Minimum Action Research Articles

On the way to a new science

In this autobiographical essay, Efim Liberman (1925–2011) looks back at his life summarizing his lifetime experience and drawing conclusions about the role of science and its future development and unification, with the ultimate goal to unite our understanding of nature and harmonize life. A new field of science suggested by Liberman and named Chaimatics combines biology, physics and mathematics. The main idea of Chaimatics is simple: not only measurement, but also calculation is a real physical operation and cannot be done for free—energy and time must be spent on calculation. Quantum physics arose on the basis of discovering the existence of the minimum action—Planck's constant. And this factor imposes physical limits on computation and sets the boundaries to the physical world and its observation. Explorations of the structure of the cell and the progress in the development of electronic computers have led us to the understanding of life and its place in the Universe …

“Experimental and FEA Investigation of V Shape Spring with Materials”

The Automobile Industry has shown keen interest for replacement of steel leaf spring with that of progressive rate spring unit, since that has good part loading and minor to maximum shock absorption properties. In this paper we have outline on the new mechanism for progressive rate spring. The main leaf spring and V- shape strip spring model is created by modeling software like Pro-E. The dimensions of an existing conventional steel leaf spring of a light commercial vehicle are taken for modeling. And the structural analysis of both springs is carried via finite element analysis using ANSYS-12 software. Result shows that, the V-shape strip spring has Total deflection 16.93 % & Strain energy 38.20 % more than steel leaf Spring for partly loading. It also shows equivalent von- misses stresses for both spring. It is observed that the V- shape strip spring is great under part loading i.e. minimum loading action and main leaf spring is superior for maximum loading condition so that the whole unit of this progressive rate spring is best suitable for carrying export quality fruit from farm to wear house or customer market and mini ambulance vehicle. All material used in this unit is easily available, so it commercially adopted in automotive mini trailer manufacturer. Also it has less complexity and economically advantageous for middle class farmer.

Unraveling the stochastic transition mechanism between oscillation states by the landscape and the minimum action path theory.

Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack of study on the stochastic transition between different oscillation states. Here, we aim to explore the stochastic transition mechanism for the switching between oscillations. By employing a landscape and flux theory for a simplified two-dimensional model, we quantify the stochastic dynamics and the global stability of the double oscillation system, and find that the system will escape the starting limit cycle at the position where the flux is large, and cross the barrier between oscillations at the position where the barrier is lower. We also calculate the transition path between limit cycle states based on the minimum action path (MAP) theory. So, the barrier height based on landscape topography and probability flux govern the stochastic transition process between limit cycles, which is further supported by the analysis of mean first passage time (MFPT). We provide a way to calculate the critical points where the switching behavior most likely occurs along a cycle. We validate these conclusions in a realistic biological system; the NF-κB gene regulatory system. The results for the potential landscape, flux and transition path further our understanding of the underlying mechanism of stochastic transitions between different oscillation states.

Spatial Attributes of Particles and Quantum Fields

According to the characteristics of manifold and the double helix structure of spacetime, four coordinate systems are established as reference frames. The grand parity principle and the general exclusion principle are proposed. The minimum action distance of electromagnetic force is obtained and the structure of intrinsic space of particle is studied. The stability of particle reaction, the reason for only three generations of leptons and the spatial significance of the electroweak equivalence are discussed by using the two principles and the four coordinate systems. The behavior of boson including condensation is described in terms of spatial structure. Finally, we suggest that symmetry between the field excited by charge and the field excited by mass should be further investigated.

ROLE OF PASSIVE SAFETY SYSTEMS IN PREVENTION AND MITIGATION OF SEVERE ACCIDENTS AT NUCLEAR POWER PLANTS

Fukushima Daiichi accidents led to the worldwide update of the NPP safety requirements. Particular attention was paid to severe accidents both during the design of new NPP units and during the safety reassessment of existing ones. Performed safety reassessment of operating units was focused on development and implementation of technical means and strategies directed to prevention and/or mitigation of severe accidents. Technical solutions that are used in modern designs of reactor facilities involve several options for providing of heat removal from the core and containment. Such options include heat removal systems from the reactor core and from the containment of reactor facility. Most of such systems are based on passive principals of operation and do not require or require a minimum action of operating personnel. At the same time, reactor facilities that are operated in Ukraine are based on old VVER designs, which do not include passive safety systems for long-term heat removal (especially for the case of total station blackout, which was in the focus during safety reassessments, so-called “stress tests”). Thus, the necessity of such systems at Ukrainian NPPs with VVER-1000 and VVER-440 was discussed together with analysis of existing types of passive systems and their prevalence. Based on the results of performed analysis the feasibility of implementation at Ukrainian NPPs of a passive heat removal system from the core for VVER-1000 and from the confinement for the VVER-440 was identified. The possibility of implementation of such systems at Ukrainian NPPs requires a separate analysis. In addition, a general information on current state of passive systems reliability assessment was described. It should be noted that despite the reliability of passive safety systems is one of the important issues it is still poorly studied and require additional analyses.

Most probable transitions from metastable to oscillatory regimes in a carbon cycle system

Global climate changes are related to the ocean’s store of carbon. We study a carbonate system of the upper ocean, which has metastable and oscillatory regimes, under small random fluctuations. We calculate the most probable transition path via a geometric minimum action method in the context of the large deviation theory. By examining the most probable transition paths from metastable to oscillatory regimes for various external carbon input rates, we find two different transition patterns, which gives us an early warning sign for the dramatic change in the carbonate state of the ocean.

Conservation through knowledge: the case study of Parma Botanic Garden

In the restoration field it is well known that the preservation of cultural heritage stands on a deep comprehension of the architectural object, material expression of a complex system made of cultural, technological, historical, social and economic issues. The knowledge of such meaningful structures requires the identification of both typological features and peculiar characteristics, within an interactive dialogue between contributions from different disciplines. Thus, the study of existing buildings is a complex process that needs to be planned: that means conceived, organized and realized with a critical method. The paper aims to show an example of this approach by presenting the knowledge path followed for the analysis of the Botanic Garden in Parma, Italy. This green area is located in the south of the city and hosts several buildings including the school of botany and the elegant greenhouse, built at the end of the 18th century. Recently, the restoration of the architectural complex has been proposed, aiming at its valorisation. The design process was supported by the studies and the analysis of the existing buildings carried out by the research group in Restoration of the University of Parma. In the specific, the constructive phases have been investigated through historical archive researches whereas the current structural systems have been studied through the geometric survey. Moreover, in-situ inspections allowed to define materials, deepening the knowledge of structural elements and their state of conservation. Finally, the survey of the crack pattern and decay allows to highlight vulnerabilities and mechanisms of collapse. In this way, it has been possible to understand the architectural structure thanks to the comparison between all data collected. On the other hand, in order to respect the historical construction, these analyses are required to reach a satisfying level of detail with the minimum action on the material construction, preferring non-destructive investigations. This approach entails assumptions and uncertainties that could be managed thanks to a critical interpretation of the results. Thus, the case study of Parma Botanic Garden shows the importance of planning the knowledge path with awareness in order to progressively deepen the comprehension with an interactive dialogue between the architectural object and the restoration issue.

Antifungal properties and mechanisms of three volatile aldehydes (octanal, nonanal and decanal) on Aspergillus flavus

The harm of Aspergillus flavus ( A. flavus ) and aflatoxin is a severe food safety problem worldwide, which causes huge economic losses every year. Therefore, it is urgent to control the growth of A. flavus and the biosynthesis of aflatoxin. Plant-derived natural compounds are superior to synthetic fungicide in inhibiting the growth of A. flavus benefiting from their high safety to the environment, humans and stock, and low cost. This study aimed to evaluate the antifungal effects and potential antifungal mechanisms of three plant-derived compounds (octanal, nonanal and decanal) against A. flavus . We determined the minimum inhibitory concentrations (MICs) and action mechanism of the three volatile aldehydes on A. flavus and also performed calcofluor white (CW) staining for visualizing the distribution of septa. Cell respiration metabolism and the pathogenicity on maize kernels were also carried out to evaluate the efficacy of the three volatile aldehydes on the growth of A. flavus . The results showed that the three volatile aldehydes could inhibit the germination of spores and mycelial growth of A. flavus , the MICs on spores and mycelia were: octanal (1.0 and 0.5 μL/mL), nonanal (0.5 and 2.0 μL/mL), and decanal (1 and 5 μL/mL). The three volatile aldehydes could strongly damage the integrity of both the cell wall and the cell membrane of A. flavus . Meanwhile, they could decrease the content of total lipid and inhibit respiration metabolism of A. flavus cell. Results of in vitro antifungal test showed that all the three volatile aldehydes could effectively prevent the growth of A. flavus on maize kernels. The study revealed that octanal, nonanal and decanal could effectively inhibit the growth of A. flavus both in culture medium and on maize kernels to different extent. The results confirmed that the plant-derived compounds could be developed into promising antifungal agents applied in the preservation of grains. This study provides a theoretical basis for the research and application of potential antifungal agents.

Feedforward of Measurable Disturbances to Improve Multi-Input Feedback Control

The availability of multiple inputs (plants) can improve output performance by conveniently allocating the control bandwidth among them. Beyond that, the intervention of only the useful plants at each frequency implies the minimum control action at each input. Secondly, in single input control, the addition of feedforward loops from measurable external inputs has been demonstrated to reduce the amount of feedback and, subsequently, palliate its sideband effects of noise amplification. Thus, one part of the action calculated by feedback is now provided by feedforward. This paper takes advantage of both facts for the problem of robust rejection of measurable disturbances by employing a set of control inputs; a previous work did the same for the case of robust reference tracking. Then, a control architecture is provided that includes feedforward elements from the measurable disturbance to each control input and feedback control elements that link the output error to each control input. A methodology is developed for the robust design of the named control elements that distribute the control bandwidth among the cheapest inputs and simultaneously assures the prescribed output performance to correct the disturbed output for a set of possible plant cases (model uncertainty). The minimum necessary feedback gains are used to fight plant uncertainties at the control bandwidth, while feedforward gains achieve the nominal output response. Quantitative feedback theory (QFT) principles are employed. An example illustrates the method and its benefits versus a control architecture with only feedback control elements, which have much more gain beyond the control bandwidth than when feedforward is employed.

A new simplified ordered upwind method for calculating quasi-potential

We present a new method for calculation of quasi-potential, which is a key concept in the large deviation theory. This method adopts the “ordered” idea in the ordered upwind algorithm and different from the finite difference upwind scheme, the first-order line integral is used as its update rule. With sufficient accuracy, the new simplified method can greatly speed up the computational time. Once the quasi-potential has been computed, the minimum action path (MAP) can also be obtained. Since the MAP is of concernin most stochastic situations, the effectiveness of this new method is checked by analyzing the accuracy of the MAP. Two cases of isotropic diffusion and anisotropic diffusion are considered. It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time. Meanwhile anisotropy will affect the accuracy of the computed MAP.

Energy and Personality: A Bridge between Physics and Psychology

The objective of this paper is to present a mathematical formalism that states a bridge between physics and psychology, concretely between analytical dynamics and personality theory, in order to open new insights in this theory. In this formalism, energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modeled by a stimulus–response model: an integro-differential equation. The bridge between physics and psychology appears when the stimulus–response model can be formulated as a linear second order differential equation and, subsequently, reformulated as a Newtonian equation. This bridge is strengthened when the Newtonian equation is derived from a minimum action principle, obtaining the current Lagrangian and Hamiltonian functions. However, the Hamiltonian function is non-conserved energy. Then, some changes lead to a conserved Hamiltonian function: Ermakov–Lewis energy. This energy is presented, as well as the GFP dynamical response that can be derived from it. An application case is also presented: an experimental design in which 28 individuals consumed 26.51 g of alcohol. This experiment provides an ordinal scale for the Ermakov–Lewis energy that predicts the effect of a single dose of alcohol.

Information geometric aspects of probability paths with minimum entropy production for quantum state evolution

We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen [Formula: see text] time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The [Formula: see text] Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-[Formula: see text] test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-[Formula: see text] test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer.

A Minimum Action Method for Dynamical Systems with Constant Time Delays

In this work, we construct a minimum action method for dynamical systems with constant time delays. The minimum action method (MAM) plays an important role in seeking the most probable transition pathway induced by small noise. There exist two formulations of the minimum action method: one is the geometric formulation based on the Maupertuis principle, and the other one is the temporal formulation. The geometric formulation relies on the conservation of Hamiltonian corresponding to the Freidlin--Wentzell action functional. For systems with time delays, the Hamiltonian does not conserve due to the explicit dependence on the time delay, which implies that the geometric MAM is not applicable. We work with the temporal formulation of MAM for problems with time delays. By defining an auxiliary path, we remove the optimization with respect to time through the optimal linear time scaling. The pointwise correspondence between the auxiliary path and the delayed transition path is dealt with by a penalty term included into the action functional. The action functional is then discretized by the finite element method, and strategies for $h$-adaptive mesh refinement have been developed. Numerical examples have been presented to demonstrate the effectiveness of our algorithm.

Tunneling splittings of vibrationally excited states using general instanton paths.

A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [J. Chem. Phys. 122, 124311 (2005)] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improves the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.

Physical Laws and Human Behavior: A Three-Tier Framework

Social sciences start by looking at the social-psychological attributes of humans to model and explain their observed behavior. However, we suggest starting the study of observed human behavior with the universal laws of physics, e.g., the principle of minimum action. In our proposed three-tier framework, behavior is a manifestation of action driven by physical, biological, and social-psychological principles at the core, intermediate, and top tier, respectively. More broadly, this reordering is an initial step towards building a platform for reorganizing the research methods used for theorizing and modeling behavior. This perspective outlines and illustrates how a physical law can account for observed human behavior and sketches the elements of a broader agenda.

The Spinor-Tensor Gravity of the Classical Dirac Field

In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, has been generalized to the curved space-time in the covariant form. Thence, the metric of space-time has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the “cosmological” gravity tensor (CGT), a generalization of the classical cosmological constant (CC), as a part of the energy-impulse tensor density (EITD). Even if the classical cosmological constant is set to zero, the CGT is non-zero, allowing a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical macroscopic limit, the general relativity equation is recovered. In the perturbative approach, the CGT leads to a second-order correction to Newtonian gravity that takes contribution from the space where the mass is localized (and the space-time is curvilinear), while it tends to zero as the space-time approaches the flat vacuum, leading, as a means, to an overall cosmological constant that may possibly be compatible with the astronomical observations. The Dirac field gravity shows analogies with the modified Brans–Dicke gravity, where each spinor term brings an effective gravity constant G divided by its field squared. The work shows that in order to obtain the classical minimum action principle and the general relativity limit of the macroscopic classical scale, quantum decoherence is necessary.

Observable and Unobservable Mechanical Motion.

A thermodynamic approach to mechanical motion is presented, and it is shown that dissipation of energy is the key process through which mechanical motion becomes observable. By studying charged particles moving in conservative central force fields, it is shown that the process of radiation emission can be treated as a frictional process that withdraws mechanical energy from the moving particles and that dissipates the radiation energy in the environment. When the dissipation occurs inside natural (eye) or technical photon detectors, detection events are produced which form observational images of the underlying mechanical motion. As the individual events, in which radiation is emitted and detected, represent pieces of physical action that add onto the physical action associated with the mechanical motion itself, observation appears as a physical overhead that is burdened onto the mechanical motion. We show that such overheads are minimized by particles following Hamilton’s equations of motion. In this way, trajectories with minimum curvature are selected and dissipative processes connected with their observation are minimized. The minimum action principles which lie at the heart of Hamilton’s equations of motion thereby appear as principles of minimum energy dissipation and/or minimum information gain. Whereas these principles dominate the motion of single macroscopic particles, these principles become challenged in microscopic and intensely interacting multi-particle systems such as molecules moving inside macroscopic volumes of gas.

Quantifying epigenetic stability with minimum action paths.

Chromatin can adopt multiple stable, heritable states with distinct histone modifications and varying levels of gene expression. Insight on the stability and maintenance of such epigenetic states can be gained by mathematical modeling of stochastic reaction networks for histone modifications. Analytical results for the kinetic networks are particularly valuable. Compared to computationally demanding numerical simulations, they often are more convenient at evaluating the robustness of conclusions with respect to model parameters. In this communication, we developed a second-quantization-based approach that can be used to analyze discrete stochastic models with a fixed, finite number of particles using a representation of the SU(2) algebra. We applied the approach to a kinetic model of chromatin states that captures the feedback between nucleosomes and the enzymes conferring histone modifications. Using a path-integral expression for the transition probability, we computed the epigenetic landscape that helps to identify the emergence of bistability and the most probable path connecting the two steady states. We anticipate the generalizability of the approach will make it useful for studying more complicated models that couple epigenetic modifications with transcription factors and chromatin structure.

Stochastic dynamics of an active particle escaping from a potential well.

Active matter systems are driven out of equilibrium by the energy directly supplied at the level of constituent active particles that are self-propelled. We consider a model for an active particle in a potential well, characterized by an active velocity with a constant magnitude but a random orientation subject to white noises. We are interested in the escape of the active particle from the potential well in multiple-dimensional space. We investigate two distinct optimal paths, namely, the shortest arrival-time path and the most probable path, by using the analytical and numerical techniques from optimal control and rare event modeling. In particular, we elucidate the relationship between these optimal paths and the reachable set using the Hamiltonian dynamics for the shortest arrival-time path and the geometric minimum action method for the most probable path, respectively. Numerical results are presented by applying these techniques to a two-dimensional double-well potential.

Minimum action solutions of nonhomogeneous Schrödinger equations

Abstract In this paper, we are concerned with the qualitative analysis of solutions to a general class of nonlinear Schrödinger equations with lack of compactness. The problem is driven by a nonhomogeneous differential operator with unbalanced growth, which was introduced by Azzollini [1]. The reaction is the sum of a nonautonomous power-type nonlinearity with subcritical growth and an indefinite potential. Our main result establishes the existence of at least one nontrivial solution in the case of low perturbations. The proof combines variational methods, analytic tools, and energy estimates.