Many Degrees Of Freedom Research Articles

Low-dimensional projection of reactivity classes in chemical reaction dynamics using supervised dimensionality reduction.

Transition state theory (TST) provides a framework to estimate the rate of chemical reactions. Despite its great success with many reaction systems, the underlying assumptions such as local equilibrium and nonrecrossing do not necessarily hold in all cases. Although dynamical systems theory can provide the mathematical foundation of reaction tubes existing in phase space that enables us to predict the fate of reactions free from the assumptions of TST, numerical demonstrations for large systems have been yet one of the challenges. Here, we propose a dimensionality reduction algorithm to demonstrate structures in phase space (called reactive islands) that predict reactivity in systems with many degrees of freedom. The core of this method is the application of supervised principal component analysis, where a coordinate transformation is performed to preserve the dynamical information on reactivity (i.e., to which potential basin the system moves from a region of interest) as much as possible. The reactive island structures are expected to be reflected in the transformed, low-dimensional phase space. As an illustrative example, the algorithm is scrutinized using a modified Hénon-Heiles Hamiltonian system extended to many degrees of freedom, which has three channels leading to three different products from one stable potential basin. It is shown that our algorithm can predict the reactivity in the transformed, low-dimensional coordinate system better than a naïve coordinate system and that the reactivity distribution in the transformed low-dimensional space is considered to reflect the underlying reactive islands.

From Complex Dynamics to Foundational Physics (Part 1)

As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradigms of foundational physics. There are, however, growing suspicions that both paradigms fail to hold somewhere above the Standard Model (SM) scale and in the realm of primordial cosmology. Evidence collected on multiple fronts indicates that emergence and complexity are universal features of far-from-equilibrium systems with many degrees of freedom. In line with these findings, Part 1 of the report explores the complex dynamics of evolving dimensional fluctuations beyond the SM scale. Part 2 outlines the role of complex dynamics in the nonintegrable sector of particle physics, Dark Matter condensation and the gravitational regime of the early Universe.

Influence of robot-guide strategies on the geometry of directed energy deposition components

Directed energy deposition (DED) for additive manufacturing applications is commonly realized by the usage of industrial robots. The DED processing end effectors are usually mounted on industrial robot systems and can, therefore, be moved and oriented in up to many degrees of freedom. However, the design of the powder nozzle and the programming of the robot can limit the movement options. For this reason, translational movements, as with conventional 3D printers, are still common today. The end effector is usually guided horizontal over the component surface although welding in position (PA) is preferred in general. It may be necessary to tilt the end effector in order to gain advantages during processing due to the constrained position. This is particularly advantageous for overhang structures and is often realized with the help of a turn-tilt positioning table in combination with an industrial robot. However, this approach is, in some cases, not possible due to geometrical constrains. To extend applications in this direction, advanced methods for slicing the components and programming the robot movements are necessary. The main aspect of this work is the development, testing, and evaluation of a multidimensional DED manufacturing approach. This is tested on a thin-walled component with defined overhang areas and compared with conventional approaches. Different strategies are assessed in terms of the geometrical match of the target geometry. Influences of strategies on the results are evaluated. It can be shown that multidimensional path planning approaches lead to a better match of the target geometry.

From Geometry of Hamiltonian Dynamics to Topology of Phase Transitions: A Review.

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point. Then, it turns out that these peculiar geometrical changes are the effect of deeper topological changes of the configuration space hypersurfaces ∑v=VN-1(v) as well as of the manifolds {Mv=VN-1((-∞,v])}v∈R bounded by the ∑v. In other words, denoting by vc the critical value of the average potential energy density at which the phase transition takes place, the members of the family {∑v}v<vc are not diffeomorphic to those of the family {∑v}v>vc; additionally, the members of the family {Mv}v>vc are not diffeomorphic to those of {Mv}v>vc. The topological theory of the deep origin of phase transitions allows a unifying framework to tackle phase transitions that may or may not be due to a symmetry-breaking phenomenon (that is, with or without an order parameter) and to finite/small N systems.

Decoherence-induced formation of sub-poissonian entangled and steerable states of collective fields

The decoherence process has a tendency to yield the evolution of a pure state into a mixed one and to cause the quantum-to-classical transition by the coupling of a system of interest to the reservoir with infinitely many degrees of freedom. This is the major obstacle to the implementation of quantum computation and hence the realization of quantum computers. We propose a scheme to create unconditionally sub-Poissonian entangled and steerable states of the collective cavity field modes by use of the dissipation process. Based on the suitable choice of combination modes, the scheme uses the inherent, efficient and controllable two-mode squeezed vacuum reservoir coupled to the combination modes of concern rather than the original cavity modes in the two-level quantum beat laser. The decoherence is shown to pull the collective modes into the sub-Poissonian entangled and steerable states in the stationary regime, while the job of the dissipation of the individual cavity fields is to give rise to the degradation of the bipartite entanglement of the two individual modes and to inhibit the occurrence of the quantum steering from one cavity mode to the other. In particular for the case that the external driving field is close to the exact resonance with the atom, the collective fields are eventually prepared asymptotically in the stationary Einstein–Podolsky–Rosen state, while the two individual cavity modes are pulled into the vacuum states and reach steady state. The disappearance of the decoherence disables the nonclassical states of the collective modes, while the ignorance of the dissipation process of the cavity field modes guarantees the generation of the entanglement between the pair of individual modes. The decoherence-induced formation of a nonclassical source is ascribed to the four-wave mixing process together with the intrinsic amplitude and phase locking.

Scalable networks of wireless bioelectronics using magnetoelectrics.

Networks of miniature bioelectronic implants would enable precise measurement and manipulation of the complex and distributed physiological systems in the body. For example, sensing and stimulation nodes throughout the heart, brain, or peripheral nervous system would more accurately track and treat disease or support prosthetic technologies with many degrees of freedom. A main challenge to creating this type of in-body bioelectronic network is the fact that wireless power and data transfer are often inefficient when communicating through biological tissues. This challenge is typically compounded as one increases the number of implants within the network. Here, we show that magnetoelectric wireless data and power transfer enable a network of millimeter-sized bioelectronic implants where the power transfer efficiency of the system improves as the number of implanted devices increases. Using this property, we demonstrate networks of wireless battery-free bioelectronics ranging from 1 to 6 implants where the wireless power transfer efficiency for the system increases from 0.2% to 1.3%, with each node in the network receiving 2.2 mW at a distance of 1 cm. We use this system for efficient and robust wireless data and power transfer to demonstrate proof-of-concept networks of miniature spinal cord stimulators and cardiac pacing devices in large animals. The scalability of this network architecture enabled by magnetoelectric wireless power transfer provides a platform for building wireless closed-loop networks of bioelectronic implants for next-generation electronic medicine.

Measuring Irreversibility from Learned Representations of Biological Patterns

Thermodynamic irreversibility is a fundamental characteristic of living matter, crucial for maintaining the complex spatiotemporal structures and functions that define biological systems. However, accurately quantifying biologically relevant irreversibility remains challenging due to noise and nonlinear interactions among many degrees of freedom. Here, we employ deep learning techniques to identify tractable, low-dimensional representations of phase-field patterns in a canonical protein signaling process—the Rho-GTPase system—as well as in complex Ginzburg-Landau dynamics. We demonstrate that factorizing variational autoencoder neural networks can robustly extract informative pattern features despite noise. These neural-network-derived representations reveal signatures of mesoscopic broken detailed balance and time-reversal asymmetry in both Rho-GTPase and complex Ginzburg-Landau wave dynamics. By applying the compression-based Ziv-Merhav estimator to these representations, we successfully recover irreversibility trends across complex Ginzburg-Landau patterns, which vary widely in spatiotemporal frequency and noise level. Our irreversibility estimates also recapitulate cell-activity trends in Rho-GTPase patterns subjected to metabolic inhibition. Furthermore, our framework distinguishes between stable and chaotic dynamical phases in these nonlinear systems. By leveraging advances in deep learning, our approach provides robust, model-free measurements of nonequilibrium and nonlinear behavior in complex living processes. Published by the American Physical Society 2024

Propose Theoretical Foundations for Analyzing the Dynamic Control and Optimizing the Structure of Multifunctional Carbon Fiber-Reinforced Material Plate Integrated Piezoelectric

In the fields of aviation, energy, construction, biomedicine, chemical technology, and some other fields, the use of functionally graded materials (FGMs) plates, multifunctional carbon nanofibers reinforced material plates, piezoelectric plates, and several others are increasingly popular. The behavior of material plates can be analyzed through partial differential equations (PDEs). However, the PDEs are for complex problems such as solid-liquid interactions, thermoelectric mechanical environments, functional material plates in multi-physics environments, and others that are very difficult or impossible to find a solution. In many numerical methods have been researched and developed, the finite element method (FEM) is a widely used and effective method to find approximate solutions of the PDEs. But the FEM has certain limitations in element techniques, discretizing the weak form for the plate structure problems with many degrees of freedom significantly, and affects the accuracy and efficiency of calculation. Proposing improvements to traditional FEM combines dynamic control analysis in the presence of piezoelectric crystals and optimization method algorithms, meeting the increasing requirements in analyzing the behavior of carbon nanofiber material plates used in many fields. On this basis, the article presents some theoretical foundations to solve the problem of dynamic control and optimizing the structure of multifunctional carbon nanofiber-reinforced material plates with integrated piezoelectric crystal.

A Simplified 4-DOF Dynamic Model of a Series-Parallel Hybrid Electric Vehicle

To research the dynamic response of a new type of dedicated transmission for a hybrid electric vehicle, a detailed dynamics model should be built. However, a model with too many degrees of freedom has a negative effect on controller design, which means the detailed model should be simplified. In this paper, two dynamic models are established. One is an original and detailed powertrain dynamics model (ODPDM), which can capture the transient response, and it is validated that the ODPDM can be used to accurately describe the real vehicle in some specific operating conditions. The other is a simplified torsional vibration dynamics model to study the torsional vibration characteristics of the hybrid electric vehicle. Compared with the full-order model, which is based on the ODPDM, the simplified model has a very similar vibration in low frequency. This study provides a basis for further vibration control of the hybrid powertrain during the process of a driving-mode switch.

Giant ultrafast dichroism and birefringence with active nonlocal metasurfaces

Switching of light polarization on the sub-picosecond timescale is a crucial functionality for applications in a variety of contexts, including telecommunications, biology and chemistry. The ability to control polarization at ultrafast speed would pave the way for the development of unprecedented free-space optical links and of novel techniques for probing dynamical processes in complex systems, as chiral molecules. Such high switching speeds can only be reached with an all-optical paradigm, i.e., engineering active platforms capable of controlling light polarization via ultrashort laser pulses. Here we demonstrate giant modulation of dichroism and birefringence in an all-dielectric metasurface, achieved at low fluences of the optical control beam. This performance, which leverages the many degrees of freedom offered by all-dielectric active metasurfaces, is obtained by combining a high-quality factor nonlocal resonance with the giant third-order optical nonlinearity dictated by photogenerated hot carriers at the semiconductor band edge.

Quantum geometrodynamics revived I. Classical constraint algebra

Abstract In this series of papers, we present a set of methods to revive quantum geometrodynamics which encountered numerous mathematical and conceptual challenges in its original form promoted by Wheeler and De Witt. In this paper, we introduce the regularization scheme on which we base the subsequent quantization and continuum limit of the theory. Specifically, we employ the set of piecewise constant fields as the phase space of classical geometrodynamics, resulting in a theory with finitely many degrees of freedom of the spatial metric field. As this representation effectively corresponds to a lattice theory, we can utilize well–known techniques to depict the constraints and their algebra on the lattice. We are able to compute the lattice corrections to the constraint algebra. This model can now be quantized using the usual methods of finite–dimensional quantum mechanics, as we demonstrate in the following paper. The application of the continuum limit is the subject of a future publication.&amp;#xD;

Performance Based Seismic Design of Reinforced Concrete Building

A novel approach is devised for the displacement-based design of diverse buildings, enabling them to withstand the seismic pressures encountered. The suggested approach necessitates figuring out the structure's yield and final displacements. These characteristics are derived from rough empirical relationships for the preliminary design. The inelastic demand spectrum corresponding to the estimated yield strength and the ductility capacity is then used to calculate the necessary strength of the structure. The structural strength required is then determined from the inelastic demand spectrum that coincides with the yield strength estimate and the ductility capacity. By converting it into an analogous single degree of freedom system, the method can be used to systems with many degrees of freedom. A modal analysis is performed on a model of the structure based on its preliminary design in order to determine the final design. For forces distributed according to the first mode, a pushover analysis of the structure now provides improved estimations of the yield and final displacements. The needed strength is then more precisely calculated using these improved estimates. To achieve convergence between the estimated and calculated values of the design displacements, it could be necessary to perform iterations. Lastly, to take into consideration the impact of higher modes on high-rise moment-resistant frames and shear wall systems.

Selective dynamic band gap tuning in metamaterials using graded photoresponsive resonator arrays.

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Research on Arrangement of Measuring Points for Modal Identification of Spatial Grid Structures

In structural health monitoring, because the number of sensors used is far lower than the number of degrees of freedom of the structure being monitored, the optimization problem of the location and number of sensors in the structures is becoming more and more prominent. However, spatial grid structures are complex and diverse, and their dynamic characteristics are complex. It is difficult to accurately measure their vibration information. Therefore, an appropriate optimization method must be used to determine the optimal positioning of sensor placement. Aiming at the problem that spatial grid structures have many degrees of freedom and the fact that it is difficult to obtain complete vibration information, this paper analyzed the typical EI method, MKE method, and EI-MKE method in the arrangement of the measuring points, and it was verified that the EI method was more suitable for the vibration detection of spatial grid structures through the example of a plane truss and spatial grid structures. Measuring points under the assumption of structural damage were explored, and it was proposed that there might have been a stable number of measuring points that could cover the possible vibration mode changes in the structures. At the same time, combined with the three-level improved Guyan recursive technique, in order to obtain better complete modal parameters, the influence of the number of measuring points on the complete vibration mode information was studied. It was concluded that MACd was better than MACn as the quantitative target.

Similarities and Differences Between Natural and Simulated Slow Earthquakes

AbstractWe investigate similarities and differences between natural and simulated slow earthquakes using nonlinear dynamical system tools. We use spatio‐temporal slip potency rate data derived from Global Navigation Satellite System (GNSS) position time series in the Cascadia subduction zone and numerical simulations intended to reproduce their pulse‐like behavior and scaling laws. We provide metrics to evaluate the accuracy of simulations in mimicking slow earthquake dynamics. We investigate the influence of spatio‐temporal coarsening as well as observational noise. Despite the use of many degrees of freedom, numerical simulations display a surprisingly low average dimension, akin to natural slow earthquakes. Instantaneous dynamical indices can reach large values (&gt;10) instead, and differences persist between numerical simulations and natural observations. We propose to use the suggested metrics as an additional tool to narrow the divergence between slow earthquake observations and dynamical simulations.

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

Why Does Inflation Look Single Field to Us?

Most high-energy constructions that realize a phase of cosmic inflation contain many degrees of freedom. Yet, cosmological observations are all consistent with single-field embeddings. We show how volume selection effects explain this apparent paradox. Because of quantum diffusion, different regions of space inflate by different amounts. In regions that inflate most, and eventually dominate the volume of the Universe, a generic mechanism is unveiled that diverts the inflationary dynamics towards single-field attractors. The formalism of constrained stochastic inflation is developed to this end.

The Energy Security of the Republic of Moldova Concerning the Policies Adopted by the European Union – A Multi-Facetted and Complex Topic

Abstract The new geopolitical dynamic has brought a series of energy security transformations in the Central and Eastern European region. The Republic of Moldova, located at the confluence of the pro-European, western, and Eastern trends, has started a series of efforts, visible on the stage of international relations, to acquire as many degrees of freedom as possible in the energy sector, limiting the effects of Russian pressures and encouraging the adoption of democratic policies. The state is a candidate for accession to the European Union, in which sense the present work aims, on the one hand, to simulate the application of the conditions of European forums in the energy field on the Moldovan market, as well as to x-ray the energy policy at the local level. The applied methodology, mostly qualitative, was based on the analysis of some documents with a European normative character, simulating the application of their provisions in the case of the Republic of Moldova. Punctually, through quantitative methods, with the use of secondary data, certain limits were determined regarding the amounts of energy resources that the Republic of Moldova should fall within to comply with European legislation. The conclusions of the paper demonstrated the pro-Western conduct of the Republic of Moldova in the energy segment in the period 2022-2023 and the state's ability to synchronize its legislation with the European one.

Collocated and non-collocated active spatial absorbers for spatial flexible structures

This article deals with the analysis and design of an active spatial mechanical vibration absorber and verification of its performance in collocated and non-collocated vibration absorption of a spatial flexible primary structure. The considered active absorber with six degrees of freedom has six identical natural frequencies. It is a so-called unifrequency absorber. The unifrequency property is achieved by delayed feedback, according to the concept of a delayed resonator. A proper tuning of the delayed feedback compensates the damping and variations in stiffness of mechanical parts, resulting in the behavior of an ideal absorber. The absorber was attached to a three-dimensional flexible frame with many degrees of freedom transformed to a reduced order model in modal coordinates. The use of a unifrequency absorber for two types of tasks is shown in this article. In the collocated case, the absorber is placed at the location where we want to suppress vibration. Such a placement is often not possible for various reasons. Therefore, the non-collocated absorber is also investigated which is remote from the point of desired vibration suppression. The absorber has considerable potential for use in improving the dynamic behavior of robots, complex rotor systems, and other mechanical systems suffering from unwanted fully spatial vibrations.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.