Finite Degrees Of Freedom Research Articles

How to build a black hole out of instantons

An often fruitful route to study quantum gravity is the determination and study of quantum mechanical models — that is, models with finite degrees of freedom — that capture the dynamics of a black hole’s microstates. An example of such a model is the superconformal quantum mechanics of Yang-Mills instantons, which has a proposed gravitational dual description as M-theory on a background of the form X7 × S4. This model arises in the strongly-coupled limit of the BFSS matrix model with additional fundamental hypermultiplets, offering a route towards useful numerical simulation. We construct a six-parameter black hole solution in this theory, which is generically non-supersymmetric and non-extremal, and is shown to arise in an “ultra-spinning” limit of the recently-found six-parameter AdS7 solution. We compute its thermodynamic properties, and show that in the supersymmetric limit the entropy and on-shell action match precisely the expected results as computed from the superconformal index of the quantum mechanics, to leading order in the supergravity regime. The low-lying spectrum thus provides access to the dynamics of near-extremal black holes, whose spectra are expected to receive strong quantum corrections.

Research on Panel Flutter Considering the Effect of Convective Active Cooling

The aeroelastic characteristics of the panel under the action of coolant are obviously different from the flutter characteristics of the traditional panel. In order to solve this problem, the dynamics model of the panel flutter was established in this paper based on von Karman’s large deformation theory and the Kirchhoff–Love hypothesis. The panel dynamics equations were discretized into constant differential equations with finite degrees of freedom by Galerkin’s method, and solved by the fourth Runge–Kutta method in the time domain. The nonlinear modified piston theory was used to predict the unsteady aerodynamic loads, and the accuracy of the flutter analysis model was verified. On this basis, the effects of the head-panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively. The results showed that reducing the pressure drop ratio, and reducing or increasing the head-panel pressure (valuing away from the freestream pressure) can improve the critical dynamic pressure when bifurcation occurs. At M∞=5.0, the pressure drop ratio causes a 22.1% increment in the critical dynamic pressure. The influence of the coolant injection direction on the panel bifurcation is mainly influenced by the head-panel pressure. The inertial resistance slows down the convergence process of the panel response, increases the limit cycle amplitude, and reduces the critical dynamic pressure of the panel, while the viscous resistance plays the opposite role. Based on these conclusions, this paper finally proposes the suppression method of panel fluttering from head-panel pressure, inertial resistance, viscous resistance, etc.

Optical Steganography via Programmable Anchoring Boundary of Soft Materials

AbstractEngineering the properties of light with multi‐channel planar elements can produce independent spectral response, and has formed the solid basis for image steganography techniques, which holds great promise for applications including information storage, optical encryption, and anti‐counterfeiting. However, most of the recently reported steganography systems suffer from limited size, sophisticated fabrication, and finite degree of freedom in encoding and decoding process. Herein, a versatile image steganography system based on soft material is proposed. The polarization and intensity of transmitted light are modulated by programing the anchoring boundary of liquid crystals, allowing arbitrary independent images multiplexing in single‐size element with high fidelity. Specifically, the stimuli‐responsiveness of liquid crystals endows the platform with a new degree of freedom to manipulate the transmitted spectrum dynamically, further sketching a prospective framework toward a new type of steganography with fascinating tunability. The proposed strategy sheds new light on multifarious display system by harnessing the stimuli‐responsiveness of soft materials, leading to promising applications in information storing, image steganography, anti‐counterfeiting, and multilevel encryption techniques.

An Analytic and Computational Condition for the Finite Degree-of-Freedom of Linkages, and Its Relation to Lie Group Methods

Abstract The finite degree of freedom (DOF) of a mechanism is determined by the number of independent loop constraints. In this paper, a method to determine the maximal number of loop closure constraints (which is independent of a specific configuration) of multiloop linkages is introduced and applied to calculate the finite DOF. It rests on an algebraic condition on the joint screws, which stems from the analytic condition that minors of certain rank and their higher derivatives vanish. A computational algorithm is presented to determine the maximal rank of the constraint Jacobian in an arbitrary (possibly singular) reference configuration. This algorithm involves screw products of constant screw vectors only. Unlike the Lie group methods for estimating the DOF of so-called exceptional linkages, this method does not rely on partitioning kinematic loops into partial kinematic chains, and it is applicable to multiloop linkages. The DOF computed with this method is at least as accurate as the DOF computed with the Lie group methods. It gives the correct DOF for any (possibly overconstrained) linkage where the constraint Jacobian has maximal rank in regular configurations. The so determined maximal rank has further significance for classifying linkages as being exceptional or paradoxical but also for detecting singularities and shaky linkages.

Heat diffusion blurs photothermal images with increasing depth

In this Tutorial, we aim to directly recreate some of our “aha” moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function. The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction.

Classical Gauge Principle - From Field Theories to Classical Mechanics

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of transformations parametrized by arbitrary functions. It is formally presented how this property can be introduced in such systems, followed by modern applications. Furthermore, Lagrangians describing classical-mechanics systems with local invariance are separated in equivalence classes according to their local structures.

Dynamic response of the building construction system with a finite degree of freedom under a special action

Introduction. In the normative documents of a number of countries on the standardization of the protection of buildings and structures from progressive collapse, for the calculation analysis under special impact, such a concept as a “zone of possible local destruction” of a structural system is used, outlined by a fragment of the building frame in places of hypothetically removed structural elements. The purpose of identifying such most stressed zones in the form of substructures is engineering visibility of the consequences of an emergency impact with an assessment of the stress-strain state of elements falling into such a zone. In this regard, in the work under consideration, a variant of modeling the dynamic additional loading of the reinforced concrete frame of a multi-storey building caused by its structural restructuring is proposed, which makes it possible to determine the parameters of the dynamic response of the substructure in the form of a two-span continuous beam with a finite number of degrees of freedom and to model in more detail the zone of possible local destruction of the elements of the building frame at the sudden removal of one of the structural structures in this area.
 
 Materials and methods. The zone of possible local destruction of the building frame is modeled by a fragment of the structural system adjacent to this zone. The process of removing a column was simulated by applying a load P(t) in the opposite direction, equal to the force in the removed column, calculated when calculating the entire frame of the building. To solve the system of equations of motion of the substructure, we use the method of expansion in terms of natural vibration modes, which is well known in the dynamics of structures.
 
 Results. The results of theoretical studies of the dynamic effect of a reinforced concrete structural system of a building with a finite number of degrees of freedom during its sudden restructuring caused by a special emergency impact in the form of a hypothetical removal of one of the load-bearing structures are presented.
 
 Conclusions. The equations of motion of a substructure in the form of a two-span continuous beam with a finite number of degrees of freedom constructed on the basis of the theory of the dynamics of structures can be used to analyze the special limiting state of reinforced concrete elements of structural systems of frames of buildings and structures.

Space and time averaged quantum stress tensor fluctuations

We extend previous work on the numerical diagonalization of quantum stress tensor operators in the Minkowski vacuum state, which considered operators averaged in a finite time interval, to operators averaged in a finite spacetime region. Since real experiments occur over finite volumes and durations, physically meaningful fluctuations may be obtained from stress tensor operators averaged by compactly supported sampling functions in space and time. The direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues and the probabilities of measuring those eigenvalues in the vacuum state, from which the underlying probability distribution can be constructed. For the normal-ordered square of the time derivative of a massless scalar field in a spherical cavity with finite degrees of freedom, analysis of the tails of these distributions confirms previous results based on the analytical treatment of the high moments. We find that the probability of large vacuum fluctuations is reduced when spatial averaging is included, but the tail still decreases more slowly than exponentially as the magnitude of the measured eigenvalues increases, suggesting vacuum fluctuations may not always be subdominant to thermal fluctuations and opening up the possibility of experimental observation under the right conditions.

Convergence theorems on multi-dimensional homogeneous quantum walks

We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. We prove that every homogeneous walks with finite degree of freedom have limit distribution. This theorem can also be applied to every crystal lattice. In this theorem, it is not necessary to assume that the support of the initial unit vector is finite. We also pay attention on 1-cocycles, which is related to Heisenberg representation of time evolution of observables. For homogeneous walks with finite degree of freedom, convergence of averages of 1-cocycles associated with the position observable is also proved.

Vibration analysis and distributed piezoelectric energy harvester design for the L-shaped beam

The vibration characteristics of a cantilever L-shaped beam perpendicular to the horizontal plane are investigated in this paper. The dynamical model of the L-shaped multi-beam structure is established by using the Euler-Bernoulli beam theory, where vibration equations of each substructure, matching conditions of the connection and boundary conditions are included. Based on the modal orthogonality, the discrete dynamical model with finite degrees of freedom is obtained. Then the distributed piezoelectric energy harvester is proposed to collect the vibration energy of the L-shaped beam. Different the most traditional energy harvester that the piezoelectric material covers the surface of the structure, the distributed energy harvester is placed on the selected points. The genetic algorithm is adopted to obtain the optimal position that can provide the maximum output power. The validation and accuracy of the present model is verified by comparison with the finite element model. Numerical results show the discrete model can perform the dynamic characteristics of the structure well with only two modes. By the comparison of different configurations, it concludes that the optimal position of the distributed piezoelectric energy harvester is close to the fixed end of the whole cantilever structure.

Власнi частоти та власнi формирегулярних ланцюгових коливальнихсистем

The classical approach in the investigation of natural oscillations of discrete mechanical oscillatingsystems is the solution of the secular equation for finding the eigenfrequencies and the system of algebraic equations for determining the amplitude coefficients (eigenforms). However, the analytical solution of the secular equation is possible only for a limited class of discrete systems, especially with a finite degree of freedom. This class includes regular chain oscillating systems in which the same oscillators are connected in series. Regular systems are divided into systems with rigidly fixed ends, with one or both free ends, which significantly affects the search for eigenfrequencies and eigenforms. This paper shows how, having a solution for the secular equation of a regular system with rigidly fixed ends, it is possible to determine the eigenfrequencies and eigenforms of regular systems with one or both free ends.

A multicycle sub-Nyquist sampling system for pulse streams with Doppler shift

Pulse streams with Doppler shift exists widely in radar, communications, and many other time-variant linear systems. One central task in identifying these systems is to recover the delay-Doppler pairs. However, the classic methods require high sampling rate for wideband pulse. In this paper, a multicycle sub-Nyquist sampling system to recover delay-Doppler pairs symmetrically is proposed. Using finite rate of innovation (FRI) theory, the unknown parameters can be estimated from the directly sampled Fourier coefficients, where FRI refers to that the sampled signals have finite degrees of freedom per unit time. Based on the sparse common support (SCS) model and symmetry of the delay-Doppler pairs, the samples from each pulse repeat interval (PRI) can be jointly used to estimate parameters, where PRI is the time interval of the transmitted pulses, and SCS refers to that each PRI of the received signal has common non-zero supports but different weights. The number of PRIs and samples required for signals with both different and identical parameters are demonstrated mathematically. When the SNR is 10 dB, the NMSEs of the estimated delay-Doppler parameters are -10 dB and -5 dB or more higher than several advanced methods respectively, which demonstrate the effectiveness of the proposed method.

Analysis of DMU40 machine centre by finite degrees of freedom

This article is part of a longer research-analytical work, because it outlines the results and conclusions of the study according to the main topic of the research and the applies method. The central theme of the research is the dynamic stiffness of machine tools and the various methods for their determination. The first such (finite element) method is modal analysis, which allows for an analytical test. The purpose of this article is to approach this study from the practical side through a specific example.

Search of QCD phase transition points in the canonical approach of the NJL model

We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.

Design optimization of air distribution systems in non-residential buildings

Centralized air distribution systems in non-residential buildings are characterized by an extensive air distribution network, that has to be built in a building environment with finite degrees of freedom. The ductwork layout, i.e., the network structure of the ducts, as well as the number and location of the fans, has a large impact on the total cost and performance of the air distribution system. Nevertheless, existing air distribution system design methods are limited to the sizing of each duct (and fan) in the network. The layout itself is considered predetermined, and thus not explicitly taken into account for optimization. In this paper, we meet this shortcoming by presenting the air distribution network design optimization method, that is able to calculate the optimal air distribution system configuration, i.e., the optimal layout and duct and fan sizes, while minimizing the total cost of the air distribution system. A multi-start local search algorithm is developed, consisting of a constructive and a local search phase. In the first phase, multiple air distribution system configurations are generated, and evaluated for feasibility. In the local search phase, all feasible solutions are further optimized in terms of material costs by decreasing and increasing the duct diameters following the steepest descent/mildest ascent approach. An application of the algorithm on a realistic test case demonstrates its usefulness in practice.

Classification of quench-dynamical behaviors in spinor condensates

Thermalization of isolated quantum systems is a long-standing fundamental problem where different mechanisms are proposed over time. We contribute to this discussion by classifying the diverse quench dynamical behaviours of spin-1 Bose-Einstein condensates, which includes well-defined quantum collapse and revivals, thermalization, and certain special cases. These special cases are either nonthermal equilibration with no revival but a collapse even though the system has finite degrees of freedom or no equilibration with no collapse and revival. Given that some integrable systems are already shown to demonstrate the weak form of eigenstate thermalization hypothesis (ETH), we determine the regions where ETH holds and fails in this integrable isolated quantum system. The reason behind both thermalizing and nonthermalizing behaviours in the same model under different initial conditions is linked to the discussion of `rare' nonthermal states existing in the spectrum. We also propose a method to predict the collapse and revival time scales and how they scale with the number of particles in the condensate. We use a sudden quench to drive the system to non-equilibrium and hence the theoretical predictions given in this paper can be probed in experiments.

English

English

A novel approach to suppression of oscillations

AbstractWe propose a novel method of determining the control force that brings a mechanical system with finite degrees of freedom from one phase state into another one in a given time. When a system is brought from an available phase state into a prescribed state of rest we can speak about the oscillation suppression. Horizontal motion of a cart with s mathematical pendula is studied as an example. At first, a control by the Pontryagin maximum principle that minimizes the functional of the squared control force is suggested. This approach results in a nonholonomic constraint of order . In order to develop a control we propose to employ the generalized Gauss principle which underlies the theory of motion of nonholonomic systems with high‐order constraints. In this case, the motion is more smooth than the Pontryagin maximum principle suggests. In addition, by increasing the order of the generalized Gauss principle (when solving the extended boundary‐value problem) one manages to get rid of jumps in the control at the beginning and end of motion which are characteristic for the Pontryagin maximum principle. We also discuss the singular points of solutions that appear when solving the extended boundary‐value problems.

Skin material influence on the flutter characteristics of the aircraft rudder

Flutter is one of the kinds of inexhaustible elastic oscillations of the aircraft parts that arises in flight as a result of aerodynamic forces.There are a number of flutter types: breakthrough flutter, baffling, self-oscillating controls including panel flutter, which determines the nature of fluctuation of the sheeting element under the action of the flow stream.The main safety criterion from the flutter is the ratio of the the flatter critical velocity Vkr and the maximum flight speed Vmax, which the aircraft can reach, that is, Vmax<Vkr [1].The value of Vkr depends on the velocity of flow, the element geometry, the conditions of the element fastening, as well as the material of the skin. The material influence on the flutter parameters, investigated in most homogeneous cases, are considered in the paper[2]. Multilayer skin, considered in various calculation cases, makes it difficult to determine the effect of the material.Computational methods for solving aeroplane problems are selected depending on the adopted elastic-mass design of the control surface. The basis of these methods is the assumption that the oscillations of the steering element of the aircraft direction can be described with sufficient accuracy by the equations for a system with finite degrees of freedom [3].The following functions can be selected as coordinates in different methods: functions describing the forms of fluctuations of the structure out of flow (the method of the given forms of oscillation "Gal'orkina - Bubnov"); the method of lumped masses is used for beam design of the structure and for the framework-caisson scheme; Finite elements can be selected as coordinate functions; the so-called Ritz method, or the method of polynomials, is convenient for the oscillations analysis of bearing surfaces of small elongation [4].This approach will allow us to investigate more accurately the dependence of the material characteristics used in the elements of the aircraft control surfaces.Using a composite material skin results in weight reduction, but the loss of properties in nonlinear effects.The use of metal skin and the use of a fader provide the best tent compared to a metal skin without the use of a fader.The calculation scheme for solving the problem of nonlinear flutter of viscoelastic elements and aircraft nodes has been improved. Comparative generalized models for nonlinear problems of flutter of viscoelastic isotropic and orthotropic plates, elements of panels and skin elements are used for the aircraft control surfaces.

Design of a vibration-free platform: Stabilization of a beam mounted on bicycle model of a car

Many high-precision measurement and control devices must be mounted on vibration-free platforms. Accuracy of those devices’ output are adversely affected by the base excitation motion, so motion of these platforms must be isolated from the excitation source. In this paper, a flexible platform, which is mounted on a car, is considered as a base on which many such measurement and control devices can be attached. To this end, mixed finite element and lumped parameter model of the platform and vehicle are used to derive the model of such a system; this results in a discrete-model with finite degree of freedom. This lumped parameter model of the system is then controlled by a linear quadratic regulator, which minimizes the amplitude of vibration at finite number of points on the platform. The mathematical model of this system was simulated on a computer and it has been shown that it is possible to minimize the vibration of this flexible platform.