Hamiltonian Energy Research Articles

Statistics of protein electrostatics.

Molecular dynamics simulations of a small redox-active protein plastocyanin address two questions. (i) Do protein electrostatics equilibrate to the Gibbsian ensemble? (ii) Do the electrostatic potential and electric field inside proteins follow the Gaussian distribution? The statistics of electrostatic potential and electric field are probed by applying small charge and dipole perturbations to different sites within the protein. Nonergodic (non-Gibbsian) sampling is detectable through violations of exact statistical rules constraining the first and second statistical moments (fluctuation-dissipation relations) and the linear relation between free-energy surfaces of the collective coordinate representing the Hamiltonian electrostatic perturbation. We find weakly nonergodic statistics of the electrostatic potential (simulation time of 0.4-1.0 μs) and non-Gibbsian and non-Gaussian statistics of the electric field. A small dipolar perturbation of the protein results in structural instabilities of the protein-water interface and multi-modal distributions of the Hamiltonian energy gap. The variance of the electrostatic potential passes through a crossover at the glass transition temperature Ttr ≃ 170 K. The dipolar susceptibility, reflecting the variance of the electric field inside the protein, strongly increases, with lowering temperature, followed by a sharp drop at Ttr. The linear relation between free-energy surfaces can be directly tested by combining absorption and emission spectra of optical dyes. It was found that the statistics of the electrostatic potential perturbation are nearly Gibbsian/Gaussian, with little deviations from the prescribed statistical rules. On the contrary, the (nonergodic) statistics of dipolar perturbations are strongly non-Gibbsian/non-Gaussian due to structural instabilities of the protein hydration shell.

Firing dynamics and coupling synchronization of memristive EMR-based Chaivlo neuron utilizing equivalent energy approach.

Firing dynamics and its energy property of neuron are crucial for exploring the mechanism of intricate information processing within the nervous system. However, the energy analysis of discrete neuron is significantly lacking in comparison to the vast literature and mature theory available on continuous neuron, thereby necessitating a focused effort in this underexplored realm. In this paper, we introduce a Chaivlo neuron map by employing a flux-controlled memristor to simulate electromagnetic radiation (EMR), and a detailed analysis of its firing dynamics is conducted based on an equivalent Hamiltonian energy approach. Our observations reveal that a range of energy-based firing behaviors, such as spike firing, coexistence firing, mixed-mode firing, and chaotic bursting firing, can be induced by EMR and injected current. To delve deeper into the synchronous firing dynamics, we establish a Chaivlo network by electrically coupling two memristive EMR-based Chaivlo neurons. Subsequently, we experimentally evaluate the synchronization behavior of this network by quantifying both the synchronization factor and the average difference of equivalent Hamiltonian energy. Our findings conclusively demonstrate that both EMR and coupling strength positively contribute to the network's synchronization ability.

A computational study and analysis of Variational Quantum Eigensolver over multiple parameters for molecules and ions

AbstractMaterial discovery is a phenomenon practiced since the evolution of the world. The discovery of materials has led to significant development in varied fields such as Science, Engineering and Technology. Computationally simulating molecules has been an area of interest in the industry as well as academia. However, simulating large molecules can be computationally expensive in terms of computing power and complexity. Quantum computing is a recent development that can improve the efficiency in predicting properties of atoms and molecules which will be useful for material design. The Variational Quantum Eigensolver (VQE) is one such quantum algorithm used to calculate the ground state energy of molecules or ions. In this study, we have done a comparative analysis of the parameters that constitute the VQE algorithm. This includes components such as basis, qubit mapping, ansatz, and optimizers used. We have also developed a database consisting of 79 single atoms and their variations of oxidation states and 33 molecules with the data of their Hamiltonian and ground state energy and dipole moment.

Complex dynamic behavioral transitions in auditory neurons induced by chaotic activity

Chaotic sequences are widely used in secure communication due to their high randomness. Chaotic resonance (CR) refers to the resonant response of a system to weak signals induced by chaotic activity, but its practical application remains limited. This study designs a simplified FitzHugh-Nagumo (FHN) auditory neuron model by simulating the physiological activities of auditory neurons and considering the combined stimulation of chaotic activity and sound signals. It is found that the neuron dynamics depend on both external sound stimuli and chaotic current intensity. Chaotic currents induce spikes in the neuron output sequence through CR, and the spikes become more frequent with increasing current intensity, eventually leading to a chaotic state regardless of the initial state. However, the sensitivity of the initial value of this chaotic sequence shifts to the chaotic current excitation system. The injection of chaotic currents can reduce the system's average Hamiltonian energy under certain conditions. By measuring the complexity of the generated sequences, we find that the addition of chaotic currents can enhance the complexity of the original sequences, and the enhancement ability increases with the intensity. This provides a new approach to enhance the complexity of original chaotic sequences. Moreover, different chaotic currents can induce different chaotic sequences with varying abilities to enhance the complexity of the original sequences. We hope our work can contribute to secure communication.

DYNAMIC ANALYSIS AND HAMILTONIAN ENERGY ASPECTS OF HYPERCHAOTIC MEGASTABLE OSCILLATOR

Megastable oscillations are a subject of significant research interest due to their broad range of potential applications. Typically, megastable systems are driven into oscillation by a forcing term. In this paper, we propose a novel megastable oscillator that utilizes a combination of Signum and trigonometric functions. To the best of our knowledge, no 3D megastable system has been found to exhibit hyperchaotic behavior without any forcing term. We demonstrate the megastability of our oscillator using phase portraits and basins of attraction and confirm the oscillations using the Hamiltonian energy method. We also conduct a stability analysis to explore the system’s nature and investigate the impact of parameters using a bifurcation diagram. Furthermore, we present a Lyapunov spectrum to identify regions of chaos, hyperchaos, and periodic oscillations. The results we obtain demonstrate the complexity of the system and its sensitivity to initial conditions, making it well-suited for applications such as random number generation and secure communication.

Distributed control of spacecraft formation under [formula omitted] perturbation in the port-Hamiltonian framework

To control the relative position and relative velocity of spacecraft formation, a time-varying nonlinear relative motion model under J2 perturbation in an elliptical orbit is established in the port-Hamiltonian (PH) framework, and a distributed control law for spacecraft formation is developed using the consensus algorithm for parameter estimation and the passivity-based control (PBC) method based on the state-error interconnection and damping assignment (IDA) technique. First, the influence of J2 perturbation on the potential energy and orbit parameters in the model is considered when the relative motion model is built in the PH frame, and the expression of the relative motion acceleration under J2 perturbation is given. Second, to solve the problem that the state of the chief spacecraft cannot be directly obtained from the deputy spacecraft under distributed communication, a consensus-based parameter estimation method is introduced, the estimated parameter of the chief spacecraft is applied to the relative motion model in the PH frame, and a state error model with the estimated parameters derived from the consistency algorithm is established. Then, after the stability analysis is conducted on the desired PH system containing the estimated parameter values, the desired Hamiltonian energy function with the estimated parameters is designed according to the time-varying errors of the relative equilibrium states of the deputy spacecraft and the errors between deputy spacecraft, and the distributed control law of spacecraft formation is derived based on the state-error IDA-PBC method. Finally, the expected relative motion trajectory designed based on the TH equation is used to simulate a spacecraft formation under J2 perturbation, and the results indicate that the spacecraft can quickly converge to the expected formation under the influence of the control law.

Probing coherent quantum thermodynamics using a trapped ion

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, where coherence and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we demonstrate the possibility to experimentally measure and benchmark a genuine quantum correction, induced by quantum friction, to the classical work fluctuation-dissipation relation. This is achieved by combining laser-induced coherent Hamiltonian rotations and energy measurements on a trapped ion. Our results demonstrate that recent developments in stochastic quantum thermodynamics can be used to benchmark and unambiguously distinguish genuine quantum coherent signatures generated along driving protocols, even in presence of experimental SPAM errors and, most importantly, beyond the regimes for which theoretical predictions are available (e.g., in slow driving).

A new four-dimensional chaotic system with rich transitional characteristics between dissipative and conservative.

The general form of the Hamiltonian function serves as the foundation for the creation of a new four-dimensional chaotic system in this study. We discover that the external excitation parameter d, the internal parameter a, and all initial values have a transforming influence on the system property. Additionally, the corresponding fractional-order chaotic system in accordance with the constructed four-dimensional chaotic system is proposed. It is found that as the order q rises, the system transforms gradually from a dissipative system to a conservative system. Multiple coexisting attraction flows based on the Hamiltonian energy magnitude are present in this dual-property chaotic system. The complexity analysis shows that the system has a high level of complexity. NIST test indicates that the chaotic sequences produced by this dual-property chaotic system exhibit good pseudo-randomness. Finally, a Digital Signal Processing-based hardware platform confirms the physical realizability of the system.

A new amplification-fitting approach in Newton-Cotes rules to tackling the high-frequency IVPs

In this paper, we will further strengthen the fitting technique of the well-known Newton-Cotes rules. First, we fit Boole's rule using the found amplification factor, and then we use it to numerically solve first-order differential equations with oscillating solutions. If the Hamiltonian energy of the system remains almost constant then we investigate whether the new amplification-fitted methods can be used as symplectic methods for numerical integration.The obtained results show the high accuracy of the new amplification-fitting Boole's rule-based methods.

Molecular simulation-based assessing of a novel metal-organic framework modified with alginate and chitosan biopolymers for anionic reactive black 5 and cationic crystal violet pollutants capture

This study employed molecular simulations to develop efficient and environmentally friendly adsorbents for removing two common dye pollutants, crystal violet (CRVT) and reactive black 5 (RBC5). The investigated adsorbents are based on biodegradable polymers alginate (ALG) and chitosan (CHAN) functionalized with carboxyl acid groups (CA) on a UIO-66 metal–organic framework (MOF). Density functional theory (DFT) analyses such as electrostatics potential (ESP), Average local ionization energy (ALIE) analysis, COSMO-RS (Conductor-like Screening Model for Real Solvents) analysis and the density of states (DOS) were performed to investigate the structures of the pollutants and adsorbents. Physical and chemical properties of the adsorbents, including density, Hamiltonian energy (HAE), the radius of gyration (ROG), and the stress autocorrelation function (SACF) were also examined. Additionally, molecular dynamics (MD) and Monte Carlo (MC) simulations were employed to study the adsorption of CRVT and RBC5 onto CA/UIO-66, CA/UIO-66/ALG, and CA/UIO-66/CHAN adsorbents. The results demonstrated that functionalizing CA/UIO-66 with CHAN and ALG significantly enhances the adsorption capacity for both CRVT and RBC5. The modified adsorbent demonstrated significantly higher affinity towards RBC5 compared to CRVT, as evidenced by the adsorption energies of −1.11 × 104 kcal/mol for CA/UIO-66-CHAN-W-CRVT and −1.36 × 107 kcal/mol for CA/UIO-66-CHAN-W-RBC5. This research highlights the potential of CHAN- and ALG-functionalized CA/UIO-66-based adsorbents as promising alternatives to current wastewater treatment methods. These adsorbents are efficient, biodegradable, and environmentally friendly, offering remarkable potential for removing dye pollutants from industrial and domestic wastewater.

Hamiltonian formalism for bistable-multilayered plates under non-mechanical stimuli

Bistable multilayered plates have attracted significant attention as morphing and adaptive structures, renowned for their unprecedented exceptional performance. However, accurately predicting both their shape and internal stresses poses formidable challenges due to their geometrically nonlinear nature. For the first time, this paper introduces a Hamiltonian formalism aimed at achieving high-resolution analysis of nonlinear multilayered plates subjected to non-mechanical stimuli, including hygro-thermo-electro-magneto-elastic responses. A canonical system is strategically developed to compute membrane behaviors, yielding symplectic dual differential equations for in-plane field variables. This method elegantly decouples out-of-plane variables from the full-state vector, leading to an exact analytical solution in the membrane problem. To predict the bending behaviors, the first variation of the Hamiltonian energy density function, expressed as a power series of the transverse deflection, ensures flexural equilibrium. The power series effectively captures all admissible out-of-plane deformations, enabling a smooth transition between linear and nonlinear plate responses, including pitchfork bifurcation and limit points. The validity and accuracy of the proposed method are rigorously assessed through convergence tests and satisfaction of boundary conditions across various equilibria, ranging from monostability to bistability. It is cross-verified with high-fidelity finite-element methods (FEM), showing excellent agreements in both deformations and stress resultants. This research presents a physics-based methodology that unveils a parametric interplay between in-plane and out-of-plane field variables, serving as an efficient approach for analyzing adaptive and morphing structures.

A 4D conservative chaotic system: dynamics and realization

This paper proposes a novel four-dimensional conservative chaotic system (4D CCS) with a simple algebraic representation, comprising only two quadratic nonlinear terms. The dynamic characteristics of the 4D CCS are investigated by Poincaré mappings, Lyapunov exponents (LE), bifurcation diagrams, equilibrium points and spectral entropy (SE) complexity algorithm. Variations in parameters, initial values, and Hamiltonian energy lead to alternations between quasi-periodic and chaotic flows in the 4D CCS. The maximum Lyapunov exponent of the 4D CCS can reach a high value of 366300 under adjusting appropriate parameters and initial values. The pseudorandom sequences generated by the 4D CCS successfully pass the NIST test. Additionally, both the electronic circuit and FPGA implementation of the 4D CCS are carried out, with the experimental results aligning closely with the simulation results.

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. This general CHNS system reduces to cases in the literature, to which we can compare.

Exergy and dynamics analyses in centrifugal turbomachinery pressurized long-distance natural gas pipelines based on Hamiltonian model

Natural gas pipelines represent intricate systems comprising diverse components, which is crucial to industry, yet demanding substantial energy consumption. However, the nuanced energy and exergy transfer dynamics within these pipelines, particularly during dynamic processes, remain relatively unexplored. Given the distributed nature and complicated component coupling among pipeline elements, coolers, and compressors, traditional energy analysis tools face challenges in their application. In this study, we introduce a novel approach utilizing Hamiltonian formalism to establish an energy and exergy analysis framework for natural gas pipelines. Specifically, we develop Hamiltonian energy functions for various components, including pipes, centrifugal compressors, and coolers, accounting for dynamic mechanisms. Through comprehensive simulations covering static and dynamic scenarios, we elucidate energy and exergy transfer processes, leveraging Hamiltonian energy function terms. Our findings validate the efficacy of the proposed analysis framework in accurately characterizing energy transfer and dissipation processes. Furthermore, validation with field data demonstrates the capability of our method to online exhibit energy transfer features effectively.

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Random matrix model of Kolmogorov-Zakharov turbulence.

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

Dynamics of solitary waves, chaotic behaviors, and Jacobi elliptic wave solutions in telecommunication systems

This research explores bifurcation of a nonlinear model concerning with the telecommunication strait. Possible all phase plane diagrams due to various parametric conditions are found. Derivation of analytical tangled wave propagating solutions following all phase orbits of the corresponding phase portraits are established. As a results, the soliton, shock wave, singular soliton, periodic wave and singular periodic solutions are obtained by direct integration from Hamiltonian energy function. The periodic solutions of the model are formulated in the form of generalized Jacobi elliptic functions, which also provide the solitonic solution setting the value of beta is unity. Additionally, chaotic and quasi-periodic behaviors have been found for a range of parameter values after adding the perturbed term. The perturbed system’s quasi-periodic and chaotic behavior have been demonstrated using sensitivity analysis. Finally, picturesque explorations are delivered exposing effects of exist parameters of the gained wave solutions. The majority of the achieved results are derived for the first time. Moreover, the solutions show that the novel schemes are very simple, outright, fruitful and successful and that they can be used in wide range of other nonlinear partial differential equations (NLPDEs), which create different kinds of dynamical features of other wave model.

Dynamics and Hamiltonian energy analysis of a novel memristor coupled Josephson junction phototub chaotic circuit

Dynamics and Hamiltonian energy analysis of a novel memristor coupled Josephson junction phototub chaotic circuit

Hamiltonian energy in a modified Hindmarsh-Rose model.

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

A novel directly energy-preserving method for charged particle dynamics

In this paper, we apply the coordinate increment discrete gradient (CIDG) method to solve the Lorentz force system which can be written as a non-canonical Hamiltonian system. Then we can obtain a new energy-preserving CIDG-I method for the system. The CIDG-I method can combine with its adjoint method CIDG-II which is also a energy-preserving method to form a new method, namely CIDG-C method. The CIDG-C method is symmetrical and can conserve the Hamiltonian energy directly and exactly. With comparison to the well-used Boris method, numerical experiments indicate that the CIDG-C method holds advantage over the Boris method in terms of energy-conserving.