refine the Petrov classification for homogeneous spaces in which the group $G_3$, which belongs to type $VIII$ according to the Petrov classification, acts simply transitively. In addition, this paper provides the complete classification of vector fields ${\ell }_{\left(a\right)}^{\alpha }$ for space $V_4$ in which the group $G_3$ acts simply transitivity on isotropic hypersurfaces. Full article

In the present work the atomic, electronic and optical properties of two-dimensional graphene, borophene, and boron carbide heterojunction bilayer systems (Graphene–BC₃, Graphene–Borophene and Graphene–B₄C₃) as well as their constituent monolayers are investigated on the basis of first-principles calculations using the HSE06 hybrid functional. Our calculations show that while borophene is metallic, both monolayer BC₃ and B₄C₃ are indirect semiconductors, with band-gaps of 1.822 eV and 2.381 eV as obtained using HSE06. The Graphene–BC₃ and Graphene–B₄C₃ bilayer heterojunction systems maintain the Dirac point-like character of graphene at the K-point with the opening of a very small gap (20–50 meV) and are essentially semi-metals, while Graphene–Borophene is metallic. All bilayer heterostructure systems possess absorbance in the visible region where the resonance frequency and resonance absorption peak intensity vary between structures. Remarkably, all heterojunctions support plasmons within the range 16.5–18.5 eV, while Graphene–B₄C₃ and Graphene–Borophene exhibit a $\pi$-type plasmon within the region 4–6 eV, with the latter possessing an additional plasmon at the lower energy of 1.5–3 eV. The dielectric tensor for Graphene–B₄C₃ exhibits complex off-diagonal elements due to the lower P3 space group symmetry indicating it has anisotropic dielectric properties and could exhibit optically active (chiral) effects. Our study shows that the two-dimensional heterostructures have desirable optical properties broadening the potential applications of the constituent monolayers. Full article

The deep learning system for e-waste management presented in this proposal is a transformative solution designed to address the escalating challenges of garbage collection and management in urban environments. Rapid urbanization has resulted in increased waste generation, necessitating a more intelligent and efficient approach to e-waste collection and disposal. This system integrates cutting-edge technologies, primarily Artificial Intelligence (AI), to improve e-waste management processes, enhance resource utilization, and contribute to the creation of cleaner and more sustainable urban spaces. Urban areas are experiencing unprecedented growth, leading to a surge in the volume of waste generated daily; as such, traditional waste management systems struggle to cope with this influx, resulting in environmental pollution, compromised public health, and inefficient resource utilization. The proposed deep learning model with accuracy of 83% seeks to revolutionize existing practices by leveraging the capabilities of AI. The aim of this research is to develop a sequential neural network using a Keras and TensorFlow image analysis: a deep learning convolutional neural network (CNN) for e-waste management. The Python programming tool will be used to develop the deep learning model as well as a GUI that will facilitate human–computer interactions. The system will be tested and the result evaluated to assess the functionality and adequacy of the system. Full article

A nontrivial conformal vector field $\omega$ on an m-dimensional connected Riemannian manifold $\left(M^m,g\right)$ has naturally associated with it the conformal potential $\theta$, a smooth function on $M^m$, and a skew-symmetric tensor T of type $(1,1)$ called the associated tensor. There is a third entity, namely the vector field $T\omega$, called the orthogonal reflection field, and in this article, we study the impact of the condition that commutator $\left[\omega ,T\omega \right]=0$; this condition that we refer to as the orthogonal reflection field is commutative. As a natural impact of this condition, we see the existence of a smooth function $\rho$ on $M^m$ such that $\nabla \theta =\rho \omega$; this function $\rho$ is called the proportionality function. First, we show that an m-dimensional compact and connected Riemannian manifold $\left(M^m,g\right)$ admits a nontrivial conformal vector field $\omega$ with a commuting orthogonal reflection $T\omega$ and constant proportionality function $\rho$ if and only if $\left(M^m,g\right)$ is isometric to the sphere $S^m\left(c\right)$ of constant curvature c. Secondly, we find three more characterizations of the sphere and two characterizations of a Euclidean space using these ideas. Finally, we provide a condition for a conformal vector field on a compact Riemannian manifold to be closed. Full article

To alleviate the power flow congestion in active distribution networks (ADNs), this paper proposes a two-stage load transfer optimization model based on Neo4j-Dueling DQN. First, the Neo4j graph model was established as the training environment for Dueling DQN. Meanwhile, the power supply paths from the congestion point to the power source point were obtained using the Cypher language built into Neo4j, forming a load transfer space that served as the action space. Secondly, based on various constraints in the load transfer process, a reward and penalty function was formulated to establish the Dueling DQN training model. Finally, according to the $\epsilon -greedy$ action selection strategy, actions were selected from the action space and interacted with the Neo4j environment, resulting in the optimal load transfer operation sequence. In this paper, Python was used as the programming language, TensorFlow open-source software library was used to form a deep reinforcement network, and Py2neo toolkit was used to complete the linkage between the python platform and Neo4j. We conducted experiments on a real 79-node system, using three power flow congestion scenarios for validation. Under the three power flow congestion scenarios, the time required to obtain the results was 2.87 s, 4.37 s and 3.45 s, respectively. For scenario 1 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by about 56.0%, 76.0% and 55.7%, respectively. For scenario 2 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by 41.7%, 72.9% and 56.7%, respectively. For scenario 3 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by 13.6%, 47.1% and 37.7%, respectively. The experimental results show that the trained model can quickly and accurately derive the optimal load transfer operation sequence under different power flow congestion conditions, thereby validating the effectiveness of the proposed model. Full article

This paper presents micromechanical analyses of an orthogonally reinforced composite with new constitutive equations of kinematic plastic hardening. The homogenization of plastic properties was performed through a numerical analysis of a representative volume using the finite element method. A modification of Prager’s theory was used to construct physical relations for an equivalent orthotropic material. In the proposed version of the theory, a special tensor for back stresses is introduced, which takes into account the difference in the rate of hardening for different types of plastic deformation. For boron–aluminum orthogonally reinforced composite with known mechanical properties of fibers and matrix, all material parameters of the theory were determined, deformation diagrams were constructed, and the equation for a plasticity surface in a six-dimensional stress space was obtained. The advantage of the developed method of numerical homogenization is that it only requires a minimal amount of experimental data. The efficiency of micromechanical analysis makes it possible to optimally design metal matrix composites with the required plastic properties. Full article

Quantum many-body systems are of great interest for many research areas, including physics, biology, and chemistry. However, their simulation is extremely challenging, due to the exponential growth of the Hilbert space with system size, making it exceedingly difficult to parameterize the wave functions of large systems by using exact methods. Neural networks and machine learning, in general, are a way to face this challenge. For instance, methods like tensor networks and neural quantum states are being investigated as promising tools to obtain the wave function of a quantum mechanical system. In this tutorial, we focus on a particularly promising class of deep learning algorithms. We explain how to construct a Physics-Informed Neural Network (PINN) able to solve the Schrödinger equation for a given potential, by finding its eigenvalues and eigenfunctions. This technique is unsupervised, and utilizes a novel computational method in a manner that is barely explored. PINNs are a deep learning method that exploit automatic differentiation to solve integro-differential equations in a mesh-free way. We show how to find both the ground and the excited states. The method discovers the states progressively by starting from the ground state. We explain how to introduce inductive biases in the loss to exploit further knowledge of the physical system. Such additional constraints allow for a faster and more accurate convergence. This technique can then be enhanced by a smart choice of collocation points in order to take advantage of the mesh-free nature of the PINN. The methods are made explicit by applying them to the infinite potential well and the particle in a ring, a challenging problem to be learned by an artificial intelligence agent due to the presence of complex-valued eigenfunctions and degenerate states Full article

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions. Full article