Conservation Laws In Mechanics Research Articles

Activation energy and convective heat transfer effects on the radiative Williamson nanofluid flow over a radially stretching surface containing Joule heating and viscous dissipation

This article recognizes the time-dependent axisymmetric flow of a non-Newtonian Williamson fluid caused by a radially stretching surface in the presence of nanoparticles in the porous medium. The combined impacts of Joule heating and viscous dissipation on the flow profiles are also discussed. Chemical reaction at the surface is implemented. The convective heat transfer model and Brownian motion are also studied for the electrically conducting nanofluid flow. The Williamson nanofluid flow has been modeled using a set of partial differential equations based on the fundamental conservation laws of mechanics. By using nondimensional quantities, these equations are first transformed into ordinary differential equations. The Galerkin weighted residual method is performed to resolve these equations numerically. Visual displays and detailed descriptions of the impacts of relevant variables on the thermal performance, concentration field, and velocity field are provided. It is noticed that the thermal profile enhances as the values of the Brownian motion parameter and temperature ratio parameter increase while declining when the values of the velocity slip parameter increase. The Biot number, activation energy, and unsteadiness parameters have proportional effects on the concentration profile, but the reaction parameter has inversely proportional effects on the concentration profile. Heat transfer rate increases with increasing the Weissenberg number and velocity slip parameter, drops with increasing the thermophoresis and unsteadiness parameters, and the Arrhenius activation energy. Finally, a comparison of the obtained numerical solution for the porous and nonporous medium are also done graphically and discussed in details.

Understanding Newton’s cradle. II: exploring a real cradle

Newton’s cradle is a well-known physics toy that is commonly used by teachers to demonstrate conservation laws in mechanics. It can also be used to investigate the physics of colliding objects, by recording motion of the balls on video film. Various experiments are described using 3-ball and 5-ball cradles, showing how different types of collision can be investigated depending on whether the balls are touching or separated. The sequence of collisions was examined as a function of time, with the surprising observation that very small gaps between the balls, invisible on video film, make a significant difference to the collision dynamics. Additional experiments illustrate the effects of changes in ball stiffness and the mass of the middle ball and provide an introduction for students and teachers into possible research projects. Each experiment is illustrated with a supplementary video.

Numerical Examination of Thermophysical Properties of Cobalt Ferroparticles over a Wavy Surface Saturated in Non-Darcian Porous Medium

Abstract In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and tables. The results show that for large values of the magnetic parameter, both the Nusselt number and the average Nusselt number decrease in ferrofluid flow. The value of the Nusselt number in the Darcy model is higher than the value of the Nusselt number in the non-Darcy model.

Eugene Garfield: from the metrics of science to the science of metrics

Quantity and quality are Aristotelian categories. Ever since Galileo, the defining feature of Science is the accurate measure of quantity, e.g., time, length and mass, to begin with. Length and mass are size dependent. Quality remained an elusive category as it is a size-independent feature. It was Archimedes who first brought a revolution in physics by defining density as a size-independent attribute. A similar revolution was effected in the measurement of science when Eugene Garfield introduced the concept of the citation as a unit of measurement and from this, separated quantity (number of publications) from quality (impact). In this article, we interpret impact as a thermodynamic mean instead of a simplistic arithmetic mean. This opens up rich analogies with the conservation laws of mechanics and thermodynamic features linking disorder and unevenness to entropy. Also as in physics, considerations of dimensional homogeneity play a defining role. Without Garfield’s bold initiative, all this will have eluded us for some time.

Rock Directed Breaking Under the Impulse Load

In the work the problem of directed chipping of facing stone material by means of managing of explosion process is considered. The technology of the mining of decorative stone by the use of explosion energy means the very rapid transfer of potential energy of elastic deformations to kinetic energy. As a result, the explosion impulse, in the expanse of the inertia of rock massive, does not cause the increase of existing cracks. In the course of explosion, the shock wave is propagated by ultrasonic velocity and in this case the medium parameters (pressure, density, temperature, velocity) increase in spurts. In spite of this fact the all three conservation laws of mechanics remain valid on basis of three laws the equations are derived by which the parameters of shock wave may be defined by means of the rock physical-mechanical properties. The load on the body volume at breaking under explosion acts over very small period of the time. Therefore, stressed-deformed state of the rock was studied when the impulse load acts on the boundary. It was considered that the mining of the blocks of facing stone is performed from the hard rocks. This means that the breaking proceeds in the zone of elastic deformation. In the conditions of mentioned assumptions, the expression of the stress tensor and displacement of vector components initiated by stressed-deformed state in the rock are written.

An Eulerian method for finite deformation anisotropic damage with application to high strain-rate problems

This paper is dedicated to establishing a thermodynamically compatible Eulerian theoretical framework for elastoplastic anisotropically damaging materials, that is applicable to high strain rate and strongly compressible problems. The proposed model comprises a system of thermodynamically compatible balance laws based upon hyperelastic-inelastic theory: the mechanical conservation laws are supplemented by kinematic evolution equations for material deformation gradients, which can be written in conservative form. The formulation is rotationally invariant and hyperbolic, with a determinable characteristic structure. An operator split approach is proposed for integrating the governing constitutive models for three-dimensional Cauchy problems, in conjunction with a ghost material numerical method to resolve internal Dirichlet boundaries. Such methods naturally allow the generation of new internal boundaries making them ideal for simulating fragmenting materials and macroscale fracture. A remarkable feature of the proposed approach is that the overall complexity compares favourably with that of the model for elastoplastic deformations only. The simulation of expanding ring and flyer plate experiments are chosen to demonstrate the effectiveness of the proposed approach.

Adaptive resolution simulation in equilibrium and beyond

In this paper, we investigate the equilibrium statistical properties of both the force and potential interpolations of adaptive resolution simulation (AdResS) under the theoretical framework of grand-canonical like AdResS (GC-AdResS). The thermodynamic relations between the higher and lower resolutions are derived by considering the absence of fundamental conservation laws in mechanics for both branches of AdResS. In order to investigate the applicability of AdResS method in studying the properties beyond the equilibrium, we demonstrate the accuracy of AdResS in computing the dynamical properties in two numerical examples: The velocity auto-correlation of pure water and the conformational relaxation of alanine dipeptide dissolved in water. Theoretical and technical open questions of the AdResS method are discussed in the end of the paper.

Coarse graining strategies at walls

We review four fundamental approaches to include system boundaries into the coarse graining formalism, particularly with regard to simulations of granular media, and formulate criteria for evaluating their usability. A simple lattice system illustrates their application and respective advantages. We show that only one of them is able to fully reproduce the conservation laws of mechanics without further restrictions. Nevertheless, some of the other schemes are found to be better suited when dynamics is not the subject of interest.

Metric space formulation of quantum mechanical conservation laws

We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an ``onion-shell'' geometry. We demonstrate the power of this approach by considering many-body systems immersed in a magnetic field, with a finite ground state current. In the associated metric spaces we find regions of allowed and forbidden distances, a ``band structure'' in metric space directly arising from the conservation of the $z$ component of the angular momentum.

The mechanical career of Councillor Orffyreus, confidence man

In the early 18th century, J. E. E. Bessler, known as Orffyreus, constructed several wheels that he claimed could keep turning forever, powered only by gravity. He never revealed the details of his invention, but he conducted demonstrations (with the machine's inner workings covered) that persuaded competent observers that he might have discovered the secret of perpetual motion. Among Bessler's defenders were Gottfried Leibniz, Johann Bernoulli, Professor Willem 's Gravesande of Leiden University (who wrote to Isaac Newton on the subject), and Prince Karl, ruler of the German state of Hesse-Kassel. We review Bessler's work, placing it within the context of the intellectual debates of the time about mechanical conservation laws and the (im)possibility of perpetual motion. We also mention Bessler's long career as a confidence man, the details of which were discussed in popular 19th-century German publications but have remained unfamiliar to authors in other languages.

Function of longitudinal бvs�� circular muscle fibers in esophageal peristalsis, deduced with mathematical modeling

We summarize from previous works the functions of circular vs. longitudinal muscle in esophageal peristaltic bolus transport using a mix of experimental data, the conservation laws of mechanics and mathematical modeling. Whereas circular muscle tone generates radial closure pressure to create a local peristaltic closure wave, longitudinal muscle tone has two functions, one physiological with mechanical implications, and one purely mechanical. Each of these functions independently reduces the tension of individual circular muscle fibers to maintain closure as a consequence of shortening of longitudinal muscle locally coordinated with increasing circular muscle tone. The physiological function is deduced by combining basic laws of mechanics with concurrent measurements of intraluminal pressure from manometry, and changes in cross sectional muscle area from endoluminal ultrasound from which local longitudinal shortening (LLS) can be accurately obtained. The purely mechanical function of LLS was discovered from mathematical modeling of peristaltic esophageal transport with the axial wall motion generated by LLS. Physiologically, LLS concentrates circular muscle fibers where closure pressure is highest. However, the mechanical function of LLS is to reduce the level of pressure required to maintain closure. The combined physiological and mechanical consequences of LLS are to reduce circular muscle fiber tension and power by as much as 1/10 what would be required for peristalsis without the longitudinal muscle layer, a tremendous benefit that may explain the existence of longitudinal muscle fiber in the gut. We also review what is understood of the role of longitudinal muscle in esophageal emptying, reflux and pathology.

A novel systems biology/engineering approach solves fundamental molecular mechanistic problems in bioenergetics and motility

A large number of new insights and further intricate details of the molecular mechanisms of ATP synthesis and muscle contraction have been offered from the perspective of the torsional mechanism of energy transduction and ATP synthesis and the rotation-uncoiling-tilt (RUT) energy storage mechanism of muscle contraction. In this paper, a new systems thermodynamics analysis of oxidative- and photo-phosphorylation has been performed. New experimental data has been reported on the inhibition of ATP synthesis by known specific anion channel blockers: the triorganotin compound, tributyltin chloride (TBTCl), and the stilbene compound 4,4′-diisothiocyanostilbene-2,2′-disulfonate (DIDS), and interpreted as supporting the new framework. A bioinformatic analysis of the interacting a–c regions in F O has been carried out to locate the anion binding pocket in the anion–proton symsequenceporter and insights into the coordination chemistry of the bound chloride in its internal cavity at the lipid–water interface have been obtained. The need to look at ATP synthesis in F O as a multisubstrate reaction has been emphasized and a detailed microscopic explanation of the mechanism of inhibition by these blockers and its relationship to the conformational cycle within F O has been postulated. Such detailed explanations of the role of membrane elements in a lipophilic region have been shown to lead to deeper understanding and to offer a more realistic and complete picture of biological energy transduction than considering the bilayer as “mere insulation”, as in chemiosmotic dogma. Details of the elementary force production events by myosin II have been provided within the novel molecular systems framework of the RUT mechanism in which the S-1, the S-1–S-2 hinge, and the S-2 coiled coil all have essential roles in the in vivo contractile process. The new paradigm is shown to be consistent with the great body of experiments usually considered to support the swinging crossbridge/lever arm models of muscle contraction, because these events also occur during the cycle but as events preliminary to the occurrence of the power stroke. The crucial role of energy storage in mechanically strained nonequilibrium conformational states of myosin, specifically as a high-energy state of S-2 with uncoiled first few N-terminal heptads is highlighted. The propensity of these heptads to recoil and regain the resting state of the coiled coil is postulated to be a primary driving force of the power stroke. The new paradigms of ATP synthesis/muscle contraction have been shown to remove the inconsistencies present in previous theories and to have the sound backing of the first and second laws of thermodynamics, the principle of electrical neutrality, the laws of Newtonian mechanics, and the great conservation laws of mechanics. A systems integration of muscle contraction has been successfully made and a systems electrical analog constructed. The unifying laws and principles in the new theories have been further applied to understand the functioning of other protein molecular machines such as kinesin, ncd and unconventional myosins. Finally, the major physical, chemical, biological and technological implications arising as a result of this research have been discussed. Taken together, the new paradigms have been shown to solve fundamental molecular mechanistic problems in bioenergetics and motility and to offer a most detailed, unified and appealing picture of energy generation, transduction, storage and utilization processes in systems of biological molecular machines.

New insight into optimization and variational problems in the 17th century

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

Transient free surface flows via a stabilized ALE finite element method

AbstractFree surface problems appear in a wide range of industrial and engineering applications, e.g. when modeling sloshing of fluid in a container or when tracking the free surface evolution in casting and molding processes. A finite element technique is presented to study time‐dependent large free surface motions of viscous, incompressible fluids. The approach is based upon an arbitrary Lagrangean‐Eulerian (ALE) representation of kinematics and field equations, i.e. continuum mechanical conservation laws. Both convective effects and equal‐order interpolation for velocities and pressure are stabilized in a Galerkin least‐squares sense. This leads to a fully stabilized finite element method (FEM) for the governing instationary incompressible Navier‐Stokes equations. The algorithmic setup is complemented by a combination of the stabilized FEM with direct time integration procedures and fixed point‐like iterative schemes. The performance of the overall algorithm is demonstrated with the help of selected two‐dimensional numerical examples.

Another surprise in mechanics

We recently published a note describing a spectacular mechanics demonstration. It illustrated simultaneously the three conservation laws of mechanics for momentum, energy, and angular momentum and resulted in an amazingly counterintuitive outcome. In this article we are reporting on a follow-up of a conjecture by Professor John Mallinckrodt of the California State Polytechnic University.

Thermodynamic equivalence of steady-state shocks and smooth waves in general media; Applications to elastic-plastic shocks and dynamic fracture

By comparing the First Law of thermodynamics in its shock wave form to its smooth wave form, and applying standard continuum mechanical conservation laws and geometrical compatibility, we prove for arbitrary media that a shock wave which propagates without rotating under steady-state conditions is thermodynamically identical to a suitably-chosen steadily propagating smooth wave (and that this is not so in general for nonsteady shocks). This legitimizes the derivation of restrictions on steady-state shock waves by the analysis of suitably-chosen steady smooth waves in purely mechanical material models. Doing so for a broad class of rate-independent elastic-plastic materials rigorously corroborates several recentlypublished shock restrictions whose derivations involved some (now validated) heuristic arguments, and substantially generalizes the material class for which these restrictions apply. Thus, e.g. within smalldisplacement-gradient theory, stress jumps are ruled out across steadily propagating shock waves in quasistatic deformations of any nonsoftening material satisfying plastic normality and positive-definiteness of the elastic modulus tensor (removing the previous limitation of this result to materials that satisfy the global maximum plastic work inequality and whose current yield locus always incorporates all prior yield loci). We also confirm that steady-state shock waves in dynamic anti-plane strain or plane strain deformations cannot exist except at elastic wave speeds for nonhardening materials in the same broad constitutive class unless the yield surface contains a linear segment. Application of these results to steady-state dynamic subsonic plane strain crack growth in elastic-ideally plastic Prandtl-Reuss-Mises material proves that this problem's solution must be shock-free. This implies that certain solutions containing strong discontinuity surfaces, obtained in a recently-published numerical finite element study of this dynamic crack growth problem, are not physically realizable. The conclusion is that either a more robust numerical procedure is necessary which incorporates the thermodynamics-mandated shock restrictions derived here, or that steadystate subsonic dynamic plane-strain elastic-plastic crack growth is not possible in this material model (and potentially not in nature for materials exhibiting plastic normality, purely nonlinear yield surfaces and no hardening).

A thought-provoking demonstration

We present and discuss a physics demonstration, similar to, but distinct from, the ballistic-pendulum demonstration, one that illustrates all three conservation laws of mechanics (for energy, momentum, and angular momentum) simultaneously.

Discussion of Thermomechanics on the Basis of Frame Invariance of Physical Law

In continuum mechanics it is not clear what principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also frame transformation laws of constitutive quantities and source (quantities are simultaneously derived for a changing frame under the assumption that the forms of the first and second laws of thermodynamics are invariant for changes of frame. Next, considering whether the reverse proposition is true or false, an explanation of the relationship between the PMFI and the invariance of the laws of thermodynamics for changes of frame is given. Then the bases of the PMFI are determined, clarifying the relationship between the PMFI and the frame invariance of the Clausius-Duhem inequality. Moreover, it is indicated that this method, which enables derivation of conservation laws using changes of frame, is equivalent to both the principle of virtual power and the method of Green and Rivlin.

Understanding conservation laws in mechanics: Students' conceptual change in learning about collisions

Understanding conservation laws in mechanics: Students' conceptual change in learning about collisions

Thermodynamical Discussions for Standpoint of Principle of Material Frame Indifference.

In continuum mechanics it is not clear what kind of principle is equivalent to the principle of material frame indifference (PMFI). In the present paper, it is first shown that not only mechanical conservation laws but also rules of frame transformation for constitutive quantities and source quantities are simultaneously derived by changing frame on the assumption that the forms of the first and second laws of thermodynamics are invariant for the changes of frame. Next, considering whether the reverse proposition is true or false, an explanation is given for the relation between the PMFI and the invarinance of the laws of thermodynamics for the changes of frame. Then the essential standpoint of PMFI is definitely placed, making the relation between the PMFI and the frame-invariance of Clausius-Duhem inequality clear. Moreover it is indicated that the method which derives the conservation laws using the changes of frame is equivalent to both the principle of virtual power and the method by Green-Rivlin.