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This article aims at this problem of adaptive neural tracking control for state-constrained systems. A general fixed-time stability criterion is first presented, by which an adaptive neural control algorithm is developed. Under the action of the proposed adaptive neural tracking controller, the tracking error converges into a small neighborhood around the origin in fixed time; meanwhile, all system states abide by the corresponding state constraints for all the time. The main difference between the present research and the previous control schemes for state-constrained systems is that this article proposes a novel and feasible approach to ensure that the constructed virtual control signals satisfy the state constraints on the corresponding states viewed as the virtual control inputs. Such an approach guarantees theoretically that all the system states cannot violate their constrained requirements at any time. Finally, two simulation examples provide support to the proposed results.

In this brief, stabilization of Boolean networks (BNs) by flipping a subset of nodes is considered, here we call such action state-flipped control. The state-flipped control implies that the logical variables of certain nodes are flipped from 1 to 0 or 0 to 1 as time flows. Under state-flipped control on certain nodes, a state-flipped-transition matrix is defined to describe the impact on the state transition space. Weak stabilization is first defined and then some criteria are presented to judge the same. An algorithm is proposed to find a stabilizing kernel such that BNs can achieve weak stabilization to the desired state with in-degree more than 0. By defining a reachable set, another approach is proposed to verify weak stabilization, and an algorithm is given to obtain a flip sequence steering an initial state to a given target state. Subsequently, the issue of finding flip sequences to steer BNs from weak stabilization to global stabilization is addressed. In addition, a model-free reinforcement algorithm, namely the Q-learning (QL) algorithm, is developed to find flip sequences to achieve global stabilization. Finally, several numerical examples are given to illustrate the obtained theoretical results.

The objective of the paper was to compare values of the muzzle brake efficiency coefficient for a rifle with active or inactive automatics systems. Special laboratory stand designed for investigating the recoil process was used. The motion of the rifle was detected by the use of the laser interferometer and the optical camera. The recoil velocity time courses were determined by smoothing and differentiation of experimental position records. The results of the experiments indicated that in the case of an active automatics system two values of the recoil velocity can be used for calculation of the energetic efficiency coefficient: the maximum recoil velocity and the final recoil velocity at the end of the automatics action cycle. The values of the coefficient, calculated using these two values of the recoil velocity, distinctly differ. However, it was shown that their values indicate the same relation between the efficiency of various muzzle brakes. The value of the efficiency coefficient, determined on the basis of the final recoil velocity value, is practically the same as that determined on the basis of the final recoil velocity value for the rifle with an inactive automatics system.

An effective path-following guidance algorithm for unmanned combat aerial vehicles by pursuing a look-ahead target-point along the desired path is devised. The concept of look-ahead pursuit for 3-D path-following was extended from the planar ${\mathcal {L}_1}$ guidance, which has been widely adopted in the application of lateral guidance of fixed-wing drone. Decoupled implementation of the planar guidance action on each of the longitudinal (vertical) and lateral (horizontal) planes supplies longitudinal-lateral acceleration commands in two perpendicular planes which is well accepted by aviation engineers. The computation of the look-ahead point utilizes a finite and iterative numerical search method by introducing an auxiliary path-related parameter. Furthermore, additional implementation-specific details such as the modification of adaptive ${\mathcal {L}_1}$ length and the protection strategies ensuring wide applicability of the algorithm indeed guarantee certain necessity to be considered in real implementation of the guidance law. The improved schemes eliminate complicated coordinate transformations and are built on the path-independent assumption, thus making them easier to be adjusted between various types of paths, including discrete optimal trajectories. Monte Carlo simulations and real-world flight tests have confirmed the effectiveness of the nonlinear guidance algorithm.

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

We study the natural action of S n on the set of k-subsets of the set { 1 , … , n } when 1 ≤ k ≤ n 2 . For this action we calculate the maximum size of a minimal base, the height and the maximum length of an irredundant base. Here a base is a set with trivial pointwise stabilizer, the height is the maximum size of a subset with the property that its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset, and an irredundant base can be thought of as a chain of (pointwise) set-stabilizers for which all containments are proper.

This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study.

Orbits and bi-invariant subsets of binary $G$-spaces are studied. The problem of the distributivity of a binary action of a group $G$ on a space $X$, which was posed in 2016 by one of the authors, is solved., 11 pages

This article provides a general framework for the use of low-impedance displacement sensors mounted on the links of a serial robot to provide an intuitive physical human–robot interaction. A general formulation is developed to handle the motion guidance problem, i.e., the mapping of the measured motion of the sensors into the required robot joint motions to provide intuitive responsiveness. The formulation is general and can be applied to any architecture of serial robot with any number of displacement sensors each having an arbitrary number of degrees of freedom. Then, the design of a novel three-degree-of-freedom low-impedance displacement sensor is presented as a particularly effective instantiation of the general concept. Partial force balancing is used to reduce the required elastic return action, thereby ensuring the low impedance of the interaction. A prototype of a three-degree-of-freedom displacement sensor is then introduced. Two such sensors are mounted on the links of a custom-built five-degree-of-freedom robot in order to demonstrate the proposed approach. Experimental results are provided and comparisons with other collaborative robots are given. It is shown that the proposed sensors and motion guidance approach yield very intuitive low-impedance interaction involving very low interaction forces.

We study games with almost perfect information and an infinite time horizon. In such games, at each stage, the players simultaneously choose actions from finite action sets, knowing the actions chosen at all previous stages. The payoff of each player is a function of all actions chosen during the game. We define and examine the new condition of individual upper semicontinuity on the payoff functions, which is weaker than upper semicontinuity. We prove that a game with individual upper semicontinuous payoff functions admits a subgame perfect $$\epsilon $$ ϵ -equilibrium for every $$\epsilon >0$$ ϵ > 0 , in eventually pure strategy profiles.

A control design framework for the coupled stability problem in robotics is presented. The proposed framework fundamentally generalizes the conventional passivity-based approaches to the coupled stability problem. In particular, it allows for stabilization of not necessarily passive robot-environment interaction where both the manipulator and the environment are dissipative systems with quadratic supply rates. In contrast with existing results, the proposed framework can be used in combination with an arbitrary robot’s tracking control algorithm, and its stabilizing action when in contact with environment does not affect the robot’s trajectory tracking performance in free space. The framework is based on the recently developed nonplanar conic systems formalism and generalized scattering-based stabilization methods. A detailed design example is presented which illustrates the capabilities of the proposed method.

Numerical analysis of collision is an important aspect of bridge seismic research. This paper introduces precise integration to the numerical analysis of seismic collision. Firstly, the collision forces of four contact element models were expressed in a unified form, including linear spring model, Kelvin-Voigt model, Hertz model, and Jan-Hertz-Damp model, and then the precision integration formula was derived for solving the collision force. Next, a collision time search method was proposed under the linear acceleration hypothesis, and the seismic collision was divided into a collision phase and a non-collision phase. Different time steps were adopted for the two phases. This strategy was verified by comparing simulation results with the data of theoretical analysis and shaking table test. The results show that precision integration ensures the accuracy of numerical calculation for bridge structure collision under seismic action, and achieves a high calculation efficiency; the contact element model and model parameters should be selected reasonably to analyze seismic collision of bridges; the Jan-Hertz-Damp model of contact elements boasts the highest simulation accuracy among the commonly used models.

Objective. Mathematical modelling of surface electromyographic (EMG) signals has been proven a valuable tool to interpret experimental data and to validate signal processing techniques. Most analytical EMG models only consider muscle fibers with specific and fixed arrangements. However, the fiber orientation and curvature may change along the fiber paths and may differ from fiber to fiber. Here we propose a subject-specific EMG model that simulates the fiber trajectories in muscles of the upper arm and analytically derives the action potentials assuming an approximate conductivity tensor. Methods. Magnetic Resonance (MR) images were acquired to identify and generate muscle fiber paths and to determine the muscle locations in a cylindrical volume conductor. While the propagation of the action potentials followed the identified curvilinear fiber paths, the conductivity tensor was not adapted to the fiber direction but approximated along the longitudinal axis of the cylindrical volume conductor. Single fiber action potentials (SFAPs) were computed by simulating the generation, propagation, and extinction of membrane current sources. To validate the assumption of the approximate conductivity tensor, two numerical models were implemented for comparison with the analytical solution. The first numerical model reproduced the analytical model and therefore included an approximation for the conductivity tensor. The second numerical model included the exact conductivity tensor derived from the fiber curvatures. Results. The motor unit action potentials generated by the proposed analytical model and the two numerical models were highly similar (cross-correlation >0.98, normalized root mean square error, nRMSE 0.04, relative error in the median frequency of the simulated waveforms of approximately 3%). The proposed analytical model was also evaluated by comparing simulated and experimentally recorded compound muscle action potentials (CMAPs). The CMAPs simulated with the proposed model better matched the experimental data (cross-correlation >0.90 and nRMSE

Robot simulation is an important way to verify the correctness of model and feasibility of design. Taking the Delta parallel mechanism as the effector of a weeding robot, this paper designs the workspace for the weeding mechanism in the field of corn seedlings, when each corn seedling has three to five leaves, and then carries out a simulation analysis on the workspace of the weeding mechanism. To realize variable rate precision spraying, the authors planned a three-segment gate-shaped trajectory for the end effector, detailed the trajectory under the joint coordinate system, and analyzed the motion law of S-curve motion profile. Then, the law of each kinematics parameter was solved on MATLAB, and plotted into graphs. Based on the simulation results, a prototype was developed for the proposed weeding mechanism, and subject to weeding experiments to obtain the end effector trajectory. Compared with the simulated results, the maximum deviation in the end effector trajectory during actual operation was 11.58%; the prototype could complete a weeding action every 2.8 s, while advancing at the speed of 0.4 m/s. The results fully demonstrate the feasibility of applying Delta parallel mechanism in weeding, and the reasonability of our workspace design and trajectory planning.

This article focuses on multiagent distributed-constrained optimization problems in a dynamic environment, in which a group of agents aims to cooperatively optimize a sum of time-changing local cost functions subject to time-varying coupled constraints. Both the local cost functions and constraint functions are unrevealed to an individual agent until an action is submitted. We first investigate a gradient-feedback scenario, where each agent can access both values and gradients of cost functions and constraint functions owned by itself at the chosen action. Then, we design a distributed primal-dual online learning algorithm and show that the proposed algorithm can achieve the sublinear bounds for both the regret and constraint violations. Furthermore, we extend the gradient-feedback algorithm to a gradient-free setup, where an individual agent has only attained the values of local cost functions and constraint functions at two queried points near the selected action. We develop a bandit version of the previous method and give the explicitly sublinear bounds on the expected regret and expected constraint violations. The results indicate that the bandit algorithm can achieve almost the same performance as the gradient-feedback algorithm under wild conditions. Finally, numerical simulations on an electric vehicle charging problem demonstrate the effectiveness of the proposed algorithms.

In this letter, we introduce an extension of the Action Governor (AG), which is an add-on, supervisory scheme to a nominal control loop to enforce safety-related requirements. This extension enables AG design based on discrete-time piecewise affine (PWA) system models with additive set-bounded disturbance inputs and non-convex exclusion-zone avoidance constraints. We establish theoretical properties and computational approaches for this robust version of AG, and illustrate its application to an autonomous vehicle control problem.

Under the inhomogeneous temperature field, the fluid flow caused by the inertia force in the liquid floated gyro will produce a viscous interference torque, which has become a bottleneck restricting the accuracy improvement of the liquid floated gyro. However, the influence factors and action mechanism of this torque are not clear, and it is often analyzed as a zero-order error. In order to investigate the influence of acceleration on the internal fluid characteristics of gyro, the coupling model of temperature field and flow field for the gyro is established in this paper. On this basis, the temperature field, flow field and interference torque under different acceleration conditions are calculated quantitatively. The results show that the acceleration has no obvious influence on the temperature distribution of the gyro, but it has a greater influence on the oil flow state and the viscous interference torque. When the acceleration direction is along the motor axis and output axis, the corresponding value of interference torque is the maximum and minimum respectively. This work will provide a theoretical guidance for the accuracy improvement of liquid floated gyros.

The goal of this paper is to provide a categorical framework that leads to the definition of shtukas a la Drinfeld and of excursion operators a la V. Lafforgue. We take as the point of departure the Hecke action of Rep ( G ˇ ) on the category Shv ( Bun G ) of sheaves on Bun G , and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

Waves action considering one of the most hydraulic phenomenon that covered by the history, the waves action hits the stones or any concert blocks that formed breakwater then the development of breakwaters became necessary so an equilibrium shape by filling the voids with more stones occur. Because of the complex of experimental work and the higher cost of models, the numerical simulations using CFD approach should be studied to show the ability of Flow 3D software to simulate the wave behavior phenomenon. The results present an improvement that the Flow 3D software able to generate the waves with different heights and periods.

We introduce a method that enables swarms of lightweight spacecrafts to correctly set up trailing formations that would allow to successfully perform continuous shooting actions aimed at deflecting NEAs by means of laser ablation. The method uses a computational procedure that provides post-Newtonian (p-N) data necessary to build up these formations, as well as to efficiently control the spacecrafts in the swarms. In fact, these data allow to coordinately shoot at cataloged NEAs and are therefore essential for the multiple action laser methods to become the most effective to deflect NEAs (if we exclude, obviously, the destructive methods). For it turns out that these data provide significant corrections to the shooting spots and instants predicted with the current formulae. The reason is that both the equations for the relative motions and the control formulae take into account (for the first time) the gravitational gradients from the spacecrafts to the NEAs.

Given an elliptic curve $E$ over a global function field $K$, the Galois action on the $n$-torsion points of $E$ gives rise to a mod-n Galois representation $\rho_{E,n}$. For $K$ satisfying some mild conditions, we show that the set of $E$ for which $\rho_{E,n}$ is as large as possible for all $n$, has density $1$., Comment: 8 pages. Minor revisions

The aim of the present article is to analyze the propagation of Rayleigh waves in a rotating fiber-reinforced electrically conducting elastic solid medium under the influence of surface stress, magnetic field and gravity. The magnetic field is applied in such a direction that the problem can be considered as a two dimensional one. The wave velocity equation for Rayleigh waves has been obtained. In the absence of gravity field, surface stress, rotation and fiberreinforcement, the frequency equation is in complete agreement with the corresponding classical results. The effects on various subjects of interest are discussed and shown graphically. Comparisons are made with the corresponding results in absence of surface stress

The set-theoretical convergence of models of continuous and discrete synthesis processes in the compositions of metals and non-metals at the action of ray sources is shown. The non-metal density function obtained by the IDS thermal impulses on the temperature axis projection has a periodic view with fi xed stationary temperatures. They coincide with the boundaries of diff erent areas of change in the speeds of metal heating. This convergence of models to the general periodic operator is possible under four conditions of beam scanning: separation, compactness, property of states, stability. Then the current reciprocity ratios of the system (metals/non-metals) allow the use of the temperature of stationary non-metals as support for metals and serves to determine the parameters of ray sources when synthesizing structures in the compositions of the volume of the material.

We prove that every irreducible component of the fixed point variety under the action of $d$-th roots of unity in a smooth Caloger-Moser space is isomorphic to a Calogero-Moser space associated with another reflection group.

This article proposes a predictive end-effector control method for manipulators operating on mobile platforms subjected to unwanted base motion. Time series is used to forecast the base motion using historical state information. Then, a trajectory specified in the inertial frame is transformed to a predicted trajectory with respect to the manipulator. By tracking this transformed trajectory, the manipulator negates the base motion. A model-predictive control problem is formulated via quadratic programming (QP) to track said trajectory over the prediction horizon. Only the first control action in the control sequence is constrained by kinematic feasibility. In this manner, QP can be swiftly solved with linear inequality constraints. It is shown that the actual joint trajectory executed by the manipulator is always kinematically feasible. Moreover, tracking error can still be reduced despite future predicted control actions being infeasible. The method is validated through both simulation and experiment. The proposed method can reduce pose error by over 60% compared to a proportional-integral feedback controller.

This paper studies the dynamic contact response of a piezoelectric half-space under the action of an insulating elastic spherical punch. By means of the perturbation method, the dynamic contact pressure distribution is deduced. Utilizing Hankel transform, the dynamic contact displacement is obtained. Combining the elastic spherical punch oscillation and the piezoelectric half-space motion through contact-displacement boundary conditions, the resonant frequency shift of the elastic sphere is derived. Numerical calculations are given to discuss the influences of the material constant, piezoelectric effect, internal friction and static force on the dynamic contact pressure and resonance frequency shift. The results show that the difference between the dynamic and static contact pressures is small at the center of the contact region, while it is large near the edge of the contact region.

We prove that under the action of GL ( 2 , q 6 ) there are ⌊ ( q 2 + q + 1 ) ( q − 2 ) / 2 ⌋ equivalence classes of maximum scattered subspaces of the form U b = { ( x , b x q + x q 4 ) : x ∈ F q 6 } in F q 6 × F q 6 . This verifies a conjecture of Csajbok, Marino, Polverino and Zanella from 2018.

For a finite group G, Turaev introduced the notion of a braided G-crossed fusion category. The classification of braided G-crossed extensions of braided fusion categories was studied by Etingof, Nikshych and Ostrik in terms of certain group cohomological data. In this paper we will define the notion of a G-crossed Frobenius ⋆-algebra and give a classification of (strict) G-crossed extensions of a commutative Frobenius ⋆-algebra R equipped with a given action of G, in terms of the second group cohomology H 2 ( G , R × ) . Now suppose that B is a non-degenerate braided fusion category equipped with a braided action of a finite group G. We will see that the associated G-graded fusion ring is in fact a (strict) G-crossed Frobenius ⋆-algebra. We will describe this G-crossed fusion ring in terms of the classification of braided G-actions by Etingof, Nikshych, Ostrik and derive a Verlinde formula to compute its fusion coefficients.

The response of the substructures and foundation of a multi-span reinforced concrete (RC) integral bridge (IB) was studied in this work. The non-linear action of soil was modelled using the Drucker–Prager yield criterion soil spring model. A five-span IB of length 156 m and having 30 m deep RC piles was considered for two different cases of soil layers. In the first cast case, a uniform soil layer was assumed throughout the entire pile depth and the abutment backfill. In the second case, soil data obtained from the targeted bridge site were used. For both cases, the pile responses due to maximum and minimum yearly and daily temperatures were analysed. A vehicle load of 100 t was coupled with the thermal load to analyse the cumulative response due to temperature, a moving load and non-linear soil behaviour. The results showed that temperature and vehicular load provide a significant contribution to the IB pile response.

The purpose of the study - receiving of exact analytical solutions of statics problems of anisotropic plates, resting on an elastic subgrade and subjected to an action of cyclic symmetrical loads. The method of compensating loads is used for solving of the formulated problems. The basic and the compensating solutions are determined. The new approach, connected with the use of Nielsens equation for receiving of the solutions, is applied. For the first time by means of the method of compensating loads the exact analytical solutions of the cycle symmetric flexure of anisotropic circular plates, resting on the elastic subgrade, are received. Various boundary conditions and the loads, distributed along circumferences and over ring surfaces, are considered. The problem of anisotropic infinite plate with the circular opening, resting on the elastic subgrade, is also examined. All the solutions are obtained in the closed form and expressed in terms of Bessel functions.

Nonsymmetric interpolation Laurent polynomials in $n$ variables are introduced, with the interpolation points depending on $q$ and on a $n$-tuple of parameters $\tau=(\tau_1,\ldots,\tau_n)$. When $\tau_i=st^{n-i}$ Okounkov's $3$-parameter $BC_n$-type interpolation Macdonald polynomials are recovered from the nonsymmetric interpolation Laurent polynomials through Hecke algebra symmetrisation with respect to a type $C_n$ Hecke algebra action. In the appendix we give some conjectures about extra vanishing, based on Mathematica computations in rank two., Comment: 32 pages, 9 figures; v5: thoroughly revised version, including a new introduction. To appear in Transformation Groups

In this study, the dynamic response of the tension leg platform (TLP) under sea waves excitation is investigated. One establishes the analytical framework consisting of mathematical modeling of TLP taking into account the tendons and the delay. We analyse the stability and determine the physical characteristics of tendon system that allow the system to be always stable. Conditions on the space parameters of the system for which harmonic, subharmonic, superharmonic, combination resonants states are obtained using the multiple time scales method. The results show that the stability area of the system decreases when the delay increases and increases when the damping coefficient increases. Furthermore, increasing the time- delay only increases the value of the maximum amplitude response of the system. However, reasonable selection of the system parameters can effectively reduce the level of vibration of the system.

In this work, we explore wormhole geometries in a recently proposed modified gravity theory arising from a non-conservative gravitational theory, tentatively denoted action-dependent Lagrangian theories. The generalized gravitational field equation essentially depends on a background four-vector $\lambda^\mu$, that plays the role of a coupling parameter associated with the dependence of the gravitational Lagrangian upon the action, and may generically depend on the spacetime coordinates. Considering wormhole configurations, by using "Buchdahl coordinates", we find that the four-vector is given by $\lambda_{\mu}=\left(0,0,\lambda_{\theta},0\right)$, and that the spacetime geometry is severely restricted by the condition $g_{tt}g_{uu}=-1$, where $u$ is the radial coordinate. We find a plethora of specific asymptotically flat, symmetric and asymmetric, solutions with power law choices for the function $\lambda$, by generalizing the Ellis-Bronnikov solutions and the recently proposed black bounce geometries, amongst others. We show that these compact objects possess a far richer geometrical structure than their general relativistic counterparts., Comment: 11 pages, 5 figures, V2: version accepted for publication in PRD

The fundamental concepts and principles of mechanics, or dynamics, were established in the 17th century. Copernicus gave the notion of reference system in 1543, and Galileo stated the principle of inertia in 1638 in his important work Discorsi e dimostrazioni mathematiche intorno a due nove scienze alla meccanica ed i movimenti locali.1 A particle on which no force is exerted has a constant velocity. Linear uniform motion is a state relative to the observer, and not a process. It is the variation of the velocity that is a process resulting from an external action. Many scientists participated in this evolution, such as Tycho Brahe, Kepler, Descartes, and Christiaan Huygens, to name a few.

Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies move under the action of the forces and moments that are exerted on them. Thermodynamics is the theory that integrates dynamics with the concept of temperature. Dynamics is a fundamental part of physics because of Newton’s second law, which describes how the momentum of a fixed quantity of matter evolves in time.

This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfaces, in particular the lines on a cubic., Dedicated to the memory of Michael Atiyah

We provide parameter dependent version of the Browder–Minty Theorem in case when the solution is unique utilizing different types of monotonicity and compactness assumptions related to condition (S)2. Potential equations and the convergence of their Euler action functionals is also investigated. Applications towards the dependence on parameters for both potential and non-potenial nonlinear Dirichlet boundary problems are given.

The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lie's group analysis of Newtonian dynamics. When applied to models of gas dynamics --~such as Euler system or Boltzmann equation,~-- in combination with Compensated Integrability, this yields new dispersive estimates. The most accurate one is obtained for mono-atomic gases. Then the space-time integral of $t\rho^\frac1d p$ is bounded in terms of the total mass and moment of inertia alone.

Influenced by continuous rainfall and water level fluctuation, a large number of landslide disasters occur in the reservoir areas in China every year, causing serious property losses and casualties. Based on the unsaturated seepage theory, the deterministic method and Monte-Carlo method are used to simulate the safety state of a reservoir bank slope under combined action of continuous rainfall and fluctuation of water level. Besides, the variation trend of safety factor, failure probability and reliability index of the slope under different working conditions are also obtained. By revealing the instantaneous variation characteristics of the equivalent plastic zone, the progressive failure mechanism of the slope is analyzed. The most dangerous condition is the time when the water level drops by 3 m/d and the rainfall changes at 30 mm/d simultaneously. This study provides a reference for risk analysis and emergency management of reservoir slope under extreme conditions.

Crystallization often proceeds in media with rich chemical compositions. In pursuit of insight into how foreign compounds interact with the structures and dynamics that comprise crystal growth, we ...

This brief studies distributed event-triggered law design of the Nash equilibrium seeking for noncooperative games under strongly connected graphs. Each player is desired to maximize its payoff function by updating its own action based on other players’ actions. An event-triggered law is proposed, and each player estimates all other players’ actions and exchanges the estimated information with their neighbors only when the triggering conditions are satisfied. Theoretical demonstration is presented to verify that the actions and estimates of players all converge to the unique Nash equilibrium under the proposed event-triggered law and Zeno behavior is excluded. Simulations are provided to show the effectiveness of the main results.

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic renormalization flow of multi-trace operators and stochastic $n$-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS$_6$. What we have found is that the stochastic time $t$ dependent 3-point function obtained from Langevin equation with its Euclidean action being given by $S_E=2I_{os}$ is identical to holographic renormalization group evolution of holographic triple trace operator as its energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi point functions and multi trace operators in each framework., Comment: 1+23 pages

In arXiv:1907.07688 Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY. Note added: The apparent discrepancy in the third constant has been resolved in arXiv:2210.11473., Comment: LaTeX file, 100 pages, This paper reports an apparent mismatch between string theory and matrix model results, hoping that someone will find an error; v2: The apparent mismatch has been resolved in arXiv:2210.11473

A liquid film that is under the action of two electric forces, an external electric field parallel to the film and a lateral voltage difference applied to both edges of the film, exhibits a universal rotational flow. In this article, we revisit this phenomena by considering an idealized so-called liquid-film motor and provide a theoretical description of the underlying physical mechanism that is responsible for the rotation. Based on this theory, the external electric field induces a non-uniform distribution of freely moving charges on the film. Then the internal field that is mainly resulted from the lateral voltage difference, will exert forces on induced charges and subsequently will result the rotational flow. We show, how the fields contribute in developing a universal flow pattern.

Within the ongoing debate about de Sitter (dS) vacua in string theory, different aspects of explicit dS proposals have come under intense scrutiny. One key ingredient is D7-brane gaugino condensation, which is usually treated using effective 4d supergravity. However, it is clearly more desirable to derive the relevant scalar potential directly from a local 10d Lagrangian. Such a local 10d description captures the interactions among the various localized sources and the background fields which are smeared in the 4d Lagrangian. While progress in this endeavour has recently been made, some form of non-locality related to the 4-gaugino term has remained hidden in the available proposals. We spell out the local counterterm removing the divergence that arises when integrating out the 3-form flux and which, upon dimensional reduction, serves to reproduce the relevant part of the 4d supergravity action. This is both a step towards a more complete understanding of 10d type-IIB supergravity as well as specifically towards better control of dS constructions in string theory involving gaugino condensation., 27 pages. v2: Minor changes; v3: Published in JHEP

We apply the BMHV scheme for non-anticommuting $\gamma_5$ to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories., Comment: 32 pages; v2: references added, minor typos corrected. Formatted for JHEP submission

We propose a brittle damage model based on linearized kinematic measures derived using a gauge theory. First, we obtain the fully nonlinear kinematic measures by considering a solid with spatial defects due to micro-cracks. To accomplish this, a non-trivial affine connection, called the gauge connection, is introduced to account for local configurational changes induced by the spatial defects. This procedure, called minimal replacement, leads to the emergence of covariant derivatives and ensures the invariance of the Lagrangian under the local action of the gauge symmetry group. The covariant derivatives furnish the configuration gradients used for constructing the invariant Lagrangian. The geometric foundations and symmetry principles of the gauge theory enable accurate characterizations of the kinematic and other important physical features pertaining to defect-induced brittle damage. Another important construct, called minimal coupling, provides the stored energy corresponding to defects via the gauge field Lagrangian. Using linearization of the fully nonlinear kinematic measures, we obtain an energy functional which is quadratic in the field variables and such an energy is invariant with respect to the local gauge transformations. The resulting Euler–Lagrange equations provide the governing laws for coupled evolutions of deformation and defects. The constitutive equations in the linearized setting are linear in the field variables. A kinematically transparent approach is thus followed for modelling different aspects of brittle damage such as material stiffness degradation, tension-compression asymmetry and energy contribution of defects. We propose different tension-compression asymmetry mechanisms based on spectral decomposition of tensile and compressive deformations, dilatation-compression split of volumetric deformation, and volumetric-deviatoric split of deformation. Towards a stable and accurate numerical implementation of the model, the governing partial differential equations are recast into an integro-differential form via the principles of peridynamics (PD). The efficacy of the model, so discretized, is established through PD-based numerical simulations of tension and shear tests on a single-edge-notched plate. For further exploration, the numerical simulation of blast-induced fracture in rock is also carried out. In this case, account is taken of the physical reaction zone developed during shock wave detonation, and the interaction between gas and solid rock.

The objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss two new averaged mathematical models for the analysis of selected dynamic thermoelasticity problems for the shells under consideration: the non-asymptotictolerance and the consistent asymptotic models. The starting equations are the well-known governing equations of linear Kirchhoff-Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation in which the heat sources are neglected. For the microperiodic shells under consideration, the starting equations mentioned above have highly oscillating, non-continuous and periodic coefficients. The tolerance model is derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. It has constant coefficients depending also on a cell size. Hence, this model makes it possible to study the effect of a microstructure size on the global shell thermoelasticity (the length-scale effect). The consistent asymptotic model is obtained using the consistent asymptotic approach. It has constant coefficients being independent of the period lengths. Moreover, the comparison between the tolerance model for biperiodic shells proposed here and the known tolerance model for cylindrical shells with a periodic structure in the circumferential direction only (uniperiodic shells) is presented.

The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.