Explicit Formulation Research Articles

A study of self-similar vector fields in bianchi type III spacetime via Rif tree approach

Abstract In this study, we use the Rif tree approach to explore self-similar vector fields in Bianchi type III spacetime. This work adopt a computer-based method to transform symmetry equations into an involutive form that is simplified and divides the integration problem into multiple cases, each represented as a tree structure. In some cases, the metric functions are subject to particular constraints. These conditions allow one to solve the system of equations governing self-similar symmetries and provide explicit formulations for the metrics and their corresponding self-similar vector fields. This approach is novel in that it covers not only the analysis of the direct integration strategy but also some metrics that are practically relevant. For a detailed investigation of the created models, stability and physical importance are also considered.

A simple explicit thermodynamic closure for multi-fluid simulations including complex vapor–liquid equilibria: Application to NH3[sbnd]H2O mixtures

This paper presents a new thermodynamic closure formulation appropriate for the simulation of subcritical multiphase flows, where two liquid/vapor components need to be considered, in addition of an arbitrary number of perfect gas non-condensable components. Assuming each component to follow the Noble-Abel Stiffened Gas (NASG) equation of state allows to derive a fully explicit formulation for the mixture pressure. A matching phase transition solver is then proposed to compute efficiently and accurately the thermochemical equilibrium of the said mixture. The model capabilities are then illustrated through a two-dimensional simulation of a liquid ammonia tank leak into 80%-saturated humid air, where water is found to significantly condensate when interacting with the ammonia jet.

Generalizing the Equal Incircles Theorem: Insights from Sangaku Problems

Sangaku problems are traditional Japanese geometrical puzzles, often displayed in religious temples, that have intrigued mathematicians for centuries. This study aims to generalize the Equal Incircles Theorem, extending Angela Drei’s proof to N-circles, by applying the trigonometric method alongside foundational mathematical tools, including mathematical induction, Heron’s formula, and the telescoping product. A generalized equation for N circles based on the Equal Incircles Theorem is derived through explicit mathematical formulation and characterization. The findings deepen our understanding of geometric relationships, highlight the historical significance of Sangaku problems, and offer potential advancements for future engineering applications, mathematics education, and research in mathematical history.

Plato on Parmenides of Elea: the Eleatic PNC case

According to several scholars, the first explicit formulations of the Principle of Non-Contradiction (PNC) can be found in Plato's works, e. g. in the Republic and the Sophist. The paper defends that, in these two dialogues, the context for that is the discussion of possible consequences of Parmenides' Poem, in which Plato seems to have seen a proto-version of the PNC: it is not possible what is not to be (DK28 B7). In that proto-version, the PNC would present itself as an exhaustive disjunction: either it is, and cannot not be, or it is not, and cannot be; and tertium non datur (DK28 B2, B8, passim). The paper shows the problematic corollaries thereof pointed to by Plato in the Republic and the Sophist, as well as it analyses the solutions that he had presented in each dialogue for those problems, namely, his own versions of the PNC.

Accretion of Vlasov gas onto a black hole in the Kalb–Ramond field

Abstract We investigate the accretion of Vlasov gas onto a static, spherically symmetric black hole (BH) influenced by the Kalb–Ramond (KR) field, focusing on the effects of Lorentz symmetry breaking (LSB) parameters. We employ the Maxwell–Jüttner distribution to model the gas at infinity and derive key quantities such as the particle current density and mass accretion rate. Our findings reveal that an increase in the LSB parameter results in a decrease in the mass accretion rate. We also present explicit formulations of the accretion rate in the high-temperature limit and find the result is quite different from the result in Bumblebee model.

Persistent Mayer Dirac

Topological data analysis (TDA) has made significant progress in developing a new class of fundamental operators known as the Dirac operator, particularly in topological signals and molecular representations. However, the current approaches being used are based on the classical case of chain complexes. The present study establishes Mayer Dirac operators based on N-chain complexes. These operators interconnect an alternating sequence of Mayer Laplacian operators, providing a generalization of the classical result . Furthermore, the research presents an explicit formulation of the Laplacian for N-chain complexes induced by vertex sequences on a finite set. Weighted versions of Mayer Laplacian and Dirac operators are introduced to expand the scope and improve applicability, showcasing their effectiveness in capturing physical attributes in various practical scenarios. The study presents a generalized version for factorizing Laplacian operators as an operator's product and its 'adjoint'. Additionally, the proposed persistent Mayer Dirac operators and extensions are applied to biological and chemical domains, particularly in the analysis of molecular structures. The study also highlights the potential applications of persistent Mayer Dirac operators in data science.

Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics

This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.

Even–Odd Layer Oscillatory Behavior of Electronic and Phononic Specific Heat in an Ultra-Thin Metal Film

Both electronic and phononic statistical and thermal properties, modulated by the quantum size effect, are suggested in a thin metal film. In order to show the quantum size effect of specific heat, the densities of the electron and phonon states of an ultra-thin film are treated within the framework of quantum statistics. It was found that strong and weak “even–odd layer oscillatory behavior” was exhibited by the ultra-thin metal film in electronic and lattice specific heat, respectively. Such a behavior, which depends on film thickness, results from the quantum confinement of electrons and phonons in the vertical (thickness) direction of the film, where both electrons and phonons form their respective quantum well standing wave modes. If, for example, the thickness of the ultra-thin metal film is exactly an integer multiple of a half wavelength of the standing wave of electrons in the thickness direction, the corresponding density of states would become maximized, and the electronic specific heat would take its maximum. In the literature, less attention has been paid to the size-dependent electron Fermi wavelength for quantum size effects, i.e., the Fermi wavelength in ultra-thin metal films has always been identified as a constant. We shall show how the Fermi wavelength varies with the size of a nanofilm, including an explicit analytic formulation for the thickness dependence of the electron Fermi wavelength. Size-dependent resonantly oscillatory behavior, depending on the ultra-thin or nanoscale film thickness, would have possible significance for researching some fundamental physical characteristics (e.g., low-dimensional quantum statistics) and may find potential applications in new thermodynamic device design.

A novel unified variational finite difference (VFD) solution method for optimal control problems

This article is aimed to propose a simple yet efficient unified numerical strategy for solving both linear and non-linear optimal control problems. To do so, the general form of quadratic performance index function and nonlinear state equations are considered first. Then, the idea of variational differential quadrature method is used to convert the integral/differential equations to the equivalent algebraic form. Since time is the only independent variable is this research, the finite difference method with an equally-spaced discretization scheme would be a more appropriate technique rather than the differential quadrature approach. So, the implemented numerical solution is called now as the variational finite difference method. The method of Lagrange multipliers is then utilized for minimization purpose and, as a result, the final set of nonlinear algebraic equations are obtained. Finally, the quadratic and triadic forms of non-linearity are considered and an explicit formulation is represented for the residual and Jacobian of the Newton-based iterative solution procedure. To demonstrate the accuracy and efficiency of the proposed approach in the quadratic optimal control area, several benchmark problems involving linear time-invariant, linear time-variant and nonlinear examples are successfully solved and the results are confirmed with those existed in the literature.

A semi-analytical time-domain model with explicit fluid force expressions for streamwise fluidelastic instability of a single and multiple flexible tube array

Fluidelastic instability (FEI) within steam generator tube arrays poses a significant safety concern for nuclear power plants. Traditionally assumed to manifest in the transverse direction, recent failures at the San Onofre Nuclear Generating Station have underscored the importance of understanding streamwise FEI (SFEI). These incidents have spurred analytical investigations into SFEI, but progress has been hindered by the lack of explicit fluid force formulations, particularly in semi-analytical SFEI models. This paper presents a novel semi-analytical time-domain SFEI model featuring an ideal geometry-based decay function and meticulously derived explicit fluid elastic force expressions. The proposed model supports both frequency-domain stability analysis and true time-domain response analysis, and it is applicable to configurations featuring either a single elastic tube in a rigid array or multiple flexible tubes in an array. Additionally, the tube motion phases are obtained by comparing time-domain responses and employing modified multi-tube frequency-domain SFEI analyses. The stability thresholds predicted for a parallel triangular array using our theoretical model closely align with reported experimental data, thereby validating its accuracy. Our work supplements and advances semi-analytical modeling, alleviating implementation challenges for analyzing SFEI phenomena.

On the Solution to Optimal Topology Adjustment in Long-Term Power System Operation with Explicit Short-Circuit Current Limitation Constraints

To restrict the excessive short-circuit current (SCC), this letter proposes an SCC-constrained optimal topology adjustment model considering the N-1 security criterion. Topology adjustment, including transmission switching (TS), bus sectionalization (BS), lines operating out of breaker bay (LOB) and commitment status of units (CU), has nonlinear relationships with SCC and is difficult to express explicitly. In this letter, an explicit formulation of SCC considering topology adjustment is proposed based on the equation of admittance matrix and nodal self-impedance, which is further recast as a mixed-integer linear programming (MILP) model. In addition, the N-1 security criterion is included for avoiding jeopardizing system security by topology adjustment. Numerical case studies validate the effectiveness and advantages of the proposed model in SCC restriction.

Diffusion distribution model for damage mitigation in scanning transmission electron microscopy.

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent reports suggest that certain types of damage can be modelled as a diffusion process and that the accumulation effects of this process must be kept low in order to reduce damage. We therefore develop an explicit mathematical formulation of spatiotemporal diffusion processes in STEM that take into account both instrument and sample parameters. Furthermore, our framework can aid the design of Diffusion Controlled Sampling (DCS) strategies using optimally selected probe positions in STEM, that constrain the cumulative diffusion distribution. Numerical simulations highlight the variability of the cumulative diffusion distribution for different experimental STEM configurations. These analytical and numerical frameworks can subsequently be used for careful design of 2- and 4-dimensional STEM experiments where beam damage isminimised.

Koiter–Newton Reduced-Order Method Using Mixed Kinematics for Nonlinear Buckling Analysis

The Koiter–Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter–Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor–corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis.

Numerical simulations of the region of possible sprite inception in the mesosphere above winter thunderstorms under wind shear

Transient luminous events (TLEs) is the collective name given to mesospheric electrical breakdown phenomena occurring in conjunction with strong lightning discharges in tropospheric thunderstorms. They include elves, sprites, halos, and jets, and are characterized by short lived optical emissions, mostly of red (665 nm) and blue (337 nm) wavelengths. Sprites are caused by the brief quasi-electrostatic field induced in the mesosphere, mostly after the removal of the upper positive charge of the thundercloud by a +CG, and they have been recorded above most of the lightning activity centers on Earth. In wintertime, there are just a few areas where lightning occurs, and of those, sprites have been observed over the Sea of Japan, the British Channel, and the Mediterranean Sea. Unlike their summer counterparts, winter thunderstorms tend to have weaker updrafts and as a result, reduced vertical dimensions and compact charge structures, whose positive and negative centers are located at lower altitudes. These storms are often susceptible to significant wind shear and as a result may exhibit a tilted dipole charge structure and a lateral offset of the upper positive charge relative to the main negative charge. We present results of numerical simulations using a three-dimensional explicit formulation of the mesospheric quasi-electrostatic electrical field following a lightning discharge from a typical mid-latitude winter thunderstorm exhibiting tilt due to wind shear and evaluate the regions of possible sprite inception. Our results show, as numerous observations suggest, that sprites can be shifted a large distance from the location of the parent +CG in the direction of the shear and will occur over a larger region compared with non-sheared storms.

Point'n Move: Interactive scene object manipulation on Gaussian splatting radiance fields

AbstractThe authors propose Point'n Move, a method that achieves interactive scene object manipulation with exposed region inpainting. Interactivity here further comes from intuitive object selection and real‐time editing. To achieve this, Gaussian Splatting Radiance Field is adopted as the scene representation and its explicit nature and speed advantage are fully leveraged. Its explicit representation formulation allows to devise a 2D prompt points to 3D masks dual‐stage self‐prompting segmentation algorithm, perform mask refinement and merging, minimize changes, and provide good initialization for scene inpainting and perform editing in real‐time without per‐editing training; all lead to superior quality and performance. The method was tested by editing both forward‐facing and 360 scenes. The method is also compared against existing methods, showing superior quality despite being more capable and having a speed advantage.

Framed DDF operators and the general solution to Virasoro constraints

We define the framed DDF operators by introducing the concept of local frames in the usual formulation of DDF operators. In doing so it is possible to completely decouple the DDF operators from the associated tachyon and show that they are good zero-dimensional conformal operators. These framed DDFs allow for an explicit covariant formulation of the general solution of the Virasoro constraints both on-shell and off-shell which depends on a unique set of tangent space lightcone polarizations. This is possible since the frame allows us to embed the SO(D-2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SO(D-2)$$\\end{document} lightcone physical polarizations into the SO(1,D-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SO(1,D-1)$$\\end{document} covariant ones in the most general way. The solution to the Virasoro constraints is not in the gauge that is usually used since the states obtained from DDF operators are generically the sum of terms which are partially transverse due to the presence of a projector but not traceless and terms which are partially traceless but not transverse. We then show that different embeddings are connected by states generated by improved Brower operators both on shell and off shell. Brower states are null on-shell and equivalent to BRST exact states. Therefore on shell one embedding is sufficient to compute all amplitudes except the ones with vanishing momentum. Off-shell a change of frame cannot be obtained by null states but only by Brower states. Improved Brower operators generate a gauge invariance associated with local frame rotations, which replaces the usual gauge invariance generated by Virasoro operators or BRST. To check the identification, we verify the matching of the expectation value of the second Casimir of the Poincaré group for some lightcone states with the corresponding covariant states built using the framed DDFs.

A study on dual quaternion based cooperative relative navigation of multiple UAVs with monocular vision-inertial integration

This paper addresses a cooperative relative navigation problem for multiple aerial agents, relying on visual tracking information between vehicles. The research aims to investigate a sensor fusion architecture and algorithm that leverages partially available absolute navigation knowledge while exploiting collaborative visual interaction between vehicles in mission flight areas, where satellite navigation-denied regions are irregularly located. To achieve this, the paper introduces a new approach to defining the relative poses of cameras and develops a corresponding process to secure the relative pose information. This contrasts with previous research, which simply linearized the relative pose information of aircraft cameras into navigation states defined in an absolute coordinate system. Specifically, the target pose in relative navigation is defined, and the pose of the camera and feature points are directly derived using dual quaternion representation, which compactly represents both translation and rotation. Furthermore, a mathematical model for the relative pose of the camera is derived through the dual quaternion framework, enabling an explicit pose formulation of relative navigation. The study investigates navigation performance in typical mission flight scenarios using an in-house high-fidelity simulator and quantitatively highlights the contributions of the proposed scheme by comparing the navigation error performance. Consequently, the proposed method demonstrates to have navigation accuracy in decimeter level even in GNSS-denied environments and an improved 3D Root Mean Square (RMS) error by 30% smaller than the conventional absolute navigation framework.

Distribution Related to All Samples and Extreme Events in the ETAS Cluster

Abstract The probabilistic approach of statistical seismology plays a fundamental role in analyzing the evolution of an earthquake sequence at different scales to deliver reliable forecasts of complex earthquake phenomena. This study contributes to the field by extending previous results relative to the extreme events probability. We derive the explicit formulation of the probability of extreme events in any seismic cluster generated by the epidemic-type aftershock sequence model, as a function of time, space, and magnitude. The results give insights into understanding the distinguishing features between mainshocks and foreshocks, thus helping to shed light on earthquake prediction.

Topology optimization of the electrodes in dielectrophoresis-based devices

This paper aims for developing topology optimization methodology to design the shape of electrodes in Dielectrophoresis (DEP)-based devices. The DEP force is due to a non-uniform electric field induced by applied voltages to the electrodes. Shape of the electrodes has the principal effect on the direction and magnitude of the DEP force. In medical therapy microfluidic devices, DEP force is used for cell sorting and cell separation. While the direction and magnitude of the DEP force are desired to be determined and maximized respectively, the magnitude of the electric field should be minimized to avoid damaging cells. Approaching these goals is counter intuitive where the existing electrode designs are basic. Therefore, a detailed finite element model (FEM) is developed for DEP force and electric field to formulate an optimization problem to maximize the DEP force in a particular direction while there is a constraint on electric field's magnitude. Using the developed FEM, explicit formulations for sensitivity analysis are derived to implement a gradient-based topology optimization. The performance of developed methodology is assessed numerically to determine the direction of the DEP force and constraining the electric field and experimentally in a practical case study of particle trapping in a microfluidic channel.

Utilising redundancy in musculoskeletal systems for adaptive stiffness and muscle failure compensation: a model-free inverse statics approach

Vertebrates possess a biomechanical structure with redundant muscles, enabling adaptability in uncertain and complex environments. Harnessing this inspiration, musculoskeletal systems offer advantages like variable stiffness and resilience to actuator failure and fatigue. Despite their potential, the complex structure presents modelling challenges that are difficult to explicitly formulate and control. This difficulty arises from the need for comprehensive knowledge of the musculoskeletal system, including details such as muscle arrangement, and fully accessible muscle and joint states. Whilst existing model-free methods do not need explicit formulations, they also underutilise the benefits of muscle redundancy. Consequently, they necessitate retraining in the event of muscle failure and require manual tuning of parameters to control joint stiffness limiting their applications under unknown payloads. Presented here is a model-free local inverse statics controller for musculoskeletal systems, employing a feedforward neural network trained on motor babbling data. Experiments with a musculoskeletal leg model showcase the controller’s adaptability to complex structures, including mono and bi-articulate muscles. The controller can compensate for changes such as weight variations, muscle failures, and environmental interactions, retaining reasonable accuracy without the need for any additional retraining.