Abstract. Deep learning has achieved remarkable success in diverse computer science appli- cations, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved several mechanics problems governed by differential equations, using physics in- formed neural networks (PINN). The PINN embeds the differential equations into the loss of the neural network using automatic differentiation. We present our developments in the context of solv- ing two main classes of problems: data-driven solutions and data-driven discoveries, and we compare the results with either analytical solutions or numerical solutions using the finite element method. The remarkable achievements of the PINN model shown in this report suggest the bright prospect of the physics-informed surrogate models that are fully differentiable with respect to all input co- ordinates and free parameters. More broadly, this study shows that PINN provides an attractive alternative to solve traditional engineering problems.
This approach has been used successfully in a wide range of settings (Geisler et al., 2001; Kersten et al., 2004; Najemnik & Geisler, 2005; Schwartz et al., 2009; Weiss et al., 2002; Yuille & Kersten, 2006) to explain how people make inferences about what object has generated visual sensory information. Here we propose that this approach can be extended to predicting people’s judgments about physics. Like in previous work (McIntyre, Zago, Berthoz, & Lacquaniti, 2001; Shepard, 1984; Zago, McIntyre, Senot, & Lacquaniti, 2009), we assume that people have an internal representation of physical constraints. We then assume that people appropriately combine this prior knowledge that is constrained by Newtonian mechanics with noisy information from the sensory system to make inferences about the physical situation. This idea was foreshadowed by Watanabe and Shimojo (2001) who proposed that people combining visual and auditory
DOI: 10.4236/wjcmp.2018.82002 27 World Journal of Condensed Matter Physics that is to penetrate the surface of the empty box (set) by any means. At the very moment we do that, we convert an empty box into a non-empty box due to penetrating this box. At a minimum the empty set will become a zero set if our examination (instrument) is infinitely subtle. The circle is now closed because finding the zero set is finding a quantum particle as opposed to the empty set quantum wave surface of the zero set   . Some readers may object to the preceding argument as being both unfamiliar, too simple and at the same time, maybe too abstract for the taste of many physicists who do not consider set theory to be part of physics. To that we can answer with what we said at the very beginning, namely that we are asking such deep and fundamental questions that are on a level where pure mathematics and pure physics are a unified entities  . Never the less we think we can convince the sceptic by returning to Equation (1) which is our most powerful evidence for what we think is a fact, namely that quantum mechanics is just a spacetime theory as Newtonian me- chanics and relativity. We wrote Equation (1) intentionally in the form of two brackets multiplication    
conclude, the flexible type of statistics of the generalized fuzzy, or neutrosophical type is defined through the quantities resulting from everything that is measured effectively, through the quantities that it could be able to measure, as well as the quantitative/qualitative indeterminacies, irrespective of the proportion in which the given information would simultaneously describe both quantity (different from 0), and quality (non-quantity), and even indeterminacy. Synthetically, the statistics of the future is measuring (quantity), gradual measuring (quantity and quality), non- measuring (quality), and (quantitative/qualitative) indeterminacy. At this final point, through the inclusion of indeterminacy, statistical thinking can meet both the flexible, minutely qualified logic of the neutrosophical type, and quantum mechanics and statistical physics.
The aim of this review is to highlighte the com- mon aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relati- vity. After a brief historical introduction, empha- sis is put on the physical foundations of Rela- tivity Theory and its essential role in the clarifi- cation of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Par- ticle Physics.
Computational mechanics are constantly being pushed to their fullest extent, such as the demand increased capabilities in speed, range, survivability, mission versatility, and reliability on next generation of military aircraft (Fischer, 2014). To satisfy these demands, one must achieve synergy between constituent sub- systems including, among others, thermal management, structures, controls, acoustic propagation, and materials. This necessary synergy, and resulting maximum plat-form performance, is only attainable through the use of a truly integrated design process. Such a process, along with the desire to identify and exploit beneficial coupling within the physics of the design domain, inherently requires leveraging higher fidelity computational simulations
Abstract Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. Statistical classical mechanics enable the derivation of the properties of large bodies by investigating the movements of small atoms and molecules which comprise these bodies using Newton's classical laws. Quantum mechanics defines the laws of movement of small particles at small atomic distances by considering them as probability waves. The laws of quantum mechanics are described by the Schrödinger equation. The laws of such movements are significantly different from the laws of movement of large bodies, such as planets or stones. The two described theories are well known and have been well studied. As these theories contain numerous paradoxes, many scientists doubt their internal consistencies. However, these paradoxes can be resolved within the framework of the existing physics without the introduction of new laws. To clarify the paper for the inexperienced reader, we include certain necessary basic concepts of statistical physics and quantum mechanics in this paper without the use of formulas. Exact formulas and explanations are included in the Appendices. The text is supplemented by illustrations to enhance the understanding of the paper. The paradoxes underlying thermodynamics and quantum mechanics are also discussed. The approaches to the solutions of these paradoxes are suggested. The first approach is dependent on the influence of the external observer (environment), which disrupts the correlations in the system. The second approach is based on the limits of the self-knowledge of the system for the case in which both the external observer and the environment are included in the considered system. The concepts of observable dynamics, ideal dynamics, and unpredictable dynamics are introduced. The phenomenon of complex (living) systems is contemplated from the point of view of these dynamics.
Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary physics, together with Newtonian, quantum and relativistic mechanics, and Maxwell’s electromagnetism. Cen- tral points of any physical theory are when and why it works, and when and why it fails. This is so for any human intellectual construct, hence for the BG theory as well. We intend to briefly discuss here when we must (or must not) use the BG entropy
Quantum physics is such a vast topic, yet to be understood properly. But, scientists have contributed their whole strength and life in improving the technology to make the world comfortable. Everything that we observe has science hidden in that. Quantum has turned the thinking from macro to nanotechnology. The study of physics is interesting and mind boggling if one understands it and can relate it with the reality. So much improvement can be made still and hence we have to keep proposing ideas and accept those ideas from different individuals
Seeing moreover in you, as I say, an earnest student, a man of considerable eminence in philosophy, and an admirer [of mathematical inquiry], I thought fit to write out for you and explain in detail in the same book the peculiarity of a certain method, by which it will be pos- sible for you to get a start to enable you to investigate some of the problems in mathematics by means of mechanics. This procedure is, I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. (Heath, 1912, p. 13):
Besides these wave phenomena, Duffing type equations describe many other kinds of nonlinear oscillatory systems in physics, mechanics and engineering systems such as the classical nonlinear spring system with odd nonlinear restoring characteristics , magneto-elastic mechanical systems , large amplitude oscillation of centrifugal governor systems , nonlinear vibration of beams and plates [12,13] and fluid flow induced vibration .
ever, as any other human intellectual construct, it has a re- stricted domain of validity. For nonlinear dynamical many- body systems the usual requirement is ergodicity, which is guaranted by strong chaos (i.e., by a positive maximal Lyapunov exponent for classical systems). For nonergodic systems (typically for systems whose maximal Lyapunov exponent vanishes), which is quite frequently the case of the so-called complex systems, there is no general reason for legitimately using the BG theory. For (some of) such anomalous systems, a generalization of the BG theory has been proposed in 1988 . It is frequently referred to as nonextensive statistical mechanics [2–4] because the total energy of such systems typically is nonextensive, i.e., not proportional to the total number of elements of the system. This generalized theory is based on the entropy
Analyzing the present definition of macrorealism, it can readily be seen that ortho- dox 4 quantum mechanics fulfills postulate (3), but violates postulates (1) and (2). Classical physics obviously satisfies postulate (1), as superposition states are confined to the realm of quantum physics, and (3) due to causality. However, at first glance, it seems that classical physics can violate postulate (2) if imperfect measurements are performed. Various approaches to close this so-called clumsiness loophole have been discussed [72, 101]. The original solution proposed by Leggett and Garg requires performing solely negative ideal measurements . In that case, the measurement process is constructed such that the measurement device interacts with the system if and only if the system has one particular value (e.g. a double-slit experiment with a detector blocking only one slit). The absence of a measurement result (no click of the detector) then indicates the opposite outcome (the photon went through the other slit). Classically, the system cannot have been influenced by a negative measurement outcome. We conclude that classical physics, with its possibility of performing non-invasive measurements, fulfills all postulates, and therefore is a macrorealistic theory.
Quantum mechanics is therefore regarded as a general theoretical framework of physical theories It consists of mathematical core which becomes physical theory when adding a set of correspondence rules telling us which mathematical objects we use in different physical situation. In contrast to classical physical theories, these corresponding rules are not intuitive as linear operators on Hilbert spaces are quite familiar (Michael M.W, 2012-8). It’s often useful to divide physical experiments into two, that is preparation and measurement and this gives out a clear distinction between quantum and classical mechanics since in the latter we don’t talk about measurement. The division of a physical experiment into a preparation on state and measurement of an observable quantity is reflected in mathematical structure of quantum mechanics. Observables are represented by Hermitian elements taken from algebra and assume that each element has an adjoint. The algebra is usually represented in terms of bounded linear operators acting on a Hilbert space H. A state in turn corresponds to a linear functional mapping observables onto a real number and hence words ‘state’ and ‘observable’ are used to refer to both physical concept and mathematical operator. And therefore in this text we explore the basic mathematical physics of quantum mechanics with a focus on Hilbert Space theory and application as well as theory of linear operators on Hilbert Space. We show how operators can be used to represent quantum observables and investigate the spectrum of various linear operators.
National Geographic answers all the questions about how things work-the science, technology, biology, chemistry, physics, and mechanics-in an indispensible book that reveals the science behind virtually everything. This clearly written and profusely illustrated book explains the science behind all the machines, gadgets, systems, and processes we take for granted. The perfect book for techies-young or old, male or female-who read Popular Science and Wired or watch "How It Works" and "How It's Made." How does the voice of a distant radio announcer make it through your alarm clock in the morning? How does your gas stove work? How does the remote control open your garage door? What happens when you turn the key in the ignition? What do antibiotics really do? Divided into four big realms-Mechanics, Natural Forces, Materials & Chemistry, Biology & Medicine-The Science of Everything takes readers on a fascinating tour, using plain talk, colorful photography, instructive diagrams, and everyday examples to explain the science behind all the things we take for granted in our modern world.
Students are permitted to use four-function, scientific, or graphing calculators to answer the questions in Section II of the AP Physics C: Mechanics Exam. Students are not allowed to use calculators in Section I. Before starting the exam administration, make sure each student has an appropriate calculator, and any student with a graphing calculator has a model from the approved list on page 42 of the 2012-13 AP Coordinator’s Manual. See pages 39–42 of the 2012-13 AP Coordinator’s Manual for more information. If a student does not have an appropriate calculator or has a graphing calculator not on the approved list, you may provide one from your supply. If the student does not want to use the calculator you provide or does not want to use a calculator at all, he or she must hand copy, date, and sign the release statement on page 40 of the 2012-13 AP Coordinator’s Manual.
With field theory, the entropy equilibrium equation com- posed of entropy flow of outside supply and irreversible entropy production of system interior is deduced. Ac- cording to the exergy general expression defined by gen- eralized metric and extensive quantity of dead state thermodynamics, through satellite differential, the total exergy equilibrium equation is analyzed including such transfer forms as heat exergy, press exergy, move exergy and potential-energy exergy, etc. Based on irreversible thermodynamics, liner phenomenon-logical equations which reflect the relationship among dynamics, resistance and rate for exergy transfer process of multi-field synergy are built up. The composition structure of dynamics potential field, resistance potential field and destination potential field in oil displacement region is differentiated with see- page mechanics, general physics and irreversible ther- modynamics. In the light of physical paraphrase of ex- ergy transfer for oil displacement with steam injection, combined with the evaluation method of enhancing re- covery in oilfield development region, the calculation index which reflects synergy relationship among dynam- ics potential fields, among dynamics and resistance po- tential fields, and among resistance potential fields of ex- ergy transfer in oil displacement process is deduced, thus the exergy transfer analysis system of multi-field synergy with steam injection is set up.