Dynamics

This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions. Full article

For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches, length scale parameters have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modeling, as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established, there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion, system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach, it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically, it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior. Full article

This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create diverse natural and engineered surface textures, governed by probabilistic principles. The model’s formulation addresses key questions related to deposition initiation, nucleation point behaviour, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. A versatile algorithm, relying on six parameters and employing nested loops and Gaussian sampling, is developed. The algorithm’s efficacy is examined through extensive simulations, involving variations in nucleation scaling densities, aggregate scaling scenarios, spread factors, and diffusion rates. Surface statistics are computed for simulated deposits and analyzed using Fast Fourier Transform (FFT). The resulting database enables quantitative comparisons of surfaces generated with different parameters, where the database-derived parallel coordinates offer guidance for selecting optimal model parameters to achieve desired surface morphologies. The proposed approach is validated against urea-derived deposits, exhibiting statistical consistency and agreement with experimental observations. Overall, the model’s adaptable framework holds promise for understanding and predicting deposit growth on surfaces in diverse practical scenarios. Full article

The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability. Full article

Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially in process engineering, the majority of the proposed surrogate models address steady-state problems, while poor studies refer to dynamic simulation modeling. For this reason, using a response function-based approach, a crystallization unit case study was set up in order to derive a dynamic data-driven model for crystal growth whose characteristic differential parameters are derived via Response Surface Methodology. In particular, multiple independent variables were considered, and a well-established sampling technique was exploited for sample generation. Then, different sample sizes were tested and compared in terms of accuracy indicators. Finally, the domain partition strategy was exploited in order to show its relevant impact on the final model accuracy. In conclusion, the outcome of this study proved that the proposed procedure is a suitable methodology for dynamic system metamodeling, as it shows good compliance and relevant improvement in terms of computational time. In terms of future research perspectives, testing the proposed procedure on different systems and in other research fields would allow for greater improvement and would, eventually, extend its validity. Full article

In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the Störmer–Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge–Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge–Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method. Full article

This paper presents an innovative entanglement-based protocol to address the Dining Cryptographers problem, utilizing maximally entangled $|GH{Z}_n⟩$ tuples as its core. This protocol aims to provide scalability in terms of both the number of cryptographers n and the amount of anonymous information conveyed, represented by the number of qubits m within each quantum register. The protocol supports an arbitrary number of cryptographers n, enabling scalability in both participant count and the volume of anonymous information transmitted. While the original Dining Cryptographers problem focused on a single bit of information—whether a cryptographer paid for dinner—the proposed protocol allows m, the number of qubits in each register, to be any arbitrarily large positive integer. This flexibility allows the transmission of additional information, such as the cost of the dinner or the timing of the arrangement. Another noteworthy aspect of the introduced protocol is its versatility in accommodating both localized and distributed versions of the Dining Cryptographers problem. The localized scenario involves all cryptographers gathering physically at the same location, such as a local restaurant, simultaneously. In contrast, the distributed scenario accommodates cryptographers situated in different places, engaging in a virtual dinner at the same time. Finally, in terms of implementation, the protocol accomplishes uniformity by requiring that all cryptographers utilize identical private quantum circuits. This design establishes a completely modular quantum system where all modules are identical. Furthermore, each private quantum circuit exclusively employs the widely used Hadamard and CNOT quantum gates, facilitating straightforward implementation on contemporary quantum computers. Full article

Two neural networks were trained to predict, respectively, the Euler characteristic and the curvature of nuclear pastas in neutron star crust conditions generated by molecular dynamics simulations of neutron star matter with 0.1 < x < 0.5, 0.040 fm⁻³ < ρ < 0.085 fm⁻³ (0.68 × 10¹⁴ g/cm³ < ρ < 1.43 × 10¹⁴ g/cm³), and 0.2 MeV < T < 4.0 MeV, where x is proton content, the density is $\rho$, and the temperature is T. The predictions of the two networks were combined to determine the nuclear pasta phase that is thermodynamically stable at a given x, $\rho$, and T, and a three-dimensional phase diagram that extrapolated slightly the regions of existing molecular dynamics data was computed. The jungle gym and anti-jungle gym structures are prevalent at high temperature and low density, while the anti-jungle gym and anti-gnocchi structures dominate at high temperature and high density. A diversity of structures exist at low temperatures and intermediate density and proton content. The trained models used in this work are open access and available at a public repository to promote comparison to pastas obtained with other models. Full article

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications. Full article

Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper, we experimentally validated a physical RC system that substitutes the effect of randomness that underpins the operation of the traditional RC algorithm for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the ‘next-generation’ improvement of the traditional RC algorithm. Full article

The development and deployment of the next generation of wind energy systems calls for simulation tools that model the entire wind farm while balancing accuracy and computational cost. A full-system wind farm simulation must consider the atmospheric inflow, the wakes and consequent response of the multiple turbines, and the implementation of the appropriate farm-collective control strategies that optimize the entire wind farm’s output. In this article, we present a novel vortex lattice model that enables the effective representation of the complex vortex wake dynamics of the turbines in a farm subject to transient inflow conditions. This work extends the capabilities of our multi-physics suite, CODEF, to include the capability to simulate the wakes and the high-fidelity aeroelastic response of multiple turbines in a wind farm. Herein, we compare the results of our GVLM technique with the LiDAR measurements obtained at Sandia National Laboratories’ SWiFT facility. The comparison shows remarkable similarities between the simulation and field measurements of the wake velocity. These similarities demonstrate our model’s capabilities in capturing the entire wake of a wind turbine at a significantly reduced computational cost as compared to other techniques. Full article

We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra $A_2^{\left(1\right)}$. The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair $L,M$. Full article

The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges. Full article

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes. Full article

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems. Full article

The symmetries of a Riemann surface $\mathsf{\Sigma }\setminus \left\{a_i\right\}$ with n punctures $a_i$ are encoded in its fundamental group ${\pi }_1\left(\mathsf{\Sigma }\right)$. Further structure may be described through representations (homomorphisms) of ${\pi }_1$ over a Lie group G as globalized by the character variety $\mathcal{C}=\mathrm{Hom}({\pi }_1,G)/G$. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere $\mathsf{\Sigma }=S_2^{\left(4\right)}$ and the ‘space-time-spin’ group $G=S{L}_2\left(\mathbb{C}\right)$. In such a situation, $\mathcal{C}$ possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface $V_{a,b,c,d}(x,y,z)$ with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or $P_{VI}$); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of $P_{VI}$. In this paper, we feature the parametric representation of some solutions of $P_{VI}$: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups $f_p$ encountered in TQC or DNA/RNA sequences are proposed. Full article

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable $\lambda$ governs the kinetic energy that is non-local in $\lambda$. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in $\lambda$, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential. Full article

Robot manipulators possess the capability to autonomously execute complex sequences of actions. Their proficiency in handling challenging and hazardous tasks has led to their widespread adoption across diverse sectors, including industry, business, household appliances, rehabilitation, and many more. However, certain tasks prove to be challenging for individual robots, primarily due to constraints in their structure and limited degrees of freedom. Cooperative robot manipulators (CRMs) emerge as a compelling solution when dealing with large, heavy, or flexible payloads. The utilization of CRMs offers a host of benefits, including enhanced manipulation performance achieved through the synergy of sensing and actuation capabilities or by tapping into increased redundancy. Numerous techniques have been devised for the control and dynamical modeling of CRMs. Nevertheless, the field continues to present technical challenges and scientific inquiries. To inspire and facilitate further research and development in this realm, this review aims to consolidate the current body of knowledge pertaining to CRMs kinematics, dynamics modeling, and various control methodologies used for payload manipulation via CRMs. Full article

In this paper, exact analytical expressions are derived for dimensionless steady-state solutions corresponding to the modified Stokes’ problems for incompressible generalized Burgers’ fluids, considering the influence of porous and magnetic effects. Actually, these are the first exact solutions for such motions of these fluids. They can easily be particularized to give similar solutions for Newtonian, second-grade, Maxwell, Oldroyd-B and Burgers’ fluids. It is also proven that MHD motion problems of such fluids between infinite parallel plates can be investigated when shear stress is applied at the boundary. To validate the obtained results, the velocity fields are presented in two distinct forms, and their equivalence is proven through graphical representations. The obtained outcomes are utilized to determine the time required to reach a steady state and to elucidate the impacts of porous and magnetic parameters on the fluid motion. This investigation reveals that the attainment of a steady state occurs later when a porous medium or magnetic field is present. Additionally, the fluid’s flow resistance is augmented in the presence of a magnetic field or through a porous medium. Thus, as was expected, the fluid moves slower through porous media or in the presence of a magnetic field. Full article