Equilibrium Spacing Research Articles

Jerk Chaotic System: Analysis, Circuit Simulation, Control and Synchronization with Application to Secure Communication

Dynamical behaviors of 3D Jerk system were examined in terms of equilibrium, stability, dissipative, and phase space attractor in this study. The system’s practical applications were demonstrated through circuit realization and synchronization scheme via active backstepping control with its effectiveness demonstrated in secure communication. The viability of the theoretical model of 3D Jerk system was confirmed using electronic circuit workbench designed in MultiSIM enviroment. A nonlinear feedback controller was designed using the recursive backstepping technique to control and track a desire function. For secure communication application, active backstepping method was adopted to synchronize two identical chaotic systems evolving from different initial conditions. It was demonstrated that when the controller was activated, the systems synchronize successfully. The results of the active backstepping designed controllers were numerically applied in the area of secure communication, with the variable of the drive being encrypted information transmitted through a coupling channel. Using an additive encryption masking scheme, the encrypted signal was a superposition of sinusoidal information specified by period function and chaotic carrier generated from a variable of the Jerk system. The transmitted information signal was successfully retrieved from the chaotic response signal using an inverse function decryption algorithm, thereby confirming the effectiveness and robustness of the designed controller.

Geometrothermodynamics of 3D Regular Black Holes.

We investigate a spherically symmetric exact solution of Einstein's gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions.

Nested solutions of gravitational condensate stars

Black holes are normally and naturally associated to the end-point of gravitational collapse. Yet, alternatives have been proposed and a particularly interesting one is that of gravitational condensate stars, or gravastars. We here revisit the gravastar model and increase the degree of speculation by considering new solutions that are inspired by the original model of gravastars with anisotropic pressure, but also offer surprising new features. In particular, we show that it is possible to nest two gravastars into each other and obtain a new solution of the Einstein equations. Since each gravastar essentially behaves as a distinct self-gravitating equilibrium, a large and rich space of parameters exists for the construction of nested gravastars. In addition, we show that these nested-gravastar solutions can be extended to an arbitrarily large number of shells, with a prescription specified in terms of simple recursive relations. Although these ultra-compact objects are admittedly very exotic, some of the solutions found, provide an interesting alternative to a black hole by having a singularity-free origin, a full matter interior, a time-like matter surface, and a compactness C→(1/2)− .

Naphthenic acid fraction compounds, produced by the extraction of bitumen from oil sands, alter survival and behaviour of juvenile yellow perch (Perca flavescens)

We evaluated whether naphthenic acid fraction compounds (NAFCs) extracted from oil sand tailings adversely affect fish survival and behaviour. Following a before–after-control-impact design, we housed wild-caught juvenile yellow perch ( Perca flavescens) in outdoor mesocosms to assess survival and behaviour under baseline conditions, then exposed fish to one of three treatments: negative control, 2 mg/L NAFC, or 15 mg/L NAFC. We performed behavioural assays (no-stimulus activity, food stimulus, and predator stimulus using a model bird) and assessed a comprehensive suite of endpoints (equilibrium losses, activity, shoaling, burst swimming, freezing, and space use). We found that exposure to 15 mg/L NAFCs substantially reduced fish survival and impaired fish equilibrium in all three behavioural tests. Furthermore, exposure to NAFCs impaired anti-predator behaviour: while the activity of control fish increased by two-fold in response to a predator stimulus, fish exposed to 2 or 15 mg/L NAFC did not change their activity levels after stimulation. No significant changes were observed in other behavioural endpoints. Overall, our findings suggest that a week-long exposure to NAFCs at concentrations commonly found in tailings ponds, constructed wetlands, and other mining-impacted waters may affect multiple facets of fish behaviour that could ultimately lead to reduced fitness in fish populations.

Stability Properties of Geometrothermodynamic Cosmological Models.

We consider a particular isotropic and homogeneous cosmological model, in which the equation of state is obtained from a thermodynamic fundamental equation by using the formalism of geometrothermodynamics (GTD). The model depends effectively on three arbitrary constants, which can be fixed to reproduce the main aspects of the inflationary era and the ΛCDM paradigm. We use GTD to analyze the geometric properties of the corresponding equilibrium space and to derive the stability properties and phase transition structure of the cosmological model.

Impact of barrow entropy on geometrothermodynamics of specific black holes

In this paper, we study the effect of Barrow entropy on the thermodynamic properties and geometry of specific black holes along with the nonlinear source. We investigate the mass, temperature, thermodynamic variable, and electric potential of the black hole as well. Furthermore, we examine the behavior of heat capacity to check the stability of a black hole. Geometrothermodynamics allows us to describe interactions between thermodynamics, critical points, and phase transitions by considering the geometric characteristics of the thermodynamic equilibrium space. Our analysis demonstrates that these findings are consistent with the results derived from the classical thermodynamics of black holes.

Ideal quantum gases: A geometrothermodynamic approach

We derive the fundamental thermodynamic equation for Fermi-Dirac and Bose-Einstein quantum gases, which contains the first order contribution due to the quantum nature of the gas particles. Then, we analyze the fundamental equation in the context of geometrothermodynamics. Although the corresponding Hamiltonian does not contain a potential, indicating the lack of classical thermodynamic interaction, we show that the curvature of the equilibrium space is non-zero and can be interpreted as a measure of the effective quantum interaction between the gas particles. In the limiting case of a classical Boltzmann gas, we show that the equilibrium space becomes flat, as expected from the physical viewpoint. In addition, we derive a thermodynamic fundamental equation for the Bose-Einstein condensation and, using the Ehrenfest scheme, we show that it can be considered as a first order phase transition which in the equilibrium space corresponds to a curvature singularity. This result indicates that the curvature of the equilibrium space can be used to measure in an invariant way the thermodynamic interaction in classical and quantum ideal gases.

A 2D‐connected automated vehicle car‐following control algorithm

AbstractCar‐following prevails in daily traffic under various scenarios. However, most connected automated vehicle (CAV) car‐following algorithms in the literature only apply to one‐dimensional CAV control, which limits the application scenarios. This paper presents a two‐dimensional (2D) CAVs car‐following strategy on curved roads in the spatial domain with vehicle‐to‐vehicle and vehicle‐to‐infrastructure communication to expand the car‐following application scenarios. This control strategy constructs a 2D car‐following equilibrium policy by extending the simplified Newell's car‐following model. Based on that, a constrained optimal CAV car‐following control in the spatial domain is constructed to maintain the inter‐vehicle spacing and speed difference while regulating the lane deviation and avoiding work zones. As demonstrated by numerical results, our proposed algorithm maintains a high degree of consistency between equilibrium spacing and vehicle speed while duplicating the trajectory of the leading vehicle, implying empirical string stability. The results also suggest the robustness of handling different scenarios.

Unified representation of homogeneous and quasi-homogenous systems in geometrothermodynamics

We analyze homogeneous and quasi-homogeneous thermodynamic systems within the formalism of geometrothermodynamics (GTD). A generalized Euler identity is used to obtain the explicit form of the three Legendre invariant metrics that are known in GTD for the equilibrium space. In so doing, we fix all the arbitrary parameters that enter the GTD metrics in terms of the quasi-homogeneous coefficients. We obtain quite general results that relate the curvature singularities of the equilibrium space with the thermodynamic stability conditions and the phase transition structure of the system. This result allows us to avoid the appearance of non-physical singularities at the level of the equilibrium space.

Geometrothermodynamic description of real gases using the law of corresponding states

We propose a geometric model for the description of the equilibrium space of real gases based on the Legendre invariant formalism of geometrothermodynamics. We investigate the curvature of three different Legendre invariant metrics and show that the corresponding singularities are related to the critical points of the response functions, the isotherms in a pressure-volume diagram, and the stability conditions. This implies that it is necessary to consider all Legendre invariant metrics to completely describe the critical behavior of real gases in terms of curvature singularities.

Equilibrium space and a pseudo linearization of nonlinear systems

This paper attempts to extend the concept of the equilibrium point to what is called equilibrium space, which can adapt to a system in which there exists an infinite number of equilibrium points. In the context of Lyapunov’s linearization method extended for the equilibrium space, this paper proposes a pseudo linearization, from which we can derive a linear representation for a nonlinear system. The equilibrium state of this pseudo linearization and its stability are shown to be the same as that of the original nonlinear system. As an example of the applicability, the proposed pseudo linearization is applied to derive a discrete-time model for a control moment gyroscope system from a nonlinear continuous-time model. Simulation results show that the discrete-time model derived using the proposed pseudo linearization yields responses that are closer to that of the continuous-time model than the discrete-time model derived by the well-known forward-difference method and the conventional pseudo linear representation method, even with a large sampling interval.

A stabilized virtual coupling scheme for a train set with heterogeneous braking dynamics capability

Virtual coupling (VC) is an advanced technology in train control systems, which enables trains to run information with a small tracking interval. Hence, it can significantly increase the capacity of rail transit. Similar to the vehicle platooning, most established VC approaches select the constant time/spacing gap commonly as the spacing policy but regards the relative braking distance as a constraint. These spacing policy diminish the priority of safety concern in train control systems due to the severity of incidents and economic loss. Motivated by this research gap, in this paper, we designed a stabilized virtual coupling scheme for a train set with heterogeneous braking dynamics capability. Specifically, a relative braking distance based spacing policy is introduced according to the braking dynamics capability of the train, which is a typical characteristic that distinguishes it from the vehicle platoon model. A linear control architecture suitable for the virtual coupled train set (VCTS) is designed to maintain the equilibrium spacing. Sufficient conditions to ensure the local stability are derived and obtained in this paper. The impact of braking dynamics capability on the string stability is analyzed in terms of acceleration and spacing difference respectively in the frequency domain by using the Laplacian transformation. For the former, the necessary and sufficient conditions to ensure the string stability are given, and for the latter, a numerical traversal method to summarize the impact of the heterogeneous braking dynamics capability on string stability is given based the former. Two sets of test examples are given, proving the correctness of the necessary and sufficient conditions of the former and the applicability of the research method of the latter, respectively.

Symplectic structure of equilibrium thermodynamics

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, Hamiltonians can be defined that describe thermodynamic processes.

Enhancing kinetic and electrochemical performance of layered MoS2 cathodes with interlayer expansion for Mg-ion batteries

Layered materials such as transition metal dichalcogenides (TMDs) are actively pursued as promising candidates for Mg-ion batteries. However, the sluggish kinetics of Mg intercalation caused by strong binding interactions remains an on-going challenge for layered electrodes. Here using first-principles calculations, we investigate the thermodynamic and electrochemical performance of MoS2 as a prototypical example of layered TMD cathodes with controllable interlayer spacing. Our calculations demonstrate that at equilibrium spacing (∼6 Å), the intercalation of Mg ions results in the H- to T-phase transformation of MoS2 at the critical Mg concentration of ∼0.22. For higher concentrations, the H-phase of magnesiated MoS2 is metastable and can co-exist with the T-phase one up to the maximum Mg concentration of 0.5. Enlarging interlayer spacing (from equilibrium 6 Å to 8 Å) significantly boosts Mg diffusivities-, and can enhance the specific capacity from 155 to 225 mAhg−1 with the maximum Mg concentration of 0.75. While the weakened binding interaction between Mg and expanded MoS2 layers reduces electrode voltages, the key findings obtained from this work provide crucial insights into an optimal balance between enhanced capacity/kinetics and reduced voltage window for the practical application of layer-expanded cathodes for Mg-ion batteries.

A Nonlinear Safety Equilibrium Spacing-Based Model Predictive Control for Virtually Coupled Train Set Over Gradient Terrains

The increasing demand for capacity in railway transportation has spawned the concept of virtual coupling (VC), which can further shorten the intertrain distance by applying communication technology. In this article, a centralized model predictive control (MPC) is developed for virtually coupled train set (VCTS) with a nonlinear safety equilibrium spacing policy over gradient rolling terrains. The tracking target of the controller in cruise phase is given based on the braking distance difference and speed difference of trains. A more precise braking distance model of trains explicitly considering the gradient is introduced for safety, based on which the state space applicable to the controller for VCTS is derived. To deal with the nonlinearities of the controller, a new optimization solving algorithm based on the continuation method and generalized minimum residual (GMRES) method is presented in this article. Finally, controller performances and empirical string stability of VCTS are verified by numerical simulations. It is proven that the proposed controller has a good effect for the safety and smoothness of the train operation on the railway line over gradient terrain through the test. The actual intertrain distance under the proposed controller is about 1 m closer to the equilibrium state than that under the same controller without considering the gradient at low speed (about 10 m/s) on the 0.3% downhill line, which verifies the safety of the controller. Besides, the influence of the parameters of the controller and optimization method on controller efficiency is analyzed, and for the latter, the simulation data show that the applied algorithm for the optimal control solver can save the calculation time more than seven times than the traditional algorithm.

Geometrothermodynamics of van der Waals systems

We explore the properties of the equilibrium space of van der Waals thermodynamic systems. We use an invariant representation of the fundamental equation by using the law of corresponding states, which allows us to perform a general analysis for all possible van der Waals systems. The investigation of the equilibrium space is performed by using the Legendre invariant formalism of geometrothermodynamics, which guarantees the independence of the results from the choice of thermodynamic potential. We find all the curvature singularities of the equilibrium space that correspond to first and second order phase transitions. We compare our results with those obtained by using Hessian metrics for the equilibrium space. We conclude that the formalism of geometrothermodynamics allows us to determine the complete phase transition structure of systems with two thermodynamic degrees of freedom.

Grid-shell design and analysis via reciprocal discrete Airy stress functions

This research paper introduces a theoretical framework for the design and analysis of compression-and-tension grid-shells in static equilibrium where the states of self-stress function as design freedoms. This is based on a synthesis of reciprocal discrete Airy stress functions in the context of graphic statics and the Force Density Method (FDM). Specifically, the former is a direct method for generating 2-dimensional global static equilibrium whereas the latter allows for its 3-dimensional implementation. As a result, creative design explorations can take place directly within the equilibrium space without the need for iterative convergence algorithms to obtain equilibrium. The use of reciprocal Airy stress functions in conjunction with the lower bound theorem gives insight and explicit control with regards to the states of self-stress as design and analysis freedoms which can define the structural form and its load path.

Ionically Generated Built‐In Equilibrium Space Charge Zones—a Paradigm Change for Lead Halide Perovskite Interfaces

Adv. Funct. Mater. 2020, 30, 2002426 DOI: 10.1002/adfm.202002426 In the originally published Supporting Information of this article, the notations of the equations were unintentionally blurred. The Supporting Information file has been corrected, and the readers can now see the detailed notations. The authors apologize for any inconvenience this may have caused. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Behavioral Harmonization of a Cyclic Vehicular Platoon in a Closed Road Network

This paper presents a method to dynamically harmonize the behaviors of cyclic vehicular platoons in a closed road network. Different from the open-chain counterpart, a cyclic platoon formulates a traffic flow ring constrained by interconnection coupling feature and finite-length geometry, which brings challenges for platoon control design and analysis. First, by exploiting the circulant structure of homogeneous cyclic platoons, the closed-loop dynamics is decomposed into a set of decoupled systems with the same low dimension as a single vehicle. Based on this decomposition, an analytical necessary and sufficient stability condition is derived for the design of distributed feedback controllers. This necessary and sufficient condition is further relaxed into sufficient conditions to remove the dependence on the platoon size. Next, the string stability is proved with the sufficient conditions derived above based on frequency-domain analysis. Then, based on integral sliding mode control, we prove that heterogeneous vehicles can behave like homogeneous ones so that the results on homogeneous cyclic platoons can be extended to heterogeneous cyclic platoons. Finally, the equilibrium velocity and spacing errors are derived to explain the effect of geometry conditions on the steady-state behavior. Numerical simulations using both linear and nonlinear vehicle models are conducted to validate our findings.

Geometrothermodynamics of black holes with a nonlinear source

We study thermodynamics and geometrothermodynamics of a particular black hole configuration with a nonlinear source. We use the mass as fundamental equation, from which it follows that the curvature radius must be considered as a thermodynamic variable, leading to an extended equilibrium space. Using the formalism of geometrothermodynamics, we show that the geometric properties of the thermodynamic equilibrium space can be used to obtain information about thermodynamic interaction, critical points and phase transitions. We show that these results are compatible with the results obtained from classical black hole thermodynamics.