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A hypothesis gaining increasing popularity is that laypeople's representations of physical phenomena might be driven by internalized physical laws. In three experiments, we tested if such hypothesis holds true for the representation of gravitational motion. Participants were presented with realistic, real-scale virtual spheres falling vertically downward from about 2 m high. The spheres appeared to be made of either polystyrene or wood. In Experiment 1, participants adjusted the falling motion pattern until it appeared to be natural. In Experiment 2, they compared the perceived naturalness of vertical free falls in a vacuum with the perceived naturalness of more realistic falls characterized by the presence of air drag. In Experiment 3, they estimated the position of the sphere after a variable interval of time from the beginning of the fall. Inconsistently with predictions from physics, results showed that representations of gravitational motion were strongly affected by the implied masses of the falling objects and did not account for air drag. This provides support for the hypothesis of weight-based heuristic representations of gravitational motion against the hypothesis of the internalization of physical laws. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

This paper concerns the existence of global weak solutions à la Leray for compressible Navier–Stokes equations with a pressure law which depends on the density and on time and space variables t and x. The assumptions on the pressure contain only locally Lipschitz assumption with respect to the density variable and some hypothesis with respect to the extra time and space variables. It may be seen as a first step to consider heat-conducting Navier–Stokes equations with physical laws such as the truncated virial assumption. The paper focuses on the construction of approximate solutions through a new regularized and fixed point procedure and on the weak stability process taking advantage of the new method introduced by the two first authors with a careful study of an appropriate regularized quantity linked to the pressure.

A new mathematics, the constructive one, characterizes a singular limit as undecidable. Hence, a singular limit between two theories actually represents a difference between two different kinds of mathematics. This particular situation suggests a mathematical definition of the notion of incommensurability. As a consequence of the resulting incommensurabilities among many couples of theories the foundations of physical theories are pluralist, not only in both epistemological and ontological senses, but also in mathematical sense. Hence since longtime the history of physics is developing along a plurilinear path., 20 pages

The article contains a systematic presentation of the results of the expansion of the special theory of relativity by additionally taking into account mass and speed in the category of content, that is, the quality of the substance contained in the body and the quality of motion, as well as the volume (space of form) and time, that is, their quantity. The interrelationships of mass, energy and speed, that play the role of physical laws, are established, and their philosophical interpretation is given from the standpoint of complementarity is given. The relativistic law of conservation of energy has been derived in the aspect of complementarity of form and content, as a reflection of changes in space (volume) and time.

This work presents the synthetical mathematical analysis of available knowledge regarding physical phenomena of research interest. The work is not focusing on providing the phenomena according to the physical laws but rather because of them, hence, it is grounded on the philosophically defined concept of "similarity", and progresses to the mathematical treatments of those factors and parameters that are involved into the similarity validation among physical phenomena.A critical validation regarding the effectiveness of such an approach was also performed, in order to conceptualize the relevance of the factors and parameters interactions as a potential control tool against engineering-based hypothesis. Such factors and parameters are generated through the description and delimitation of the system of interest. A "matrix" is used for the classification of the existing knowledge regarding this system. It is consisted of the categorical descriptors of the system in question and the levels of these descriptors.A mathematical analysis of this "matrix" supports that all the existent perceptions of a physical phenomenon constitute a four-dimensional vector space. Within this space, the concept of similarity allows for the definition on which of a specific non-linear mapping that might be applied to strictly classify the existing knowledge about the phenomenon in question.Similarity is used here to define the conditions and the constrains that this mapping must satisfy. In conclusion, the applicability of the suggested approach on an engineering approach regarding a physical problem, was also demonstrated in this study.

Derk Pereboom has posed an empirical objection to agent-causal libertarianism: The best empirically confirmed scientific theories feature physical laws predicting no long-run deviations from fixed conditional frequencies that govern events. If agent-causal libertarianism were true, however, then it would be virtually certain, absent ‘wild coincidences’, that such long-run deviations would occur. So, current empirical evidence makes agent-causal libertarianism unlikely. This paper formulates Pereboom’s ‘Problem of Wild Coincidences’ as a five-step argument and considers two recent responses. Then, it offers a different response: The Problem of Wild Coincidences does not show that current empirical evidence makes agent-causal libertarianism unlikely, even if all events are governed by physical laws featuring fixed long-run conditional frequencies and even if agents can ‘overrule’ normal physical laws.

Differential equations are of fundamental importance in Mathematics, Physical Sciences and Engineering Mathematics. Many mathematical relations and physical laws appeared in the form of such equations. This paper reviewed an application of these equations in solving mathematical model on electric circuit problems using the First order linear differential equation. The analytical approached in solving the equations confirmed that solving electric circuits using first order linear ordinary differential equations gives accurate and reliable result. Therefore, the application is of importance and great need. However, complex problems need higher order differential equations, which are nonlinear and have entirely different approach in finding their solutions.

Two different ways of constructing the discrete equations and the corresponding physical laws of continuous Birkhoffian systems are respectively proposed in this paper. The corresponding mathematical methods and geometric structures are formulated and compared. The determining equations of the Noether symmetries are obtained via the Lie point transformations acting on the difference equations. Two types of the discrete conserved quantities of the systems are presented using the structure equation satisfied by the gauge functions. The algorithms can be developed based on these two approaches applied to the nonholonomic systems with symmetries. As a result, the geometric structure and the Noether invariants are numerically preserved. The numerical simulations based on the two approaches demonstrate the high precision and the long-time stability of the algorithms compared with the standard Runge–Kutta method.

Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed.

In frame of this work only physically realizable systems will be considered, namely such systems, which may be presented as unity of physical elements, structurally adjusted each to another and interacted with external medium. The physical modeling for such systems, that it is based on theory of similarities on starting stage of projecting, works as useful source of knowledge about their properties. It is known that theory of similarities studies the conditions for similarities of physical processes. Two physical processes are called similar, when they obey the same physical laws. Each quantitative characteristic for one of them is obtained from another by means of multiplication on the constant value. This value is called the constant of similarity, and it is the same for all uniform values, which are involved in process under investigation. It is a rule in theory of similarities, that two phenomena are similar if and only if, when they are qualitatively similar and have equal values for some dimensionless parameters, which are called criterions of similarities. It is also rule in theory of similarities, that dimension of any physical value may be only the multiplication of values, which are in powers, and taken as basis values. Dimensions for both parts of equality, that presents same physical law, must be the same. Dimensionless multiplications of different powers are called as criteria of similarity. In this work some features of calculation processes, connected with definitions of numerical values for criterions of similarities, will be presented. Due to the fact, that numerical values of the similarity criterions are obtained from the experimental results, these results are defined with some error, which influences the decision about similarities of the systems under comparison. To define this influence the procedure of calculation for criterions and indicators of similarities with the interval numbers is used, defined in the system center-radius. In this work the algorithm of consecutive multiplication in the interval-based view of factors, each of those presents a power function, and the algorithm for derivation of the similarity indicator are presented. The interval evaluation for the similarity indicators is obtained, depending on value of the definition intervals for corresponding values. Algorithms for numerical integration with trapezoidal rule with regular and arbitrary distribution of nodes are presented. It is shown, that for relatively simple, in respect of calculation, criteria of similarities, the neglect by experimental errors may lead to misleading conclusions about quality of the models proposed. Numerical example with evaluation of the quality for proposed physical model is considered, comparison was done for Reynolds criterion., Цель работы состоит в разработке методов вычисления и численного интегрирования критериев и индикаторов подобия, аргументами которых служат интервальные числа, заданные в системе центр – радиус. Результаты. Описано применение интервальных вычислений в системе центр-радиус для определения значений критериев и индикаторов подобия. Предложена методика численного интегрирования таблично заданной подынтегральной функции с произвольным расположением узлов интегрирования при условии, что исходные данные представлены в виде интервальных чисел, определённых в системе центр – радиус. Приведен численный пример, иллюстрирующий полученные результаты. Показано, что вычисление критериев и индикаторов подобия и функций от них без учёта их возможных интервалов определения может приводить к ошибочным выводам о результатах моделирования., Мета роботи полягає в розробці методів обчислення і чисельного інтегрування критеріїв і індикаторів подібності, аргументами яких служать інтервальні числа, задані в системі центр – радіус. Результати. Описано застосування інтервальних обчислень в системі центр- радіус для визначення значень критеріїв і індикаторів подібності. Запропонована методика чисельного інтегрування таблично заданої підінтегральної функції з довільним розташуванням вузлів інтегрування за умови, що початкові дані представлені у вигляді інтервальних чисел, визначених в системі центр – радіус. Наведено чисельний приклад, що ілюструє отримані результати. Показано, що обчислення критеріїв і індикаторів подібності і функцій від них без урахування можливих інтервалів визначення може приводити до помилкових висновків про результати моделювання.

In this paper, based on the reformulation of the Nernst–Planck equations, we construct an unconditionally stable semi-implicit linearized difference scheme for the time dependent Poisson–Nernst–Planck system. The method preserves several important physical laws at full discrete level without any constraints on the time step size, including: mass conservation, ion concentration positivity, free energy dissipation. The proposed method is a linearized method, which can be implemented efficiently. Furthermore, the method can be extended to the case of multi-ions without any difficulty. The paper ends with supporting numerical results which confirm well with theoretical findings.

The physical law of the equivalence of measures between the random process and the regular process and the stochastic equations of continuum have opened the new way in stochastic theory of turbulence. An experimental method for determining the dimension of an attractor for hydrodynamic flows suggests re-conducting an enormous complex of experiments for flows for which data on the measurement of statistical moments have already been obtained. This article proposes the dependence for the calculation of the dimensions of the attractor based on statistical moments. In addition, applying this formula and the results obtained in the stochastic theory of turbulence based on the theory of the equivalence of measures, the new dependence for the dimension of the attractor as a function of initial perturbations in a hydrodynamic flow is presented. Calculated portraits of the correlation dimension of the attractor in the cross section of a circular pipe and in the cross section of the boundary layer on a flat plate are presented.

Wiener process, also known as Brownian motion, was first proposed by Robert Brown, a biologist of the UK, in 1827 based on observing the physical phenomenon that pollen particles “move irregularly” on the liquid surface. Einstein gave a mathematical description of the physical law of this phenomenon for the first time in 1905, which made a remarkable progress in this subject.

Scale or dimension is critical for all physical laws, and different scales might result in distinct and sometimes contradicting laws for the same phenomenon. In this study, the idea of the two-scale fractal is utilized to model the time-fractional tsunami wave traveling on an unsmooth surface. Mass and momentum conservation equations are established in a fractal space. To covert the considered fractional model into a differential equation, the fractional complex transform is used, then He’s variational iteration method is adopted to solve the resultant equation. The fractal model helps in studying the dynamic behavior of tsunami wave and their prevention through boundary control. The present study sheds new light on two-scale fluid mechanics.

By rigorously accounting for dimensional homogeneity in physical laws, the Pi theorem and the related self-similarity hypotheses allow us to achieve a dimensionless reformulation of scientific hypotheses in a lower dimensional context. This paper presents applications of these concepts to the partitioning of water and soil on terrestrial landscapes, for which the process complexity and lack of first principle formulation make dimensional analysis an excellent tool to formulate theories that are amenable to empirical testing and analytical developments. The resulting scaling laws help reveal the dominant environmental controls for these partitionings. In particular, we discuss how the dryness index and the storage index affect the long term rainfall partitioning, the key nonlinear control of the dryness index in global datasets of weathering rates, and the existence of new macroscopic relations among average variables in landscape evolution statistics. The scaling laws for the partitioning of sediments, the elevation profile, and the spectral scaling of self-similar topographies also unveil tantalizing analogies with turbulent fluctuations.

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities -- qua part of a physical law -- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature., Comment: 29 pages, 2 figures, accepted for publication in Synthese

It is merely encountered that in several branches of sciences, including physics, chemistry, mathematics, and biology, the appearance of ordinary and partial differential equations plays an important role. The dynamical behaviors are based on the physical significance of the problem. Qualitatively, these are the several branches of physics. Such applications are laid down as population growth, potential field, electrical circuit, biological behavior of trees, etc. However, differential equations are obtained from the physical laws. The solution of linear differential equation is quite easy to handle but though some of the nonlinear differential equation admits analytical solution, it is difficult for many. Some classical methods are proposed to get approximate analytical solution. In the present situation, we adopt the Laplace transformation technique embodies with Adomian decomposition method (ADM). Validation of the present result is also obtained with earlier published work and conformity of the solution achieved.

In this chapter, the fundamental mechanisms of mass transfer are discussed and computational approaches to study them are analyzed. The main goal is to present these concepts through their application in different food-processing techniques in a simplistic overview. In food processing, most studies on the mass transfer require/gather experimental data and use model fitting. The study of mass transfer is facilitated through evaluation of the nature of the transfer and utilization of proper physical laws and models to gain more knowledge about the system. The mass transfer modeling is an important parameter for estimating the yield of different processes such as drying, impregnation, and rehydration.

While interacting with objects during every-day activities, e.g. when sliding a glass on a counter top, people obtain constant feedback whether they are acting in accordance with physical laws. However, classical research on intuitive physics has revealed that people’s judgements systematically deviate from predictions of Newtonian physics. Recent research has explained at least some of these deviations not as consequence of misconceptions about physics but instead as the consequence of the probabilistic interaction between inevitable perceptual uncertainties and prior beliefs. How intuitive physical reasoning relates to visuomotor actions is much less known. Here, we present an experiment in which participants had to slide pucks under the influence of naturalistic friction in a simulated virtual environment. The puck was controlled by the duration of a button press, which needed to be scaled linearly with the puck’s mass and with the square-root of initial distance to reach a target. Over four phases of the experiment, uncertainties were manipulated by altering the availability of sensory feedback and providing different degrees of knowledge about the physical properties of pucks. A hierarchical Bayesian model of the visuomotor interaction task incorporating perceptual uncertainty and press-time variability found substantial evidence that subjects adjusted their button-presses so that the sliding was in accordance with Newtonian physics. After observing collisions between pucks, which were analyzed with a hierarchical Bayesian model of the perceptual observation task, subjects transferred the relative masses inferred perceptually to adjust subsequent sliding actions. Crucial in the modeling was the inclusion of a cost function, which quantitatively captures participants’ implicit sensitivity to errors due to their motor variability. Taken together, in the present experiment we find evidence that our participants transferred their intuitive physical reasoning to a subsequent visuomotor control task consistent with Newtonian physics and weighed potential outcomes with a cost functions based on their knowledge about their own variability., Author Summary During our daily lives we interact with objects around us governed by Newtonian physics. While people are known to show multiple systematic errors when reasoning about Newtonian physics, recent research has provided evidence that some of these failures can be attributed to perceptual uncertainties and partial knowledge about object properties. Here, we carried out an experiment to investigate whether people transfer their intuitive physical reasoning to how they interact with objects. Using a simulated virtual environment in which participants had to slide different pucks into a target region by the length of a button press, we found evidence that they could do so in accordance with the underlying physical laws. Moreover, our participants watched movies of colliding pucks and subsequently transferred their beliefs about the relative masses of the observed pucks to the sliding task. Remarkably, this transfer was consistent with Newtonian physics and could well be explained by a computational model that takes participants’ perceptual uncertainty, action variability, and preferences into account.

Capable of classifying huge amount of texts, translating hundreds of languages, predicting the rise and fall of global markets, even driving unmanned automobiles, Deep Learning systems are the hope of the fifth industrial revolution. However, recent studies have found that Deep Learning systems can be easily manipulated, i.e., in image recognition and in natural language understanding. The nature of one system of the mind (System 1), which Deep Learning systems simulates, dictates that any given data would be put into a coherent story, even at the cost of logic. Another system of the mind (System 2) manages logical thinking by following rules and structures, which symbolic AI simulates. How to combine Deep Learning with symbolic structures remains an open debate.

Cyclic mechanic is intended as a suitable generalization both of quantum mechanics and general relativity apt to unify them. It is founded on a few principles, which can be enumerated approximately as follows: 1. Actual infinity or the universe can be considered as a physical and experimentally verifiable entity. It allows of mechanical motion to exist. 2. A new law of conservation has to be involved to generalize and comprise the separate laws of conservation of classical and relativistic mechanics, and especially that of conservation of energy: This is the conservation of action or information. 3. Time is not a uniformly flowing time in general. It can have some speed, acceleration, more than one dimension, to be discrete. 4. The following principle of cyclicity: The universe returns in any point of it. The return can be only kinematic, i.e. per a unit of energy (or mass), and thermodynamic, i.e. considering the universe as a thermodynamic whole. 5. The kinematic return, which is per a unit of energy (or mass), is the counterpart of conservation of energy, which can be interpreted as the particular case of conservation of action “per a unit of time”. The kinematic return per a unit of energy (or mass) can be interpreted in turn as another particular law of conservation in the framework of conservation of action (or information), namely conservation of wave period (or time). These two counterpart laws of conservation correspond exactly to the particle “half” and to the wave “half” of wave-particle duality. 6. The principle of quantum invariance is introduced. It means that all physical laws have to be invariant to discrete and continuous (smooth) morphisms (motions) or mathematically, to the axiom of choice. The list is not intended to be exhausted or disjunctive, but only to give an introductory idea.

The significance of the correspondence between the classical limit of quantum theories and the laws of classical physics is explained. It is proved that this correspondence yields constraints on acceptable quantum theories. The variational principle is taken as the basis of the analysis. The discussion shows that the first order Dirac equation abides by these constraints, whereas second order quantum equations fail to do that.

Training prescription and load monitoring in running activities have benefited from power output (PW) data offered by new technologies. Nevertheless, to date, the sensitivity of PW data provided by these tools is still not completely clear. The aim of this study was to analyze the level of agreement between the PW estimated by five commercial technologies and the two main internationally theoretical models based on laws of physics, in different environments and running conditions. Ten endurance-trained male athletes performed three submaximal running protocols on a treadmill (indoor) and an athletic track (outdoor), with changes in speed, body weight, and slope. PW was simultaneously registered by the commercial technologies Stryd (StrydApp and StrydWatch), RunScribe, GarminRP and PolarV, whereas theoretical power output (TPW) was calculated by the two mathematical models (TPW1 and TPW2). Statistics included, among others, the Pearson's correlation coefficient (r) and standard error of measurement (SEM). The PolarV, and above all Stryd, showed the closest agreement with the TPW1 (Stryd: r ≥ 0.947, SEM ≤ 11 W; PolarV: r ≥ 0.931, SEM ≤ 64 W) and TPW2 (Stryd: r ≥ 0.933, SEM ≤ 60 W; PolarV: r ≥ 0.932, SEM ≤ 24 W), both indoors and outdoors. On the other hand, the devices GarminRP (r ≤ 0.765, SEM ≥ 59 W) and RunScribe. (r ≤ 0.508, SEM ≥ 125 W) showed the lowest agreement with the TPW1 and TPW2 models for all conditions and environments analyzed. The closest agreement of the Stryd and PolarV technologies with the TPW1 and TPW2 models suggest these tools as the most sensitive, among those analyzed, for PW measurement when changing environments and running conditions.

Regression is a common technique in engineering when physical laws are unknown. Practitioners usually look for a unique set of true parameters that optimally explain the observed data. This...

In this paper, a mathematical model for fractal-time space is given involving Fα-calculus. Differential equations corresponding of the free fall motion and simple harmonic oscillator on fractal-time space are given and solved. Moreover, using scale transformation and invariant properties of physical laws we obtained the generalized Kepler’s Third Law of motion on fractal-time space. Keywords: Fractal calculus, Fractal triadic Cantor set, Fractal-time spaces, Kepler’s Third Law, Local derivative on fractals

Quantumhash functions are similar to classical (cryptographic) hash functions and their security is guaranteed by physical laws. However, security of a primitive does not automatically mean that protocols based on this primitive are secure. We propose protocols based on quantum hash function and assess their security using Holevo entropy and recently introduced notion of quantum information cost.

The physical laws characterizing the relation between stresses and strains are considered and analyzed in the general modern theory of elastoplastic deformations and in its postulates of macroscopic definability and isotropy for initially isotropic continuous media. The fundamentals of this theory in continuum mechanics were developed by A.A. Il’yushin in the mid-twentieth century. His theory of small elastoplastic deformations under simple loading became a generalization of Hencky’s deformation theory of flow, whereas his theory of elastoplastic processes which are close to simple loading became a generalization of the Saint-Venant–Mises flow theory to the case of hardening media. In these theories, the concepts of simple arid complex loading processes arid the concept of directing form change tensors are introduced; the Bridgman law of volume elastic change and the universal Roche–Eichinger laws of a single hardening curve under simple loading are adopted; and the Odquist hardening for plastic deformations is generalized to the case of elastoplastic hardening media for the processes of almost simple loading without consideration of a specific history of deformations for the trajectories with small arid mean curvatures. In this paper we discuss the possibility of using the isotropy postulate to estimate the effect of forming parameters in the stress-strain state appeared due to the strain-induced anisotropy during the change of the internal structures of materials. We also discuss the possibility of representing the second-rank symmetric stress and strain tensors in the form of vectors in the linear coordinate six-dimensional Euclidean space. An identity principle is proposed for tensors and vectors.

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics (SM), progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I focus on two objections in the literature: claims that coarse-graining makes time-asymmetry (i) ‘illusory’ and (ii) ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility

Reaction-infiltration instability, in which chemical reactions can dissolve minerals and therefore create preferential pore-fluid flow channels in fluid-saturated rocks, may play an important role in controlling groundwater quality in groundwater hydrology. Although this topic has been studied for many years, there is a recent debate, which says that the use of large-density asymptotics in the previous studies is invalid. However, there is a crucial conceptual mistake in this debate, which leads to results and conclusions that are inconsistent with the fundamental laws of physics. It is well known that in terms of distance, time and velocity, there are only two independent variables. But they are treated as three independent variables, a procedure that is the main source of the physically unrealistic results and conclusions in the debate. In this paper, we will discuss the results and conclusions related to the debate, with emphasis on the issues leading to the corresponding errors. In particular, we demonstrate that there is an unappreciated constraint condition between the dimensional/dimensionless distance, time and velocity in the debate. By using this constraint condition, it can be confirmed that as the ratio of the reactant concentration in the incoming fluid stream to the mineral concentration approaches zero, the dimensionless transport parameter, H, automatically approaches infinity. Therefore, it is further confirmed that the previous work conducted by Chadam and others remains valid.

In September of 2020, Arctic sea ice extent was the second-lowest on record. State of the art climate prediction uses Earth system models (ESMs), driven by systems of differential equations representing the laws of physics. Previously, these models have tended to underestimate Arctic sea ice loss. The issue is grave because accurate modeling is critical for economic, ecological, and geopolitical planning. We use machine learning techniques, including random forest regression and Gini importance, to show that the Energy Exascale Earth System Model (E3SM) relies too heavily on just one of the ten chosen climatological quantities to predict September sea ice averages. Furthermore, E3SM gives too much importance to six of those quantities when compared to observed data. Identifying the features that climate models incorrectly rely on should allow climatologists to improve prediction accuracy.

The process of dispersion in porous media is the effect of combined variability in fluid velocity and concentration at scales smaller than the ones resolved that contributes to spreading and mixing. It is usually introduced in textbooks and taught in classes through the Fick-Scheidegger parameterization, which is introduced as a scientific law of universal validity. This parameterization is based on observations in bench-scale laboratory experiments using homogeneous media. Fickian means that dispersive flux is proportional to the gradient of the resolved concentration while the Scheidegger parameterization is a particular way to compute the dispersion coefficients. The unresolved scales are thus associated with the pore-grain geometry that is ignored when the composite pore-grain medium is replaced by a homogeneous continuum. However, the challenge faced in practice is how to account for dispersion in numerical models that discretize the domain into blocks, often cubic meters in size, that contain multiple geologic facies. Although the Fick-Scheidegger parameterization is by far the one most commonly used, its validity has been questioned. This work presents a method of teaching dispersion that emphasizes the physical basis of dispersion and highlights the conditions under which a Fickian dispersion model is justified. In particular, we show that Fickian dispersion has a solid physical basis provided that an equilibrium condition is met. The issue of the Scheidegger parameterization is more complex but it is shown that the approximation that the dispersion coefficients should scale linearly with the mean velocity is often reasonable, at least as a practical approximation, but may not necessarily be always appropriate. Generally in Hydrogeology, the Scheidegger feature of constant dispersivity is considered as a physical law and inseparable from the Fickian model, but both perceptions are wrong. We also explain why Fickian dispersion fails under certain conditions, such as dispersion inside and directly upstream of a contaminant source. Other issues discussed are the relevance of column tests and confusion regarding the meaning of terms dispersion and Fickian.

This article considers the relationships between the character of physical law in quantum theory and Bohr’s concept of complementarity, under the assumption of the unrepresentable and possibly inconceivable nature of quantum objects and processes, an assumption that may be seen as the most radical departure from realism currently available. Complementarity, the article argues, is a reflection of the fact that, as against classical physics or relativity, the behavior of quantum objects of the same type, say, all electrons, is not governed by the same physical law in all contexts, specifically in complementary contexts. On the other hand, the mathematical formalism of quantum mechanics offers correct probabilistic or statistical predictions (no other predictions are possible on experimental grounds) in all contexts, here, again, under the assumption that quantum objects themselves and their behavior are beyond representation or even conception. Bohr, in this connection, spoke of “an entirely new situation as regards the description of physical phenomena that, the notion of complementarity aims at characterizing.” The article also considers the relationships among complementarity, entanglement, and quantum information, by basing these relationships on this understanding of complementarity.

The main objectives of this paper are five-fold. The first is to introduce a general dynamic law for all physical motion systems, based on a new variational principle with constraint-infinitesimals. The second is to postulate the potential-descending principle (PDP). We show that PDP is a more fundamental principle than the first and second laws in thermodynamics, and gives rise to dynamical equations for non-equilibrium systems. The third is to demonstrate that the PDP is the first principle to describe irreversibility of all thermodynamic systems, with ther-modynamic potential as the basic physical quantity, rather than entropy. The fourth objective is to examine the problems faced by the Boltzmann equation. We show that the Boltzmann is not a physical law, is created as a mathematical model to obey the entropy-increasing principle (for dilute gases), and consequently is unable to faithfully describe Nature. The fifth objective is to prove an orthogonal-decomposition theorem and a theorem on variation with constraint-infinitesimals, providing the needed mathematical foundations of the dynamical law of physical motion.

Resource-allocation systems are ubiquitous in the human society. But how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model. Because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory, here we combine the Ising model with the market-directed resource-allocation game, yielding an Ising game. Based on the Ising game, we show theoretical, simulative and experimental evidences for a formula, which offers a clear expression of nonequilibrium steady states (NESSs). Interestingly, the formula also reveals a convertible relationship between the external field (exogenous factor) and resource ratio (endogenous factor), and a class of saturation as the external field exceeds certain limits. This work suggests that the Ising game could be a suitable model for studying external-field effects on resource-allocation systems, and it could provide guidance both for seeking more relations between NESSs and equilibrium states and for regulating human systems by choosing NESSs appropriately.

Is ours the only universe? In this article I review how the idea of “multiverse” in cosmology and quantum theories. Vast space-time were generated during inflation, for which the observable part is limited by horizon and only a tiny small fraction of the whole, and different effective physical laws may be found in the different parts. In quantum mechanics, according to the many world interpretation, during each quantum measurement the world split into different branches which evolve independently. However, whether such different branches should be considered “really exist” is more a question of philosophy than science. The concept of multiverse is however almost impossible to be tested with experiments or observations, thus raising the question whether they are meaningful science questions at all.

We have seen how, in the first thirty years following its birth and with the first encouraging results obtained through the study of simple model systems, molecular simulation had grown in all possible directions, imposing the effectiveness of its own methods for a complete realization of the programme of statistical mechanics: derivation and explicit calculation, starting from the basic building blocks (i.e., atoms) and from the fundamental laws of physics, of the properties of the aggregate states of matter in its various forms, and of the transitions between them.

In this chapter we shall talk about the laws that can be considered as the basis of all modern physics. Newton’s Philosophiae Naturalis Principia Mathematica constitutes the first (known) formal, mathematical formulation of the physical laws. Here we will present Newton’s formulation of Classical Mechanics, also the equivalence principle, and introduce the concepts of inertial reference frames, momentum, conservative and non-conservative forces, angular momentum, torque, work, energy and the corresponding conservation laws. We will also introduce Galilean relativity and re-discuss the notion of inertial reference frames.

There is a renaissance in forest modelling due to the application of mathematics and physics. There are some classical theories including pipe model theory, Metzger’s theory, self-thinning rule, Da Vinci’s tree form concept, Logarithmic spiral technique, etc., which have greater significance in forestry science. With advanced computational tools from the IT revolution at disposal, a better understanding of the above-mentioned theories is now possible. In meantime, plants’ architecture and design have been a source of inspiration for biomechanists, as mechanics is an inseparable part of the abiotic realm. It is based on one important principle “all structures, whether engineered or natural, must obey the laws of physics”. Trees grow, adapt and acclimate to maintain their stability. This demands a trade-off between their mechanical stability and other physiological functions. It is also vivid that mechanical forces can manipulate the tree architecture and root architecture and influence thigomorphogensis. For this reason, it is important to understand the impact of mechanical forces on tree growth. Forest modelling can take a leap forward by infusing these theories and biomechanics. The present chapter narrates some of the classical theories in forestry and simultaneously showcases the relevance of these theories based on research work done. Furthermore, it deliberates on the utilization of modelling to provide greater impetus in forest science in order to explore prudent silvicultural practice for enhancing forest productivity and product quality.

To organize all knowledge in biology in a coherent axiomatic system like mathematics or physics has been a dream for every scientist. This paper investigates the question how to formulate a set of axioms or fundamental laws governing all biological phenomena. We are able to identify a broad class of phenomena in biology including human society cannot be explained or forecasted by the existing fundamental laws of physics. However, the combination of existing fundamental laws of physics with laws in the recently-created Choice Axiomatic System in physics seems to be able to cover all known biological phenomena. This result enables this paper to propose a complete set of fundamental laws of biology for the first time in the history. Establishing a complete set of fundamental laws of biology provides a solid foundation for theoretical biology, and points to new directions of future biophysics research. We conclude that biology should not have any fundamental law of its own, all fundamental laws of biology are simply a subset of fundamental laws of physics, and identifying this complete set of fundamental laws of biology opens the door for an axiomatization of biology, social science, and humanities.

The Wiener process is widely used in the degradation modeling, life prediction, and maintenance decision of products in aerospace, high-speed rail and marine field. In the basic Wiener process model, the drift parameter represents the degradation rate and the diffusion parameter represents the degradation fluctuation, and they are independent of each other, which is not conform to the laws of physics and existing research experience. According to the physical knowledge and the widely known accelerated degradation test experience, when the environmental stress level increases, the degradation rate and degradation fluctuation of the product will increase accordingly. Thus, there is a positive correlation between the rate parameter and the diffusion parameter in the Wiener process model. Ignoring this positive correlation of the drift parameter and the diffusion parameter in Wiener process will lead to imprecise degradation modeling and life prediction results. In this paper, a novel parameter-related Wiener process model is proposed by considering the positive correlativity between the drift and the diffusion parameter. The statistical properties of the novel parameter-related Wiener process model are derived. The method proposed in this paper is demonstrated by applied to a set of ageing test data of rubber. First, the ageing path is simulated based on the proposed model. Then, the remaining useful life of the rubber is predicted using the novel parameter-related Wiener process model proposed in this paper. The predicted results are compared with those of the basic Wiener process model, with the following conclusions

This article presents results obtained by the author in an attempt to introduce new parameters that influence the working process of agricultural soil working machines, in the classical formulas that mathematically model the tillage draft force. This article naturally introduces soil moisture. To introduce soil moisture into the calculation formulas of the tillage draft force, other physical parameters affected by soil moisture were used: density, cohesion, adhesion, etc. In this article, is explicitly describes, only the variation of soil density with its moisture. Considering some phenomena such as soilswellingorshrinkage, required the development of an adequate mathematical model of the expression of the density of soil-water mixture, concerning the concentration of water and the densities of dry soil and water. The final formulas obtained are tested to experimental results from the literature. Finally, the author sets out his opinion regarding the use of the results in design calculations and regarding the elevation to the rank of physical law of a mathematical model represented by a formula with a large number of parameters, which in turn are still dependent on many others parameters.

Quantum key distribution (QKD) can help two distant peers to share secret key bits, whose security is guaranteed by the law of physics. In practice, the secret key rate of a QKD protocol is always lowered with the increasing of channel distance, which severely limits the applications of QKD. Recently, twin-field (TF) QKD has been proposed and intensively studied, since it can beat the rate-distance limit and greatly increase the achievable distance of QKD. Remarkalebly, K. Maeda et. al. proposed a simple finite-key analysis for TF-QKD based on operator dominance condition. Although they showed that their method is sufficient to beat the rate-distance limit, their operator dominance condition is not general, i.e. it can be only applied in three decoy states scenarios, which implies that its key rate cannot be increased by introducing more decoy states, and also cannot reach the asymptotic bound even in case of preparing infinite decoy states and optical pulses. Here, to bridge this gap, we propose an improved finite-key analysis of TF-QKD through devising new operator dominance condition. We show that by adding the number of decoy states, the secret key rate can be furtherly improved and approach the asymptotic bound. Our theory can be directly used in TF-QKD experiment to obtain higher secret key rate. Our results can be directly used in experiments to obtain higher key rates.

Entanglement is a prediction of quantum mechanics that suggests that our physical laws cannot be described by a local causal model. This has led to much debate, including Einstein's famous suggestion that quantum mechanics is an incomplete theory, and we may one day discover a deeper theory that can be described by a locally causal model. However, loophole free violations of Bell inequalities demonstrate that this is not the case. Bell's theorem is independent of quantum mechanics, and it shows that any theory attempting to supplant quantum mechanics must be somehow nonlocal. Since then, there have been many experimental violations of Bell inequalities using different physical systems, culminating in three loophole-free experiments [1–3].

We present examples of peak estimation to measurements of Raman, Infrared and NMR spectra by the piecewise monotonic data approximation method. The structural differences of these spectra, the complexity of the underlying physical laws and the error included in the measurements make this a good test of the effectiveness of the method. Precisely, if a number of monotonic sections of the data is required, then the optimal turning points and the least sum of squares of residuals are computed in quadratic complexity with respect to the number of data. This is a remarkable result because the problem may require an enormous number of combinations in order to find the optimal turning point positions. Our results exhibit some strengths and indicate certain advantages of the method. Therefore, they may be helpful to the development of new algorithms that are particularly suitable for peak estimation in spectroscopy calculations.

The performance of communication through a quantum conductor is limited by the laws of physics. The optimum channel capacity, the maximum rate at which information can be transmitted under a given signal power, i.e., the heat current, connects the theory of communication, quantum physics, and thermodynamics. Here, the author calculates the distribution of fluctuations of self-information and finds a Jarzynski equality like universal relation connecting the fluctuations of information, the R\'enyi entropy of order zero, and the optimum capacity.

Hysteresis is a complex phenomenon that occurs in many areas of science and engineering. To model hysteresis, scientists combine first laws of physics with fictitious equations to obtain phenomenological models that aim to match the macroscopic behavior of hysteresis processes. In this paper we focus on a model of hysteresis that was proposed by the physicist P. Duhem starting from thermodynamical considerations. On the one hand, we strengthen the results obtained by the mathematician I. Babuška in relation with the existence and uniqueness of a global solutions and of a periodic solution when the input is periodic. On the other hand, we specialize into a specific form of the Duhem model proposed by Babuška. For Babuška’s model we determine the explicit analytic expression of the hysteresis loop. We apply our findings to dry friction modeling and to asymmetric hysteresis loop matching.

The study of cooling materials is essential to analyse the thermal properties of substances, electronic devices, among many others. The physical law for describing the temporal temperature decrease has been dominated by Newton’s law of cooling (NLC), which assumes that the natural cooling occurs by following an exact exponential trend. However, several studies have questioned the broad validity of this law by arguing that cooling occurs following an approximate rather than an exact exponential trend. In this way, to mitigate the difficulties of a reliable-description of the natural cooling processes, we introduce in this work a new formulation of NLC in the context of the q- and κ -calculus, which are obtained from the Tsallis q- and Kaniadakis κ -generalised statistical mechanics. The NLC in the Tsallis and Kaniadakis frameworks, in which we call q-NLC and κ -NLC, respectively, are derived from the related deformed derivative operators. The q- and κ -NLC describes the cooling process through the deformation of the ordinary exponential function. To empirically validate our proposal, we consider two real data sets: in the first one, a water-cooling case-study; and then, in the second one, the cooling of a power battery pack. The results show that the NLC based on generalised statistics outperform the classical NLC, which demonstrates a new path to cooling-analyses.

Hitherto, the Caratheodory Principle proved useful in the proof of existence of entropy. Here, we prove existence in reversible as well as irreversible material bodies, on the basis of a physical law. In the presence of a reversible and adiabatic process, this law, which we call the adiabat, is a constraint on the independence of the state variables and is in fact a functional relation between temperature and deformation. The adiabat leads to the integrability of the First Law and the existence of entropy density. We show that the integrating denominator is a function of temperature alone, a result that has far-reaching consequences.

E T Bell, the famous author of ‘Men of Mathematics’, has described mathematics as the ‘Queen of Arts and Servant of Science’. What he meant is that mathematics serves science by entering into the picture as soon as a proper mathematical model is set up by the scientist, and then after a purely mathematical analysis of the model, the final mathematical step is interpreted scientifically. The purpose of the present article is to convince the readers that sometimes the roles of science and mathematics are reversed, and a mathematical problem is interpreted as a physics problem; the laws of physics are utilized for a physical analysis, and the final result of the physical analysis is interpreted mathematically. We shall illustrate this by means of few examples.

The unificationist theory of causal explanation offers a theory of causation and explanation with no causal primitives. Kitcher proposed that it offered an account of explanatory asymmetry, but his proposal has been criticized for being too dependent on contingent facts and surreptitiously supposing causal realism. In addition, critics have argued that unificationism cannot account for asymmetry in a world with symmetric laws of physics (such as ours) and is lead to accept backwards explanation in certain epistemic situations. Unificationism has been defended from some of these objections. We critique those defenses, rejecting some and developing others, as well as adding new ones. In doing so, we argue that objectors are wrong to treat explanatory asymmetry as an a priori matter and that unificationism is appropriately sensitive to the right sort of empirical facts.