Energy Theorem Research Articles

Advancement in the thermodiffusion theory of anisotropic inhomogeneous shells

ABSTRACTThis article represents the latter advancement in the modeling of diffusion processes in deformable solids. Special attention is given to the development of models for thin-walled shells with both thermal and atomic types of diffusion. Based upon these models, a number of general theorems and principles (i.e., the D'Alembert principle, Hamilton principle, mass forces analogy, Clapeyron theorem, fundamental energy theorem, and reciprocity theorem) are formulated and proved. These theorems allow for developing efficient methods for the solution of relevant boundary-value problems for the shells of this kind.

Study on Application of New Theorem of Kinetic Energy

Study on Application of New Theorem of Kinetic Energy

Proof of Positive Energy Theorem by spacetime foliations

Here we present an alternative approach, requiring only basic tools of differential geometry. This method was conceived by Kijowski and first presented during the IV Marcel Grossman Meeting on General Relativity in Rome (1986). It was later published in a generalized form by J. Jezierski, J. Kijowski in 1987 (Positivity of total energy in general relativity, Physical Review D {\bf 36} (1987), 1041-4). We summarize these results briefly and present a new foliation gauge.

Heavy Quark Entropy Shift: From the Hadron Resonance Gas to Power Corrections

A heavy quark placed in the medium modifies its specific heat. Using a renormalization group argument we show a low energy theorem in terms of the defect in the trace of the energy-momentum tensor which allows the unambiguous determination of the corresponding entropy shift after imposing the third principle of thermodynamics for degenerate states. We show how recent lattice QCD data can be understood in the confined phase in terms of a single-heavy hadronic spectrum and above the phase transition through power corrections which are analyzed by means of a dimension 2 gluon condensate of the dimensionally reduced theory.

On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature

Acceleration effects of heat flow are included in the law of heat conduction by eliminating the acceleration term between the equation of motion for a spinless electron and the Boltzmann equipartition energy theorem differentiated with respect to time. The resulting law of heat conduction is a capite ad calcem in temperature as given in Equations (17), (19) and (20). (qz/k)z = -(δT/δz) - 1/vh(δT/δt). Evaluation of use of this equation using the entropy production term reveals that as long as the flux, q, and the temperature accumulation both have the same signs, the law does not violate the second law of thermodynamics. For systems that obey the first law of thermodynamics, this is the case. σ == q/T2(q/k + 1/vh • q(δT/δt)). In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Bessel composite function in space and time of the first order and first kind. This is when τ > X. X > τ the solution is in terms of the Bessel composite function in space and time of the first order and first kind. The wave temperature is a decaying exponential in time when X = τ. An approximate expression for dimensionless temperature was obtained by expanding the binomial series in the exponent in the Laplace domain and after neglecting fourth- and higher-order terms before inversion from the Laplace domain. The Fourier model, the damped wave model and the a capite ad calcem in temperature/concentration model solutions are compared side by side in the form of a graph. The a capite ad calcem model solution is seen to undergo the convex to concave transition sooner than the damped wave model. The results of the a capite ad calcem temperature model for distances further from the surface are closer to the Fourier model solution.

Rigid–elastic-thermal coupling dynamics and its application

Spacecraft dynamics belongs to rigid–elastic coupling dynamics in general. If thermal stress and thermal effect are further considered, it will cause the more complex rigid–elastic-thermal coupling dynamics. For the aforementioned kind of coupling dynamics, it is difficult to establish the basic equations directly. It has proved that a suitable way to study complex coupling problems is by work–energy theorem and the law of conversation of energy. Using the energy method, Hamilton principle of rigid–elastic-thermal coupling dynamics is established. The stationary value conditions of Hamilton principle of rigid–elastic-thermal coupling dynamics are derived. The physical meaning of the stationary value conditions is indicated. As an application of rigid–elastic-thermal coupling dynamics, the actual example of spacecraft is given to reveal that there existed thermal stiffening or softening problems in rigid–elastic-thermal coupling dynamics, just like dynamic hardening or softening problems in spacecraft dynamics.

Feynman and the kinetic energy of an ice skater

By employing the angular momentum and mechanical energy theorems, we analyse the increase of the angular velocity for an ice skater who changes his arms, initially in an horizontal position, along the axis of the body, first with respect to the lab frame, in which a variation of kinetic energy is observed, and then with respect to the rotating frame moving with the skater. In the last one, while there is no variation of kinetic energy between initial and final positions, the work of the centrifugal force is the opposite to the variation of kinetic energy in the lab frame. We discuss the explanation given by Richard Feynman in his Mechanics course.

Recent progress on the positive energy theorem

We give a short review of recent progress on the positive energy theorem in general relativity, especially for spacetimes with nonzero cosmological constant.

MATHEMATICAL MODELS OF A REQUIRED POWER DESIGN FOR IRRIGATION WITH SMALL-SIZED ELECTRIC MOTORS

Irrigation methods in rural areas usually consist of pumping water from dams and reservoirs by engines connected to the electric power station or powered with diesel oil. Current assay establishes mathematical models for scaling low-power electric motors for irrigation in small cultivated areas. Equations of engine power were determined by numerical integration and by the theorem of kinetic energy. A geometric model was established with a paraboloid of revolution to determine the volume of the reservoir. A 3600 m² area was irrigated during 4 h, 380 m distant from the dam, with a 21° slope, for simulation purposes. The amount of water for irrigation was 5 U m² by means of a dam with diameter 14 m and 5 m deep. The establishment of mathematical models scaled up a 2.5 hp engine with a removal of 5000 L of water from a 385 000 L dam, with a variation of 7.2 cm and the immersion of the engine below this borderline.

Elastic buckling behavior of steel trapezoidal corrugated shear walls with vertical stiffeners

This paper investigates the elastic buckling behavior of steel trapezoidal corrugated shear walls (STCSWs) with vertical stiffeners. On the basis of an orthotropic plate model, by utilizing the theorem of minimum potential energy and the Ritz method, the buckling loads of stiffened STCSWs can be precisely calculated using MATLAB. Then, a value of transition rigidity of stiffener is suggested and, hence formulas of elastic buckling coefficients of stiffened STCSWs are proposed. Finally, the verification of proposed formulas using a FE model shows that the formulas are validated and applicable in estimating the elastic buckling loads of stiffened STCSWs.

Axion induced oscillating electric dipole moments

The axion electromagnetic anomaly induces an oscillating electric dipole for {\em any} static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low energy theorem which is a consequence of the space-time dependent cosmic background field of the axion in the limit that it is only locally time dependent $(\overrightarrow{\beta}=0)$. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\sim 10^{-32}$ e-cm, three orders of magnitude above the nucleon, and within four orders of magnitude of the present standard model DC limit. This may suggest sensitive new experimental venues for the axion dark matter search.

The positive energy theorem for asymptotically anti-de Sitter spacetimes

We establish the inequality for Henneaux–Teitelboim's total energy–momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary t-slice in anti-de Sitter spacetime. In particular, when t = 0, it generalizes Chruściel–Maerten–Tod's inequality in the center of AdS mass coordinates. We also show that the determinant of energy–momentum endomorphism Q is the geometric invariant of asymptotically anti-de Sitter spacetimes.

Suitability of optimized truss model to predict the FRP contribution to shear resistance for externally bonded FRP strengthened RC beams without internal stirrups

Shortcoming in the current design guidelines on externally bonded FRP shear strengthened members has initiated a motivation to relook the whole shear design approach. It is understood that effective FRP strain models used in present design guidelines are basically calibrated from the experimental data based on the conservative and unrealistic 45-deg truss model. This paper is intended to propose an optimized truss model that derived from the principle of minimum total strain energy theorem to improve the present 45-deg truss model. The proposed optimized truss model is characterized with limiting failure criteria that reflects truly to the actual FRP strengthened beam behaviour. One of the most important failure criteria is the FRP debonding failure. To characterize it, limiting effective FRP strain εfrp,e model is incorporated into the optimized truss model. Six most recent effective strain models are chosen for the analysis, included three of the international design guidelines. Performance of each effective strain model will be evaluated along with the optimized and 45-deg truss models in order to assess their respective accuracy in predicting the FRP contribution to the shear strength. The validation of optimized truss model is done through comparing with experimental test results collected from the literature. The results obtained indicated that the optimized truss model is indeed more viable representative to the actual internal stress distribution and accurate than existing 45-deg truss model. So it might have a great potential to be used in the derivation of a new effective FRP strain model that can be implemented in the current design guidelines.

Transport properties of hadronic matter in magnetic field

We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to 0.1 GeV and increases with magnetic field while ratio ζ/s decreases with magnetic field. We also find that shear viscosity coefficient of hadronic matter decreases with magnetic field.

Positive energy theorem forP(X, ϕ)theories

We describe a positive energy theorem for Einstein gravity coupled to scalar fields with first-derivative interactions, so-called P(X,phi) theories. We offer two independent derivations of this result. The first method introduces an auxiliary field to map the theory to a lagrangian describing two canonical scalar fields, where one can apply a positive energy result of Boucher and Townsend. The second method works directly at the P(X,phi) level and uses spinorial arguments introduced by Witten. The latter approach follows that of arXiv:1310.1663, but the end result is less restrictive. We point to the technical step where our derivation deviates from theirs. One of the more interesting implications of our analysis is to show it is possible to have positive energy in cases where dispersion relations following from locality and S-Matrix analyticity are violated.

Parametric instability of flexible rotor-bearing system under time-periodic base angular motions

Parametric instability of flexible rotor-bearing system under time-periodic base angular motions is analyzed in this paper. The accurate finite element model for the flexible rotor-bearing system under time-varying base angular motions is derived based upon the energy theorem and Lagrange’s principle. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Considering the time-varying base movements, the second order differential equations of the system will have time-periodic gyroscopic and stiffness coefficients. The discrete state transition matrix (DSTM) method is introduced for numerically acquiring the instability regions. Based upon these, instability computations for a rotor-bearing system with one base motion alone and two base motions together are conducted, respectively. The effects of rotating speed, amplitudes of base motion and phases between two base motions on both the primary and combination instability regions are discussed in detail.

Energy conversion within infrared plasmonic absorption metamaterials for multi-band resonance

The energy conversion within the cross-shaped plasmonic absorber metamaterials (PAM) was investigated theoretically and numerically in the infrared range based on the Poynting's theorem of electromagnetic energy. From the microscopic details, the heat generation owing to the electric current accounts for the majority of the energy conversion, while the magnetic resonance plays a negligible role. The PAMs possess three distinct resonant peaks standing independently, which are attributed to the polarization sensitive excitation of plasmonic resonance. Field redistribution and enhancement associated with multiplex resonant electromagnetic wave passing through the PAM medium provided insight into the energy conversion processes inside the nanostructure. The research results will assist the design of novel plasmon enhanced infrared detectors with multiple-band detection.

Bulk and shear viscosities of hot and dense hadron gas

We estimate bulk and shear viscosity at finite temperature and baryon densities of hadronic matter within hadron resonance gas model. For bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For shear viscosity coefficient, we estimate the same using molecular kinetic theory to relate the shear viscosity coefficient to average momentum of the hadrons in the hot and dense hadron gas. The bulk viscosity to entropy ratio increases with chemical potential and is related to the reduction of velocity of sound at nonzero chemical potential. The shear viscosity to entropy ratio on the other hand, shows a nontrivial behavior with the ratio decreasing with chemical potential for small temperatures but increasing with chemical potential at high temperatures and is related to decrease of entropy density with chemical potential at high temperature due to finite volume of the hadrons.

Asymptotics with a positive cosmological constant: I. Basic framework

The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant Λ is zero. The resulting framework lies at the foundation of research in diverse areas in gravitational science. Examples include: (i) positive energy theorems in geometric analysis; (ii) the coordinate invariant characterization of gravitational waves in full, nonlinear general relativity; (iii) computations of the energy–momentum emission in gravitational collapse and binary mergers in numerical relativity and relativistic astrophysics; and (iv) constructions of asymptotic Hilbert spaces to calculate S-matrices and analyze the issue of information loss in the quantum evaporation of black holes. However, by now observations have led to a strong consensus that Λ is positive in our universe. In this paper we show that, unfortunately, the standard framework does not extend from the case to the case in a physically useful manner. In particular, we do not have positive energy theorems, nor an invariant notion of gravitational waves in the nonlinear regime, nor asymptotic Hilbert spaces in dynamical situations of semi-classical gravity. A suitable framework to address these conceptual issues of direct physical importance is developed in subsequent papers.

Hyperbolic positive energy theorem with electromagnetic fields

We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein–Maxwell initial data sets by Wittenʼs spinoral techniques.