Formula For Energy Research Articles

An empirical approach for parameters estimation of underwater electrical wire explosion

An electrical wire explosion is a complicated process consisting of several physical phenomena such as acoustic, optical, mechanical, electromagnetic, and thermal phenomena. The shock wave from such an explosion not only has a wide range of practical applications but it also plays an important role in analyzing the process of the explosion itself. In this paper, we propose an empirical approach to estimate the pressure and energy of the shock wave in an underwater electrical wire explosion. First, the discharge process is divided into several typical phases, and the deposited electrical energy, power, and time interval between adjacent phases are calculated. Then, the shock wave peak pressure is measured and the total mechanical energy is calculated, respectively. Finally, a multiparameter fitting method is adopted to deduce an empirical formula for peak pressure and shock wave energy, and the formula was the exponential function of the deposited electrical energy, power, and the discharge time interval. In this way, the shock wave pressure and energy are quickly and reliably estimated for given discharge parameters. As for 155 shots of the discharge experiment, the average relative error and the standard deviation of peak pressure are 8.45% and 5.47%, respectively, and those of the shock wave energy of are 12.2% and 11%, respectively. This empirical approach would be very useful in pulsed power device design and in the parameters involved in electrical wire matching.

Calculation of Spectroscopic Parameters of Diatomic Molecules with an Open Electron Shell

The spectroscopic parameters of the BeH and CH molecules with an open electron shell are calculated in the basis of the Slater functions. An analytical expression for the total electron energy of molecules with an open electron shell is obtained. The total electron energy of the BeH and CH molecules was calculated by the Hartree–Fock–Roothaan (HFR) method for seven internuclear distances, including the equilibrium internuclear distance. A table of total energy values is constructed depending on the internuclear distance R. The total energy of a diatomic molecule is approximated as a third-degree polynomial in R. Applying the least squares method to energy values from the above-mentioned table, an analytical formula for the total energy of the BeH and CH molecules is obtained as a function of R. The analytical formula for E(R) has allowed the spectroscopic parameters ωe (harmonic vibrational frequency), ωexe (anharmonicity constant), Be (rotational constant), and αe (rovibrational interaction constant) to be calculated.

Homogenization of cohesive fracture in masonry structures

We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist of (i) a linear elastic contribution within the blocks, (ii) a Barenblatt’s cohesive contribution at contact surfaces between blocks, and (iii) a suitable unilateral condition on the strain across contact surfaces, and are governed by a small parameter representing the typical ratio between the length of the blocks and the dimension of the structure. Using the terminology of Γ -convergence and within the functional setting supplied by the functions of bounded deformation, we analyze the asymptotic behavior of such energy functionals when the parameter tends to zero, and derive a simple homogenization formula for the limit energy. Furthermore, we highlight the main mathematical and mechanical properties of the homogenized energy, including its non-standard growth conditions under tension or compression. The key point in the limit process is the definition of macroscopic tensile and compressive stresses, which are determined by the unilateral conditions on contact surfaces and the geometry of the blocks.

An energy-based criterion of crack branching and its application on the multidimensional space method

In this paper, a criterion of crack branching based on the energy release rate is proposed. Theory of multidimensional space method for crack branching is established in the framework of the extended finite element method (XFEM), in which the formula of the boundary shift energy is deduced. The boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model. The energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy. Further, the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching. If the crack tip branching, the criteria of crack branching are applied to determine the direction of the branching cracks, otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks. Moreover, a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method.

Spin Systems on Bethe Lattices

In an extremely influential paper Mezard and Parisi put forward an analytic but non-rigorous approach called the cavity method for studying spin systems on the Bethe lattice, i.e., the random $d$-regular graph [Eur. Phys. J. B 20 (2001) 217--233]. Their technique was based on certain hypotheses; most importantly, that the phase space decomposes into a number of Bethe states that are free from long-range correlations and whose marginals are given by a recurrence called Belief Propagation. In this paper we establish this decomposition rigorously for a very general family of spin systems. In addition, we show that the free energy can be computed from this decomposition. We also derive a variational formula for the free energy. The general results have interesting ramifications on several special cases.

Symptom: Postauricular Mass

Symptom: Postauricular Mass

Corporate power purchase agreement: Formulation of the related levelized cost of energy and its application to a real life case study

For corporate and industries the reducing of its environmental footprint is becoming more and more important, in order to improve the ‘green and social brand’ of their products and services. Many instruments may be used to this purpose but in recent years Corporate Power Purchase Agreement (CPPA) is the form of contract that is used more and more frequently. CPPA is a contract between an energy producer, from renewable sources and an end-user. Using CPPAs, the ‘green brand’ for a corporation and its product and services could be achieved. The main concern is related to the costs: still today, renewables are more expensive with respect to fossil fuels, therefore this results in higher prices for products and services, so a fair trade off between CPPA price and the gain of ‘green brand’ has to be determined. In this paper, the authors propose a method based on an opportune Levelized cost of energy formula able to support a stakeholder to define CPPA price and contractual length. A case study with significant results for a PV plant in the Italian real life application is provided. From the performed simulations emerges realistic ranges CPPA’s contractual length and price convenient for involved stakeholder. In particular the length should be not less than 7 years and not more than 10 years while the price should be in the range between 75 €/MWh and 100 €/MWh.

On the question of spin assignment and quantized alignment in the A~ 100-140 superdeformed mass region

The structure of the superdeformed (SD) mass region, A~ 100-140 is re-studied by using a direct approach based on the rotational energy formula E (I, K). To determine the lowest spin (If) and the K-value of the considered SD bands; namely, 104Pd(b1), 132Ce(b1), 134Nd(b1), 136Nd(b2), 142Sm(b1), 148Eu(b1, b2), 131Ce(b1, b2), 133Ce(b1, b2), 133Pr(b1, b3), 137Sm(b1) and 143Eu(b1), we study the dependence of the dynamic, (2) and static, (1) , moments of inertia on the rotational frequency (ℏω). Using a search method, the higher order inertial parameters A and B of such method were determined by fitting the proposed transition energies with their observed ones. The calculated transition energies are strongly dependent on the identified spins. It was found that, when an accurate bandhead spin (I0) is assigned, a good agreement is achieved between the calculated and observed transition energies. The results for the spin are in satisfactory agreement with other theoretical results and available experimental data. A good agreement between the calculated and corresponding experimental transition energies of the SD bands is obtained which supports our methodology. The incremental alignment and also the angular momentum alignment, for the identical SD bands exist among the considered ones, have been studied and the results verified well Stephens’s law of alignment.

Design Procedure and Experimental Verification of a Broadband Quad-Stable 2-DOF Vibration Energy Harvester.

Vibration-based energy harvesters brought the idea of self-powered sensors to reality in the past few years. Many strategies to improve the performance of linear vibration energy harvesters that collect energy over a limited bandwidth have been proposed. In this paper, a bi-stable two degrees of freedom (2-DOF) cut-out vibration energy harvester employing a pair of permanent magnets is designed through a proposed design methodology. Based on this methodology, the nonlinear harvesters can be optimally designed such that the bandwidth can be widened for a targeted output voltage. The proper selection of the harvester parameters as well as the gap distances between the tip and the fixed magnets are the bases of this methodology. The mathematical modeling of the proposed harvester and the formula for the potential energy between the tip and the fixed magnets are presented. Additionally, to enhance the performance of the bi-stable energy harvester (BEH), a quad-stable energy harvester (QEH) was configured by adding more fixed magnets. Experiments were performed to validate the numerical simulations and the results showed that, the simulation and experimental results are consistent. The results indicate that, the QEH covers a wider bandwidth than the BEH and based on a figure of merit the QEH shows the best performance among many harvesters presented in the literature.

Coulson integral formula for the vertex energy of a graph

The energy of a graph was introduced by Gutman (1978), this concept is related with the Hückel Molecular Orbital theory (1930), which is dedicated to the determination of energies of molecular orbitals of π electrons in conjugated hydrocarbons in theoretical chemistry. Later, Arizmendi and Juarez (2016) proposed the concept of vertex energy, with the characteristic of that energy of a graph G can be calculated by adding the individual energies of the vertices of G, since then, several advances and proposals to calculate this vertex energy has been made. In this study we prove that the vertex energy of a graph, can be also calculated in terms of a Coulson integral formula, we provide this formula and prove their effectivity and use. We present examples, and we show some applications, particularly to bipartite graphs, which includes families as paths, stars, and trees. Covering graphs for certain families were also addressed in terms of this proposal.

Calculating temperature-dependent properties of Nd2Fe14B permanent magnets by atomistic spin model simulations

Temperature-dependent magnetic properties of Nd$_2$Fe$_{14}$B permanent magnets, i.e., saturation magnetization $M_\text{s}(T)$, effective magnetic anisotropy constants $K_i^\text{eff}(T)$ ($i=1,2,3$), domain wall width $\delta_w(T)$, and exchange stiffness constant $A_\text{e}(T)$, are calculated by using \textit{ab-initio} informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd$_2$Fe$_{14}$B by using the Heisenberg exchange of Fe$-$Fe and Fe$-$Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions which is approximately expanded into an energy formula featured by second, fourth, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, $M_\text{s}(T)$, $\delta_w(T)$, and $K_i^\text{eff}(T)$ agree well with the experimental results. $A_\text{e}(T)$ is estimated through a general continuum description of the domain wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. $A_\text{e}$ is found to decrease more slowly than $K_1^\text{eff}$ with increasing temperature, and approximately scale with normalized magnetization as $A_\text{e}(T) \sim m^{1.2}$. This work provokes a scale bridge between \textit{ab-initio} calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

A theoretical framework for the biophysics of tubulins

Microtubules (MTs), the intracellular structures, are made-up of polar polymers that are composed of [Formula: see text] and [Formula: see text] tubulins. The functions of MTs are shape the way for vesicles movement and asexual mitosis division. However, one of the main functions of MTs is stability of cells. Fewer geometrical methods are available in the literature to explore the molecular dynamics (MDs) of a MT, which is a difficult task due to its microscopic size and complex structure. A structural mechanics model with rather similar properties to MT can demonstrate the dynamics of MT. The first and most important step for this process is to obtain the interaction force between tubulins, and a mechanical model can be used to simulate the mechanical and dynamical properties of MTs by using meso- and macro-scale simulations. This work reports the interaction properties of [Formula: see text]–[Formula: see text] tubulin in MT. During this research, with the aid of the MD simulations, the interaction energy in [Formula: see text]–[Formula: see text] dimer is evaluated. The alpha-beta force–distance diagram is sketched with the aid of force and energy formulae. Thus, the graphical analysis supported the findings of this study.

Activation energy and dual stratification effects for Walter-B fluid flow in view of Cattaneo-Christov double diffusionon

The purpose of the present article is to explore the novel aspects of activation energy in nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo-Christov double diffusion model over a permeable stretched sheet. Generalized forms of Fourier's and Fick's law are utilized through Cattaneo-Christov double diffusion. Walter-B nanomaterial model is used that describes the significant slip mechanism namely Brownian and thermophoresis diffusions. Double stratification, heat generation/absorption and chemical reaction are considered. Modified Arrhenius formula for activation energy is implemented. The acquired nonlinear system is cracked through homotopic analysis method. Effects of emanating variables are examined through graphs and tables. It is evident that temperature distribution and thermal boundary layer thickness is monotonically dwindling function of thermal stratification parameter(P1), thermal relaxation time (δ2) and upsurge for the thermophoresis parameter (Nt), heat generation/absorption parameter (B₁), Brownian motion parameter (Nb). Nanoparticle concentration is directly comparable to the activation energy of reaction and impact of thermal relaxation time is qualitatively opposite to that of thermophoretic force.

The Symmetrical Parabolic Approximation in College Physics

Complicated functions appearing in physics are frequently simplified by a symmetrical parabolic approximation for obtaining useful results. The symmetrical parabolic approximation is employed in many different problems in a first year college physics course. Some examples of this approximation are explored in this article. With the aid of Hamilton’s equations it is shown that the classical formula for the kinetic energy of a particle is a symmetrical parabolic approximation for the more general relativistic formula.

A simple measurement of the relative efficiency of human locomotion

Elementary formulas for gravitational potential energy, heat capacity, and Newton’s law of cooling are used to measure and compare the efficiencies of a person walking uphill and downhill. Good agreement is found for their ratio with more sophisticated experiments in the literature made by measuring respiration to determine metabolic power. A simple argument explains why human muscles are less than 50% efficient at converting chemical into mechanical energy.

Relativistic mass due to a dilatant vacuum leads to a quantum reformulation of the relativistic kinetic energy

Relativistic mass change with speed is considered here as the effect of a viscous, dilatant vacuum, whose apparent viscosity is related to the Lorentz factor. Transient solid-like vacuum due to shear stress is presented as the reason why vacuum prevents the speed of massive objects from being indefinitely increased. Such a vacuum – that in a previous study allowed to exactly calculate the Pioneer anomaly, Mercury’s perihelion precession, and was shown to be compatible with stable planetary orbits – leads here to a quantum formula for the relativistic kinetic energy. A formula which distinguishes between the case of accelerated charges in a vacuum, for which a Stokes–Einstein radius comes into play, and the case of accelerated macroscopic bodies, for which the quantum potential term vanishes. In this way, incidentally, one obtains again correct results for the Pioneer 10, confirming the role of vacuum’s viscous force. This description of a quantum mechanism underlying the relativistic kinetic energy may be also helpful in constructing a theory of quantum relativity and may even tell us more about the interactions of matter with the Higgs field and the dark sector: two issues which can be themselves linked to a dilatant vacuum.

Tremor Estimation and Removal in Robot-Assisted Surgery Using Lie Groups and EKF

SummaryThis paper aims at estimating the tremor torque using extended Kalman filter (EKF) applied to a two-link 3-DOF robot with nonlinear dynamics modelled using Lie-group and Lie-algebra theory. Later, it is generalised to d number of links with (d + 1) -DOF. The configuration of each link at any time is described by its rotation relative to the preceding link. Using this formulation, an elegant formula for the kinetic energy of the (d + 1) -DOF system is obtained as a quadratic form in the angular velocities with coefficients being highly nonlinear trigonometric functions of the angles. Properties of the Lie algebra generators and the Lie adjoint map are used to arrive at this expression. Further, the gravitational potential energy and the torque potential energy are expressed as nonlinear trigonometrical functions of the angles using properties of the SO(3) group. The input torque comprises a nonrandom intentional torque component and a highly nonlinear tremor torque component. The tremor torque is modelled as a stochastic differential equation (sde) satisfying Ornstein–Uhlenbeck (OU) process with diffusion and damping coefficients. Further, the tremor is treated as the disturbance. The Euler–Lagrange equations for the angles are derived. These form a system of sdes, and the EKF is used to get a more accurate disturbance estimate than that provided by the usual disturbance observer. The EKF is based on noisy angle measurements and yields as a bonus the angle and angular velocity estimates on a real-time basis. The parameters in the OU process model of the tremor torque, and parameters of the Fourier components of the intentional torque have also been estimated.

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume constraint. When the volume of the gas is forced away from its typical value, the system undergoes a phase transition of the third order separating two phases (pulled and pushed). We prove this result (i) for the eigenvalues of one-cut, off-critical random matrices (log-gas in dimension d=1) with hard walls; (ii) in arbitrary dimension dge 1 for a gas with Yukawa interaction (aka screened Coulomb gas) in a generic confining potential. The latter class includes systems with Coulomb (long range) and delta (zero range) repulsion as limiting cases. In both cases, we obtain an exact formula for the free energy of the constrained gas which explicitly exhibits a jump in the third derivative, and we identify the ‘electrostatic pressure’ as the order parameter of the transition. Part of these results were announced in Cunden et al. (J Phys A 51:35LT01, 2018).

Empirical evidence of a superrigid structure of “flat” superdeformed bands

For the first time, we present the empirical evidence of superrigid character of the ``flat'' superdeformed bands in the Tl and Pb isotopes. For this purpose, we have used various rotational energy formulas. The free parameters of superdeformed (SD) bands in the Tl and Pb isotopes have been extracted and systematically studied to obtain the proposed empirical evidence. In particular, the intraband transition energies of the SD bands have been split into rotational and shape fluctuation energies. The role of the vibrational factor in the evolution of dynamic moment of inertia, softness parameter, alignment, and effective pairing gap parameter of the flat SD bands has been studied. Using these models, two distinct natures have been identified for the SD bands in the Tl and Pb isotopes. Our study establishes the role of shape fluctuations, vibrational effect, deformation, and pairing correlations for the unusual behavior of the dynamic moment of inertia in the flat SD bands of the $A\ensuremath{\approx}190$ mass region.

On the number and spin of photons in classical electromagnetic fields

A relativistically invariant expression for the number of photons in a free classical electromagnetic field through the currents, that created the field, is derived based on the formula for the total energy–momentum of the field. It is demonstrated that it corresponds to the classical limit of the photon number operator known from the quantum electrodynamics. An expression for the total spin moment of the classical electromagnetic field is derived and it is shown that it can be interpreted in terms of spin moments of elementary photons. Similar to the total number of photons the classical spin moment is the limit of the quantum operator of the total spin. It is revealed that the total number of photons as well as the total spin moment are related to each other through a second order tensor, which can be expressed through currents that created the field.