Minimum Action Research Articles

Toward the Chemical Structure of Diborane: Electronic Force Density Fields, Effective Electronegativity, and Internuclear Turning Surface Properties.

The chemical structure of diborane was elucidated through the superposition of the vector fields of the electron density gradient ∇ρ(r), the electrostatic force Fes(r), and the kinetic force Fk(r), together with the analysis of the cumulative charges of the atoms and pseudoatoms delimited in the aforementioned fields. It was proposed that the Fk-pseudoatomic charge could be employed as a metric for quantifying the ionic component of a related atomic charge. The electron permeability across an internuclear turning surface─specifically, the zero-flux surface in Fk(r)─was characterized by probing it through mapping the total static potential φem(r). The conceptualization of post hoc electronegativity was presented for consideration. Our analysis revealed that the ordinary B-H and bent B-μ-H bonds in diborane demonstrate the polar covalent character with minor contributions of the ionic component. The former bond exhibits a greater electron permeability through the internuclear turning surface, indicating a stronger tendency for electron sharing between the corresponding nucleus-dominated regions. The electron density accumulation along the bent B-μ-H bond path diverges from the minimum action trajectories of the forces Fes(r) and Fk(r). This phenomenon can be associated with the structural strain within the angled, three-center two-electron bonding B-μ-H-B. The internuclear B···B paths were identified in Fes(r) and Fk(r), in contrast to ∇ρ(r). This fact, in conjunction with a pronounced electron permeability through the mutual turning surface between the two boron nuclei, implies a certain degree of electron exchange between the boron-dominated pseudoatomic regions. Furthermore, the anomalous [B-]H···μ-H intermolecular polar interactions were described between the strongly negatively charged hydrogen atoms in the monoclinic crystalline β-phase of diborane. In fact, the ionic contributions to the charges of the hydrogen atoms are shown to be relatively small.

Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method.

Nonequilibrium phase transitions are notably difficult to analyze because their mechanisms depend on the system's dynamics in a complex way due to the lack of time-reversal symmetry. To complicate matters, the system's steady-state distribution is unknown in general. Here, the phase diagram of the active Model B is computed with a deep neural network implementation of the geometric minimum action method (gMAM). This approach unveils the unconventional reaction paths and nucleation mechanism in dimensions 1, 2, and 3, by which the system switches between the homogeneous and inhomogeneous phases in the binodal region. Our main findings are (i)the mean time to escape the phase-separated state is (exponentially) extensive in the system size L, but it increases nonmonotonically with L in dimension 1; (ii)the mean time to escape the homogeneous state is always finite, in line with the recent work of Cates and Nardini [Phys. Rev. Lett. 130, 098203 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.098203]; (iii)at fixed L, the active term increases the stability of the homogeneous phase, eventually destroying the phase separation in the binodal for large but finite systems. Our results are particularly relevant for active matter systems in which the number of constituents hardly goes beyond 10^{7} and where finite-size effects matter.

Convergence analysis for minimum action methods coupled with a finite difference method

Abstract The minimum action method (MAM) is an effective approach to numerically solving minima and minimizers of Freidlin–Wentzell (F-W) action functionals, which is used to study the most probable transition path and probability of the occurrence of transitions for stochastic differential equations (SDEs) with small noise. In this paper, we focus on MAMs based on a finite difference method with nonuniform mesh, and present the convergence analysis of minimums and minimizers of the discrete F-W action functional. The main result shows that the convergence orders of the minimum of the discrete F-W action functional in the cases of multiplicative noises and additive noises are $1/2$ and $1$, respectively. Our main result also reveals the convergence of the stochastic $\theta $-method for SDEs with small noise in terms of large deviations. Numerical experiments are reported to verify the theoretical results.

Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical.

Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method.

Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime’s dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group Mp(n), the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the metaplectic-group symmetry generators and the physical states (the mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov–Klauder type defined by the action of the metaplectic group that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 1/4 and 3/4, respectively, from which two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4- and 3/4-spin-weight states, plus their symmetric and antisymmetric combinations, have spin contents s=0,1/2,1,3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) spacetime for n→∞. (vii) There emerges a relation between the eigenvalue α of our coherent-state metric solution and the black-hole area (entropy) as Abh/4lp2=α, relating the phase space of the metric found, gab, and the black hole area, Abh, through the Planck length lp2 and the eigenvalue α of the coherent states. As a consequence of the lowest level of the quantum-discrete-spacetime spectrum—e.g., the ground state associated to n=0 and its characteristic length—there exists a minimum entropy related to the black-hole history.

Зарубежный опыт фискальных механизмов преференциальной экономики

The subject of the study is the fiscal instruments of the preferential economy, which provides for the establishment of a special preferential business taxation regime for research and development (hereinafter referred to as R&D) and innovation activities in the OECD countries, the EU and partner economies. The objectives of the work are to identify tools to stimulate the commercialization of R&D and highlight general trends in the development of these tools and tax policies of developed countries in the R&D sector. The availability of tax support tools for the commercialization of R&D in almost all the studied countries and their application, along with the provision of tax incentives for R&D expenses to stimulate innovation at different stages of the life cycle of intellectual property objects, is demonstrated. It has been established that the volume of such support is steadily growing. Tax regimes for income from R&D abroad comply with the minimum standard BTPS Action 5, aimed at more effectively countering harmful tax practices that may harm other jurisdictions. The characteristics of income-based tax benefits for R&D are highlighted. It is concluded that it is necessary to introduce the BEPS Action 5 minimum standard in Russia in order to stimulate the IT industry and significantly expand income tax incentives for the commercialization of breakthrough technologies and innovations in other industries.

A Hierarchical Lane-Changing Trajectory Planning Method Based on the Least Action Principle

This paper presents a hierarchical lane-changing trajectory planner based on the least action principle for autonomous driving. Our approach aims to achieve reliable real-time avoidance of static and moving obstacles in multi-vehicle interaction scenarios on structured urban roads. Unlike previous studies that rely on subjective weight allocation and single weighting methods, we propose a novel trajectory planning strategy that decomposes the process into two stages: candidate trajectory generation and optimal trajectory decision-making. The candidate trajectory generation employs a path-velocity decomposition method, using B-spline curves to generate a multi-objective optimal lane-changing candidate path. Collision checking eliminates paths at risk of collision with static obstacles. Dynamic programming (DP) and quadratic programming (QP) are then used to plan the velocity of safe paths, generating candidate lane-changing trajectories based on curvature checking. The optimal trajectory decision-making process follows the decision mechanism of excellent drivers. We introduce a comprehensive evaluation function, the average action, which considers safety, comfort, and efficiency based on the least action principle. Feasible trajectories are ranked based on their average action, and the trajectory with the minimum average action and no collision risk with moving obstacles is selected as the tracking target. The effectiveness of the proposed method is validated through two common lane-changing scenarios. The results demonstrate that our approach enables smooth, efficient, and safe lane-changing while effectively tracking the planned velocity and path. This method offers a solution to local trajectory planning problems in complex environments and holds promising prospects in the field of autonomous driving.

The most likely transition path for a class of distribution-dependent stochastic systems

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.

Computing non-equilibrium trajectories by a deep learning approach

Predicting the occurrence of rare and extreme events in complex systems is a fundamental problem in non-equilibrium physics. These events can have huge impacts on human societies. New approaches have emerged in recent years, which better estimate tail distributions. They often use large deviation concepts without the need to perform heavy direct ensemble simulations. In particular, a well-known approach is to derive a minimum action principle and find its minimizers.The analysis of rare reactive events in non-equilibrium systems without detailed balance is notoriously difficult both theoretically and computationally. They can often be described in the limit of small noise by the Freidlin-Wentzell action. Here, we propose a method which minimizes the geometric action instead using neural networks: it is called deep gMAM. It relies on a natural and simple machine-learning formulation of the classical gMAM approach when the Lagrangian is known. We provide a detailed description of the method as well as many examples: from bimodal switches in nonlinear stochastic (partial) differential equations, including a codimension-1 nucleation in an Allen-Cahn-Ginzburg-Landau 5-D stochastic partial differential equation, to quasi-potential estimates and extreme events in Burgers turbulence.

Auto Triggerring Weapon System for Border Security using Internet of Things

Border surveillance is the utmost essential responsibility in the realm of national defense and security. It is imperative to maintain constant vigilance over a nation's borders to uphold tranquility and ensure the safety of its populace. Safeguarding border areas rigorously from such activities is particularly critical in the present climate, where terrorist infiltrations and illicit movements of both animate and inanimate entities have become commonplace due to technological advancements. Offering uninterrupted surveillance is the minimum action required to prevent such incidents in border regions. At present, the manual monitoring of borders is carried out by the border security forces responsible for this task.Due to the vast distances between the borders and the harsh terrain and climate, it requires a lot of people and resources. Designing it is therefore analytically critical to create an automatic weapon system that could also complete even without monitoring task requirement for human involvement. Implementing this system eliminates the need to continuously deploy personnel in hazardous situations. Moreover, the system should possess the ability to make appropriate decisions and take necessary actions while also notifying human controllers when suspicious activities are detected. Central control rooms can be located away from the border region. Once an alert is sent, humans must determine the subsequent course of action. When implemented effectively, this approach helps conserve resources and reduces risks to human life. Full automation of border monitoring is not currently viable due to safety concerns, but such technologies can certainly assist and work in conjunction with armed forces to protect a nation's borders

Stochastic transitions: Paths over higher energy barriers can dominate in the early stages.

The time evolution of many physical, chemical, and biological systems can be modeled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of the reaction rate theory for determining the rates of transitions apply in the long-time limit. However, at short times, the system can, instead, choose to pass over higher energy barriers with a much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also apply a version of the geometric minimum action method algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. 128, 061103 (2008)] to determine the most likely path at both short and long times.

Analysis of transition path ensemble in the exactly solvable models via overdamped langevin equation

Transition of a system between two states is an important but difficult problem in natural science. In this article we study the transition problem in the framework of transition path ensemble. Using the overdamped Langevin method, we introduce the path integral formulation of the transition probability and obtain the equation for the minimum action path in the transition path space. For the effective sampling in the transition path ensemble, we derive a conditional overdamped Langevin equation. In two exactly solvable models, the free particle system and the harmonic system, we present the expression of the conditional probability density and the explicit solutions for the conditional Langevin equation and the minimum action path. The analytic results demonstrate the consistence of the conditional Langevin equation with the desired probability distribution in the transition. It is confirmed that the conditional Langevin equation is an effective tool to sample the transition path ensemble, and the stationary action principle actually leads to the most probable path.

Optimization of Impedance-Accelerated Inverse-Time Over-Current Protection Based on Improved Quantum Genetic Algorithm

This paper proposes an impedance-accelerated inverse-time over-current protection optimization scheme based on the improved quantum genetic algorithm. First, the speed of remote backup protection is improved by increasing the optimization level of backup protection. Second, to ensure the coordination of protection when the distributed generation is connected to the distribution network, a mathematical model for the optimization of inverse time protection parameters is established. The mathematical model takes the minimum total action time of the optimized main and backup protection as the objective function, and the selectivity and sensitivity requirements of the protection as the constraints. In addition, the genetic algorithm is improved from four aspects: coding method, population initialization, quantum revolving gate, and variational evolution. The theoretical analysis and simulation results show that the proposed scheme can effectively improve the selectivity and operation speed of the protection.

The propagation paths of fluid-driven fractures in layered and faulted rocks

AbstractFractures that form when fluid pressure ruptures the rock are referred to as fluid-driven fractures or hydrofractures. These include most dykes, inclined sheets and sills, but also many mineral veins and joints, as well as human-made hydraulic fractures. While considerable field and theoretical work has focused on the geometry and arrest of hydrofractures, how they select their propagation paths, particularly in layered and faulted rocks, has received less attention. Here I propose that of all the possible paths that a given hydrofracture may follow, it selects the path of least (minimum) action as determined by Hamilton’s principle. This means that the selected path is that along which the energy transformed (released) multiplied by the time taken for the propagation is a minimum. Hydrofractures advance their tips/fronts in steps, with a time lag between the fracture front and the fluid front. In the present framework, each step is then controlled by Hamilton’s principle. The results suggest that when the hosting rock body is regarded as homogeneous, isotropic and non-fractured, hydrofracture paths are everywhere perpendicular to the trajectories of the minimum compressive (maximum tensile) principal stress σ3 and follow the trajectories of the maximum principal compressive stress σ1. When applied to layered and faulted rock body, the results indicate that hydrofracture paths may follow existing faults for a while, depending primarily on (1) the dip of the fault (steep faults are the most likely to be used by vertically propagating hydrofractures), and (2) the tensile strength across the fault compared with the tensile strength of the host rock along a path following the direction of σ1. The results suggest that hydrofractures may use faults as parts of their paths primarily if the fault is steeply dipping and with close to zero tensile strength.

Effects of Different Degrees of Hydrophobic Treatment on Soil–Water Characteristic Curves and Infiltration Coefficients of Hygroscopic Soils

Soil treated with silicone hydrophobic material for a long time can effectively improve the saturated permeability of the ground, which has been confirmed. However, the long time will increase the cost in engineering construction. Secondly, the mechanism of alteration of soil–water properties by silicone hydrophobic materials is not understood. This lack of understanding is not conducive to the engineering application of silicone hydrophobic materials. Therefore, variable-head permeability and matrix suction tests under 15 different test conditions were conducted with different hydrophobic material dosage and action time as variables in this paper. The soil–water characteristic curve (SWCC) was plotted according to the test results, the unsaturated permeability coefficient was calculated, and curve fitting was performed. It can be seen from the test data that, with the increase in the dosage of hydrophobic materials and the action time, the permeability coefficient and the air-entry value showed a downward trend. Nevertheless, as the reaction proceeded, a mutation occurred at 4 h. When the minimum dosage and action time were used, the soil’s permeability coefficient and air-entry value decreased by 80.65% and 71.09%. The test results show that, even when the action time was 2 h, the hydrophobic material could maintain the permeability of the soil and reduce its air-entry value; thus, the hydrophobic material could effectively reduce the rise of capillary water in the soil and protect the roadbed.

Strategies and resources to optimise the management of Psoriatic Arthritis patients: The CREA Project

Background and aimPsoriatic arthritis (PsA) is a chronic immune-mediated inflammatory disease that affects the musculoskeletal system and skin, and manifests heterogeneously, with a variable course. In current clinical practice, variability and limitations in its follow-up have been observed. The aim of the CREA project was to agree on strategies to improve the initial assessment and follow-up of patients with PsA in Spain. Materials and methodsA survey was conducted among a representative sample of expert rheumatologists in Spain, containing 33 questions on current clinical practice, available resources, and current limitations in the follow-up of patients with PsA. The results were discussed in regional meetings and 105 strategies were proposed and finally evaluated by 85 experts in a Delphi consensus. ResultsThe most important limitations in the follow-up of PsA were lack of consultation time, lack of nursing staff, and delays in performing imaging tests. A total of 108 strategies were proposed related to the assessment of quality of life and disease-impact indices; comorbidities and extra-articular manifestations; laboratory tests; imaging tests; physical examination and metrology; and activity and function indices. Of the total, 53 were considered highly advisable, with no regional differences in consensus values. Discussion and ConclusionsThe proposals offered in the current study are applicable to the entire country, respond to the unmet needs detected in the initial survey, form a minimum action framework, and ensure optimal follow-up of patients with PsA.

A stochastic framework for the assessment of horizontally curved aluminium bridge decks on steel girders

A purpose-developed structural reliability assessment (SRA) framework for the evaluation of horizontally curved aluminium alloy bridge decks on steel I-girders of centre subtended angle, θ≤34.4 with precinct on the American association of state highway and transportation officials (AASHTO) load resistance factor design (LRFD) specification is presented. The finite element analysis (FEA) simulations were performed in the ABAQUS© CAE, whilst the probabilistic assessment model was developed using the first-order reliability method (FORM). Besides performing detailed design checks and a validation exercise, the developed SRA framework was used to examine the structural behaviour of the bridge assembly in the presence of stochastic design truck axle loads, structure’s self-weight, among other loads, whilst varying geometric properties. The most critical structural responses chosen at salient points obtained via FEA simulation is applied in deriving the limit state function (LSF), which is then substituted into the stochastic model within the purpose-developed iterative FORM algorithm to calculate the reliability index (RI), β of the structure. It is shown that the proprietary AlumadeckTM system conforms with the LRFD specification, which stipulates that the target value of RI is 3.5 for resistance factor (RF) of 1.0 (assuming 80% composite action compression flange). The result also reveals that the RI shows a strong dependence on the composite action between the deck and the girder for RF of 1.0 full composite action (considering the failure of the bottom flange), indicating the safety index is within acceptable limits. Furthermore, it is revealed that the minimum composite action for safety is 40%, corresponding to a safety index of 1.16. Hence, it can be inferred from the foregoing that the AlumadeckTM can withstand the stochastic axle load it is subjected to considering the HL-93 load design condition and satisfies all design criteria considered from a stochastic perspective based on the AASHTO LRFD guidelines, provided the minimum stiffner thickness tstiffner of 7mm is adopted (based on the FEA simulation results). A case study conducted herein established that the structural configuration selected (i.e. depth at 2.4m, flange thicknesses at 21mm, flange width at 50cm and web thickness at 16mm) demonstrates the structural safety and durability of the bridge system coupled using the AlumadeckTM.

Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions.

We present an information geometric characterization of quantum driving schemes specified by su(2;C) time-dependent Hamiltonians in terms of both complexity and efficiency concepts. Specifically, starting from pure output quantum states describing the evolution of a spin-1/2 particle in an external time-dependent magnetic field, we consider the probability paths emerging from the parametrized squared probability amplitudes of quantum origin. The information manifold of such paths is equipped with a Riemannian metrization specified by the Fisher information evaluated along the parametrized squared probability amplitudes. By employing a minimum action principle, the optimum path connecting initial and final states on the manifold in finite time is the geodesic path between the two states. In particular, the total entropy production that occurs during the transfer is minimized along these optimum paths. For each optimum path that emerges from the given quantum driving scheme, we evaluate the so-called information geometric complexity (IGC) and our newly proposed measure of entropic efficiency constructed in terms of the constant entropy production rates that specify the entropy minimizing paths being compared. From our analytical estimates of complexity and efficiency, we provide a relative ranking among the driving schemes being investigated. Moreover, we determine that the efficiency and the temporal rate of change of the IGC are monotonic decreasing and increasing functions, respectively, of the constant entropic speed along these optimum paths. Then, after discussing the connection between thermodynamic length and IGC in the physical scenarios being analyzed, we briefly examine the link between IGC and entropy production rate. Finally, we conclude by commenting on the fact that an higher entropic speed in quantum transfer processes seems to necessarily go along with a lower entropic efficiency together with a higher information geometric complexity.

Novel molecular insights into ATP synthesis in oxidative phosphorylation based on the principle of least action

In previous papers in Chemical Physics Letters, the author has analyzed the coupled nonequilibrium processes of ATP synthesis in oxidative phosphorylation (OXPHOS) with succinate as substrate. It was shown experimentally that the system evolves with time to a minimum unit action of 1.4×10-3 J s natom O–1 mg protein–1. Here the experimental value of the average unit action is suitably normalized. It is shown that the average unit action per elementary ion (proton or anion/countercation) translocation event through the FO portion of the FOF1-ATP synthase yields a value of 6.70×10-34 J s. This is equal to the value of the Planck’s constant, h to within1%. The results provide a novel molecular interpretation of energy transduction by ATP synthase in OXPHOS under optimal conditions, linking it to a fundamental physical constant.

An Efficient Jet Marcher for Computing the Quasipotential for 2D SDEs

We present a new algorithm, the efficient jet marching method (EJM), for computing the quasipotential and its gradient for two-dimensional SDEs. The quasipotential is a potential-like function for nongradient SDEs that gives asymptotic estimates for the invariant probability measure, expected escape times from basins of attractors, and maximum likelihood escape paths. The quasipotential is a solution to an optimal control problem with an anisotropic cost function which can be solved for numerically via Dijkstra-like label-setting methods. Previous Dijkstra-like quasipotential solvers have displayed in general 1st order accuracy in the mesh spacing. However, by utilizing higher order interpolations of the quasipotential as well as more accurate approximations of the minimum action paths, EJM achieves second-order accuracy for the quasipotential and nearly second-order for its gradient. Moreover, by using targeted search neighborhoods for the fastest characteristics following the ideas of Mirebeau, EJM also enjoys a reduction in computation time. This highly accurate solver enables us to compute the prefactor for the WKB approximation for the invariant probability measure and the Bouchet–Reygner sharp estimate for the expected escape time for the Maier–Stein SDE. Our codes are available on GitHub.