Static Equilibrium Conditions Research Articles

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown (HB) strength criterion can reflect rock’s inherent failure nature, so it is more suitable for analyzing the stability of rock slopes. However, the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb (EMC) strength parameters instead of the nonlinear HB strength criterion. Therefore, a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework. The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stress σ 0 obtained without considering the effect of inter-slice forces, and it can satisfy all static equilibrium conditions of the sliding body, so the current method can obtain the reasonable and strict factor of safety (FOS) solutions. Compared with the results of other methods in some examples, the feasibility of the current method was verified. Meanwhile, the parametric analysis shows that the slope angle β has an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters. For β≤45°, both of the results are similar, showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability, but for β>60°, the differences of both the results are obvious, showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods, and then the current method should be used.

Compact stars with specific mass function

Aims: In the present work we search for a new model of compact star within embedding class one spacetime i.e., four dimensional spacetime embedded in five dimensional Pseudo Euclidean space.Methods: In particular we propose a new mass function to obtain an exact analytic solutions of the Einstein field equations. For this specific mass function, obtained solutions are well-behaved at the centre of the star, satisfy all energy conditions and the mass–radius relation fall within the limit proposed by Buchdahl (1959).Results: The static equilibrium condition has been maintained under different forces. We have discussed the solutions in detail and compare with a set of astrophysical objects like 4U1608-52, PSR J1903+327, PSR J1614-2230 and X-ray pulsar Vela X-1 is also explored.

Dynamic response and transfer function of social systems: A neuro-inspired model of collective human activity patterns

The interaction of social networks with the external environment gives rise to non-stationary activity patterns reflecting the temporal structure and strength of exogenous influences that drive social dynamical processes far from an equilibrium state. Following a neuro-inspired approach, based on the dynamics of a passive neuronal membrane, and the firing rate dynamics of single neurons and neuronal populations, we build a state-of-the-art model of the collective social response to exogenous interventions. In this regard, we analyze online activity patterns with a view to determining the transfer function of social systems, that is, the dynamic relationship between external influences and the resulting activity. To this end, first we estimate the impulse response (Green’s function) of collective activity, and then we show that the convolution of the impulse response with a time-varying external influence field accurately reproduces empirical activity patterns. To capture the dynamics of collective activity when the generating process is in a state of statistical equilibrium, we incorporate into the model a noisy input convolved with the impulse response function, thus precisely reproducing the fluctuations of stationary collective activity around a resting value. The outstanding goodness-of-fit of the model results to empirical observations, indicates that the model explains human activity patterns generated by time-dependent external influences in various socio-economic contexts. The proposed model can be used for inferring the temporal structure and strength of external influences, as well as the inertia of collective social activity. Furthermore, it can potentially predict social activity patterns.

Covariant chiral kinetic equation in the Wigner function approach

The covariant chiral kinetic equation (CCKE) is derived from the 4-dimensional Wigner function by an improved perturbative method under the static equilibrium conditions. The chiral kinetic equation in 3-dimensions can be obtained by intergation over the time component of the 4-momentum. There is freedom to add more terms to the CCKE allowed by conservation laws. In the derivation of the 3-dimensional equation, there is also freedom to choose coefficients of some terms in $dx_{0}/d\tau$ and $d\mathbf{x}/d\tau$ ($\tau$ is a parameter along the worldline, and $(x_{0},\mathbf{x})$ denotes the time-space position of a particle) whose 3-mometum integrals are vanishing. So the 3-dimensional chiral kinetic equation derived from the CCKE is not uniquely determined in the current approach. To go beyond the current approach, one needs a new way of building up the 3-dimensional chiral kinetic equation from the CCKE or directly from covariant Wigner equations.

A simplified model for predicting grout flow in fracture channels

Simulation of rock grouting plays an important role for improving grouting technology and practice. Most of the current models for simulating grouting of fracture channels assume that grout flow between two parallel plates is in a state of static equilibrium, neglecting the influence of inertia forces, thus the average velocity obtained from the governing equation is not simple with nonlinear terms, making it time consuming to simulate grout penetration in a complex fracture network with hundreds of single fractures. However, a simple solution can be derived, if the inertia force is included into the governing equation. Though the process of equation solving is complex, the dimensionless average velocity can be expressed as a constant number finally. Capability of the new model proposed for grouting simulation is studied based on an orthogonal test through comparing with the traditional model. It is found that, the simplified new model can well describe the overall characteristics presented by the traditional model; the accuracy of the new model is high and acceptable, and the relevant computational efficiency is greatly improved.

Kinematic error modeling and identification of the over-constrained parallel kinematic machine

Abstract Kinematic calibration has proved to be an effective method in improving the kinematic accuracy of the parallel kinematic machine (PKM). Though the PKM's kinematic calibration method has achieved substantial progress, its application is limited and can be only utilized in non-redundant PKM. Over-constrained PKM parts are forced to deform under redundant constraint forces to satisfy the assembly condition, which does not meet the assumptions made in the present PKM's kinematic calibration method in which all the parts are rigid. To deal with this issue, the present study investigates the kinematic error modeling and identification of the over-constrained PKM considering the deformations of the parts. A 2-DOF over-constrained PKM is taken as the object of study and its kinematic error model is derived based on the analyses of the link's deformations and the machine's static equilibrium condition. The method of least squares and the Regularization method are adopted to identify the kinematic errors of the over-constrained PKM. Finally, simulation analyses are carried out to verify the feasibility and effectiveness of the proposed method.

A mass transport model with a simple non-factorized steady-state distribution

We study a mass transport model on a ring with a sublattice-parallel update, where a continuous mass is randomly redistributed along distinct links of the lattice. The redistribution process on a given link depends on the masses on both sites, in contrast to the zero range process and its continuous mass generalizations. We show that the steady-state distribution takes a simple non-factorized form that can be written as a sum of two inhomogeneous product measures. A factorized measure is recovered for symmetric mass redistribution, corresponding to an equilibrium process. A non-equilibrium free energy can be explicitly defined by the partition function. For a certain class of transition rates, a condensation transition is obtained, with a critical density which depends on the driving force. We also evaluate different characterizations of the ‘distance’ to equilibrium, either dynamic or static: the mass flux, the entropy production rate, the Gibbs free-energy difference between the equilibrium and non-equilibrium stationary states, and the derivative of the non-equilibrium free energy with respect to the applied driving force. The connection between these different non-equilibrium parameters is discussed.

Transition and turbulence in horizontal convection: linear stability analysis

The linear instability mechanisms of horizontal convection in a rectangular cavity forced by a horizontal buoyancy gradient along its surface are investigated using local and global stability analyses for a Prandtl number equal to unity. The results show that the stability of the base flow, a steady circulation characterized by a narrow descending plume and a broad upwelling region, depends on the Rayleigh number, $Ra$. For free-slip boundary conditions at a critical value of $Ra\approx 2\times 10^{7}$, the steady base flow becomes unstable to three-dimensional perturbations, characterized by counter-rotating vortices originating within the plume region. A Wentzel–Kramers–Brillouin (WKB) method applied along closed streamlines demonstrates that this instability is of a Rayleigh–Taylor type and can be used to accurately reconstruct the global instability mode. In the case of no-slip boundary conditions, the base flow also becomes unstable to a self-sustained two-dimensional instability whose critical Rayleigh number is $Ra\approx 1.7\times 10^{8}$. Beyond this critical $Ra$, two-dimensional equilibrium stationary states of the Navier–Stokes equations are computed using the selective frequency damping method. The two-dimensional onset of instability is shown to be characterized by a family of modes also originating within the plume. A local spatio-temporal stability analysis shows that the flow becomes absolutely unstable at the origin of the plume. Taken together, these results illustrate the mechanisms behind the onset of turbulence that has been observed in horizontal convection.

Quasistatic crack growth in 2d-linearized elasticity

In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed boundary load, we derive a time-continuous quasistatic crack growth in the framework of generalized special functions of bounded deformation (GSBD). As the time-discretization step tends to zero, the major difficulty lies in showing the stability of the static equilibrium condition, which is achieved by means of a Jump Transfer Lemma generalizing the result of [19] to the GSBD setting. Moreover, we present a general compactness theorem for this framework and prove existence of the evolution without imposing a-priori bounds on the displacements or applied body forces.

Diagnosis of enterprise static and dynamic financial equilibrium

The article investigates the financial equilibrium for the purpose of distinction between its static and dynamic states, characteristics of their quantitative parameters, detection of display features, reasons for deviations from equilibrium conditions. The measures of balancing financial condition for enterprise sustainable development are grounded. Achieving the desired goal is implemented by using the following general scientific and specific research methods: dialectical approach, induction and deduction, ratio analysis, ranking and trend analysis. The financial condition of JSC «Motor Sich» for compliance with the conditions of static and dynamic financial equilibrium is analyzed. The reasons for deviations of financial condition of this enterprise from static and dynamic parameters of financial equilibrium are identified. The measures to achieve financial equilibrium of JSC «Motor Sich» in its static and dynamic forms are proposed, that will strengthen the enterprise financial capacity.

System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines

A data driven multivariate adaptive regression splines (MARS) based algorithm for system reliability analysis of earth slopes having random soil properties under the framework of limit equilibrium method of slices is considered. The theoretical formulation is developed based on Spencer method (valid for general slip surfaces) satisfying all conditions of static equilibrium coupled with a nonlinear programming technique of optimization. Simulated noise is used to take account of inevitable modeling inaccuracies and epistemic uncertainties. The proposed MARS based algorithm is capable of achieving high level of computational efficiency in the system reliability analysis without significantly compromising the accuracy of results.

Photonic Devices Out of Equilibrium: Transient Memory, Signal Propagation, and Sensing

Soft photonic materials are important for sensors, displays, or energy management and have become switchable under static equilibrium conditions by integration of responsive polymer features. The next step is to equip such materials with the ability for autonomously dynamic and self-regulating behavior, which would advance their functionality and application possibilities to new levels. Here, this study shows the system integration of a nonlinear, biocatalytic pH-feedback system with a pH-responsive block copolymer photonic gel, and demonstrates autonomous transient memories, remotely controlled signal propagation, and sensing. This study utilizes an enzymatic switch to program the lifetime of the reflective state of a photonic gel, and induces propagation of pH-waves extinguishable by illumination with UV-light. The described combination of nonlinear chemistry and responsive photonic gels opens pathways toward out-of-equilibrium photonic devices with active and autonomous behavior useful for sensing, computation, and communication.

Application of the Virtual Fields Method to Rubbers Under Medium Strain Rate Deformation Using Both Acceleration and Traction Force Data

This paper describes an experimental technique for characterizing the uniaxial stress–strain relationship of rubbers under medium strain rate deformation. This method combines the virtual fields method (VFM) and high-speed imaging with digital image correlation. The VFM can be expressed so that force measurement during dynamic loading is no longer required; instead, surface measurements of acceleration, which occurs as a result of wave propagation in the specimen, are used as a ‘virtual load cell’. In a previous paper, the authors have utilized this technique for characterizing material parameters for the dynamic behaviour of rubbers using a drop-weight apparatus. One limitation of this technique is that the stability of the parameter estimation depends on the length of the specimen. When the loading stress wave reaches the fixed end of the specimen, a static equilibrium state is instantaneously achieved. At this instant, the acceleration fields are no longer able to provide information, and the identification is unstable. In order to overcome this limitation, the present paper proposes a VFM based method able to produce stable identification even at this equilibrium instant. This procedure utilizes both inertial and external forces, and a new experiment apparatus has been developed for simultaneously measuring these two sets of data. This new procedure is described using results from simulations; then, the experimental system and results will be presented.

Population cycles and species diversity in dynamic Kill-the-Winner model of microbial ecosystems

Determinants of species diversity in microbial ecosystems remain poorly understood. Bacteriophages are believed to increase the diversity by the virtue of Kill-the-Winner infection bias preventing the fastest growing organism from taking over the community. Phage-bacterial ecosystems are traditionally described in terms of the static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced by losses due to phage predation. Here we consider a more dynamic scenario in which phage infections give rise to abrupt and severe collapses of bacterial populations whenever they become sufficiently large. As a consequence, each bacterial population in our model follows cyclic dynamics of exponential growth interrupted by sudden declines. The total population of all species fluctuates around the carrying capacity of the environment, making these cycles cryptic. While a subset of the slowest growing species in our model is always driven towards extinction, in general the overall ecosystem diversity remains high. The number of surviving species is inversely proportional to the variation in their growth rates but increases with the frequency and severity of phage-induced collapses. Thus counter-intuitively we predict that microbial communities exposed to more violent perturbations should have higher diversity.

Effectiveness of Somatic Balance Restoration Therapy to Alleviate Pain of Musculoskeletal System

Chronic pain and general physical discomfort are common symptoms among those seeking medical or physiotherapy treatment, as it relates to disorders found in the Human Musculoskeletal System (HMS). Since this system is highly complex and large in scale, clinical pain research has been confounded by many complex factors. The goal of our research is to overcome these obstacles by applying multidisciplinary approaches including systems engineering, traditional oriental techniques, conventional medicine and related sciences. To pursue such an integrated approach this paper examines the therapist-guided exercise for restoring human musculoskeletal balance called the Somatic Balance Restoration Therapy (SBRT). The SBRT is a simple but effective self-exercise therapy with minimal assistance by a trained therapist. This therapy is analyzed by a mechanical engineering method by modeling the human body as a multi-body subject to a static equilibrium condition. In addition, the wording has been rewritten in functional anatomical terms, enabling smooth communication between specialists of three different disciplines: therapy, conventional medicine and systems engineering. Examples will be given to demonstrate an integrated and systematic approach for identifying and remedying malfunctions within the HMS.

Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces

This study deals with the non-linear finite element computation of thin flexible structures loaded by hydrostatic forces due to the presence of an internal liquid at rest. In aerospace application, the dynamic behaviour of structures containing an inviscid incompressible fluid (i.e. launcher with liquid propellant, tank of satellite, etc.) is generally computed considering an equilibrium state resulting from a linear fluid-structure interaction problem. It is important to note that in this case, the gravity plays an important role in vibrations and the so called elastogravity operator should be taken into account [1,2]. In the present work, we consider the large deformation behavior of a structure loaded by hydrostatic follower forces in order to obtain an accurate static equilibrium state. The solution is computed using a Newton-Raphson algorithm considering the geometrical and material tangent stiffness matrices as well as the contribution of the follower forces [3]. Those linearized operators of the iterative algorithm are used to compute the dependancy between the incremental horizontal level of the free surface, under the fluid volume conservation constraint [4]. Special attention is paid to the finite element discretization of the wetted surface, considering a level-set method [6,7]. Some numerical examples are analyzed to show the efficiency of the proposed approach.

Low Frequency Excess Noise Source Investigation of Off-Diagonal GMI-Based Magnetometers

The equivalent magnetic noise spectral densities of off-diagonal giant magnetoimpedance (GMI)-based magnetometers exhibit significant low-frequency excess noise, proportional to 1/f noise. As it represents a serious limitation to the ultimate sensing performances of high sensitivity magnetometers, possible sources of this 1/f noise are under investigation. Low-frequency magnetization fluctuations have been proposed as the noise source in the case of classical GMI-based sensors. Here, we apply this model to off-diagonal GMI-based magnetometers. This requires the inclusion of magnetization fluctuation noise sources, in addition to white noise sources from electronic conditioning in the GMI effect equations. A pessimistic scenario is presented, predicting the upper limit of low-frequency excess noise from material characteristics. The equivalent magnetic noise level is then computed from the sensitivity of each term of the sensing element impedance matrix to the magnetization angle at the static working point (for both axial and circumferential static magnetic field) and to conditioning circuitry. Based on this, it appears that magnetization fluctuations similarly affect all modes of operation of the two-port network sensing element, inducing identical impedance fluctuations. It also appears that this noise depends only upon the static equilibrium condition. This condition is governed by the effective anisotropy of the magnetic wire and by both axial and circumferential static components of the working point.

Moisture‐radiative cooling instability

AbstractRadiative‐convective equilibrium (RCE)—the statistical equilibrium state of the atmosphere where convection and radiation interact in the absence of lateral transport—is widely used as a basic‐state model of the tropical atmosphere. The possibility that RCE may be unstable to development of large‐scale circulation has been raised by recent modeling, theoretical, and observational studies, and could have profound consequences for our understanding of tropical meteorology and climate. Here, we study the interaction between moisture and radiative cooling as a contributor to instability of RCE. We focus on whether the total atmospheric radiative cooling decreases with column water vapor; this condition, which we call moisture‐radiative cooling instability (MRCI), provides the potential for unstable growth of moist or dry perturbations. Analytic solutions to the gray‐gas radiative transfer equations show that MRCI is satisfied when the total column optical depth—linked to column water vapor—exceeds a critical threshold. Both the threshold and the growth rate of the instability depend strongly on the shape of the water vapor perturbation. Calculations with a realistic radiative transfer model confirm the existence of MRCI for typical tropical values of column water vapor, but show even stronger dependence on the vertical structure of water vapor perturbation. Finally, we analyze the sensitivity of atmospheric radiative cooling to variability in column water vapor in observed tropical soundings. We find that clear‐sky MRCI is satisfied across a range of locations and seasons in the real tropical atmosphere, with a partial growth rate of ∼1 month.

Vectorised graphics processing unit accelerated dynamic relaxation for bar and beam elements

Dynamic relaxation is an analysis method that can be used to find the static equilibrium state of a structure undergoing large displacements. Due to the algorithm's iterative nature, which derives from a damped dynamic oscillations approach, it can take considerable time when solving models with dense node counts. This research looks at a vectorised dynamic relaxation implementation, executed on a graphics card's processing unit (GPU) for the most computationally demanding calculations, and compared to traditional computations on the central processing unit (CPU), to determine if time savings can be found with the change in processor type. The programming language Python and module PyCUDA are utilised on a desktop graphics card with over two thousand shader cores, and compared to a quad-core processor using the same code layout. A vectorised formulation for bar elements and reduced degree-of-freedom beam elements is used, to analyse the absolute and relative run-times for three benchmark cases. It is found that for models with low node counts, the CPU is faster, while for medium to highly dense models, the GPU acceleration can reduce absolute run-times by a factor of three to just over eight. Most benefit is gained when the executed code allows the GPU cores to be overloaded, such that complex calculations involving large arrays of data can be spread over the many cores. This was evident in the GPU load demand, which increased steadily with increasing node count but remained below 100%, while the CPU was readily activated to maximum load for even simple models. The time savings are of interest to architects, engineers and researchers utilising the dynamic relaxation method with medium to complex models, as the benefits can be harnessed with minimal code alteration.