Formula For Energy Research Articles

Crashworthiness assessment of thin-walled double bottom tanker: Influences of seabed to structural damage and damage-energy formulae for grounding damage calculations

This work presents results of numerical analyses with focus on structural performance accounting for seabed topology, and investigation of energy formulae for application in calculation of grounding damage. Study in this work is divided into three stages, i.e. finite element method (FEM) verification using laboratory experiment, numerical calculation of ship grounding using FEM, and comparison of the FEM results with empirical formulae of damage-energy calculation. Fundamental formula of Minorsky is considered with other improvement expression, such as Woisin and Zhang. Investigation suggested that the recent-developed expression produces the closest estimation to the verified FEM results. On the other hand, fundamental formulae of Minorsky is the farthest compared to the FEM, which indicates constant value in the expression needs to be more specific as improved in the Woisin formula.

Interfacial mechanical properties of graphene/titanium in composites based on beam search algorithm

AbstractThe interface mechanical properties of graphene and titanium composites in traditional studies lack molecular dynamics simulation and cannot construct composite interface model. A method for studying the interfacial mechanical properties of graphene/titanium in composite materials based on beam search algorithm is proposed, using the beam search algorithm to simulate the tensile deformation of graphene and titanium to establish the graphene/titanium single and dual interface model. Using the molecular dynamics method to simulate the mechanical behavior of multilayer graphene interface, the interface model of graphene/titanium composites is constructed according to the simulation results, and the calculation formula of interface interaction energy is obtained. The experimental results show that using the proposed method, the graphene/titanium dual interface model has higher interlayer electron density than the single interface model, the electronic characteristics are smoother at the interface transition, and the interface is more stable. Graphene has an interfacial interaction with the titanium atoms adjacent to the upper and lower layers, and has the strongest covalent interaction with the nearest titanium atom layer, which is beneficial to reduce the energy of the composite system and improve the stability of the graphene/titanium composites.

Energy partition for anharmonic, undamped, classical oscillators

Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of |x|ν, (ν > 0) type energies are equipartitioned for the harmonic potential only. For potential wells weaker than parabolic potential energy dominates, while for potentials stronger than parabolic kinetic energy prevails. Due to energy conservation, the variances of kinetic and potential energies are equal. In the limiting case of the infinite rectangular potential well (ν → ∞) the whole energy is stored in the form of the kinetic energy and variances of energy distributions vanish.

Pocket formula for alpha decay energies and half-lives of actinide nuclei

Abstract It is important to construct the correct formula for alpha decay half-lives. The present work verifies the validity of Geiger–Nuttall law (GNL) for actinides and hence presenting the simple empirical formula for alpha decay energies and halflives for actinides based on the available experimental results. We have studied the variation of logarithmic halflives with Z d n Q − 1 / 2 ${Z}_{d}^{n}{Q}^{-1/2}$ for different values of n (0.2–1). The variation of logarithmic halflives with Z d n Q − 1 / 2 ${Z}_{d}^{n}{Q}^{-1/2}$ is found to be linear for which n = 0.6. The values produced by the present formula compared with that of experiments. The present formulae successfully produces the alpha decay half-lives and Q-value in the actinide region. This formula is specially for actinide parent nuclei only.

Ignition criteria for x-ray fast ignition inertial confinement fusion

The derivation of the ignition energy for fast ignition inertial confinement fusion is reviewed and one-dimensional simulations are used to produce a revised formula for the ignition energy of an isochoric central hot-spot, which accounts for variation in the radius of the hot-spot rh as well as the density ρ. The required energy may be as low as 1 kJ when ρrh≈0.36 g cm−2, T≈20 keV, and ρ≥700 g cm−2. Although there are many physical challenges to creating these conditions, a possible route to producing such a hot-spot is via a bright source of non-thermal soft x-rays. Further one-dimensional simulations are used to study the non-thermal soft x-ray heating of dense DT and it is found to offer the potential to significantly reduce hydrodynamic losses as compared to particle driven fast ignition due to the hotspot being heated supersonically in a layer-by-layer fashion. A sufficiently powerful soft x-ray source would be difficult to produce, but line emission from laser-produced-plasma is the most promising option.

Effects of nonlinear parameter of fluid-solid coupling on acoustic field in porous media.

The purpose of this Letter to the Editor is to demonstrate the effects of the nonlinear parameter of fluid-solid coupling on the acoustic field in porous media. The nonlinear acoustic field excited by a one-dimensional finite-amplitude shear wave propagating in the uniform and infinite saturated porous media is studied. Researchers use the complete strain energy formula with third-order terms of strain in saturated porous media. The formula for calculating the fluid-solid coupling nonlinear parameter γ from the dynamic compatibility condition is given. To illustrate the effect of the fluid-solid coupling nonlinear term on the nonlinear acoustic field excited by the longitudinal and transverse waves, this study compares nonlinear acoustic fields excited by a finite amplitude wave with and without nonlinear parameter γ. The results show that the nonlinear parameter γ has an influence on the nonlinear acoustic field excited by the one-dimensional shear wave, but it has no influence on the nonlinear acoustic field excited by the one-dimensional longitudinal wave.

Toverline{T} and EE, with implications for (A)dS subregion encodings

We initiate a study of subregion dualities, entropy, and redundant encoding of bulk points in holographic theories deformed by Toverline{T} and its generalizations. This includes both cut off versions of Anti de Sitter spacetime, as well as the generalization to bulk de Sitter spacetime, for which we introduce two additional examples capturing different patches of the bulk and incorporating the second branch of the square root dressed energy formula. We provide new calculations of entanglement entropy (EE) for more general divisions of the system than the symmetric ones previously available. We find precise agreement between the gravity side and deformed-CFT side results to all orders in the deformation parameter at large central charge. An analysis of the fate of strong subadditivity for relatively boosted regions indicates nonlocality reminiscent of string theory. We introduce the structure of operator algebras in these systems. The causal and entanglement wedges generalize to appropriate deformed theories but exhibit qualitatively new behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads to subtleties which we express in terms of the Hamiltonian and modular Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points, including the cosmological case.

Improved Multilayered (Bi,Sc)O3-(Pb,Ti)O3 Piezoelectric Energy Harvesters Based on Impedance Matching Technique.

As a piezoelectric material, (Bi,Sc)O3-(Pb,Ti)O3 ceramics have been tested and analyzed for sensors and energy harvester applications owing to their relatively high Curie temperature and high piezoelectric coefficient. In this work, we prepared optimized (Bi,Sc)O3-(Pb,Ti)O3 piezoelectric materials through the conventional ceramic process. To increase the output energy, a multilayered structure was proposed and designed, and to obtain the maximum output energy, impedance matching techniques were considered and tested. By varying and measuring the energy harvesting system, we confirmed that the output energies were optimized by varying the load resistance. As the load resistance increased, the output voltage became saturated. Then, we calculated the optimized output power using the electric energy formula. Consequently, we identified the highest output energy of 5.93 µW/cm2 at 3 MΩ for the quadruple-layer harvester and load resistor using the impedance matching system. We characterized and improved the electrical properties of the piezoelectric energy harvesters by introducing impedance matching and performing the modeling of the energy harvesting component. Modeling was conducted for the piezoelectric generator component by introducing the mechanical force dependent voltage sources and load resistors and piezoelectric capacitor connected in parallel. Moreover, the generated output voltages were simulated by introducing an impedance matching technique. This work is designed to explain the modeling of piezoelectric energy harvesters. In this model, the relationship between applied mechanical force and output energy was discussed by employing experimental results and simulation.

The Energy of the Electrostatic Field

The work is actual due to the increased role of electrostatic energy in connection with the beginning of mass production of ionistors used in the power supply system of electric vehicles, and the need for the development of theoretical support. (Research purpose) The research purpose is in increasing the correctness of electrostatic calculations that exclude the possibility of obtaining unreliable results in the form of infinite electrostatic energy. (Materials and methods) Authors have used methods of mathematical modeling and analysis, studied the mathematical model as the equivalent of an object that reflects in mathematical form its most important properties, such as the laws that it obeys, and the relationships inherent in its constituent parts. (Results and discussion) Authors have studied the electrostatic field created by a system of two charges of the same name or different names. The article presents calculations for charges located in bodies that have the shape of balls. It was found that the results could be generalized to any form of charged objects. They gave three definitions: first, the total stored energy is the energy of the system or object, equal to the maximum work that the system or object can do if it is given such an opportunity. Second, the conditional realized stored energy is a part of the total stored energy of the system or object, equal to the work that the system or object can produce, limited by a condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. The third is a conditional impossible reserved energy as a part of a complete stored energy system or an object that is equal to the work system or object can do and limited by the condition, which excludes the possibility of making a system or object maximum work that target system or object could hypothetically do. Five theorems were proved. (Conclusions) It was found that the main drawback of the actual potential energy formula is an infinitely large increase in energy at radius tending to 0. The obtained formulas for stored electrostatic energy are devoid of this drawback.

The SK Model Is Infinite Step Replica Symmetry Breaking at Zero Temperature

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

COLLECTIVE POTENTIAL FOR HEAVY ION NUCLEAR REACTIONS

It is shown that the nuclear charge polarisation during heavy ion nuclear reactions enhances the secondary maximum of the collective energy surface and produces a secondary minimum in the deformation energy near R ~ Rmin + 2fm. The potential energy and mass formulas are given as a function of A and Z. It has been shown that charge polarisation without shape deformation and indeed of the prolate type does not produce any secondary minimum. It is also seen that the relativity effect consists in shifting the secondary minimum towards higher rest excentricities. For deformation of the oblate type the collective potential has a similar form like that in the spherical case. Entry and exit channel collective potentials are also given for the case of strong nucléon transfer. The mass for the two-body interacting system has been calculated and for large distances it tends to the corresponding reduced mass. The present theory is based on a particular form of the single particle potential following from the scalar π-meson classical field theory.

QUANTUM ALGEBRAIC SYMMETRIES IN NUCLEAR AND MOLECULAR PHYSICS

The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are presented. Rotational spectra of even-even nuclei are described by the quantum algebra SUq(2). The two parameter formula given by the algebra is equivalent to an expan- sion in terms of powers of j(j + 1), similar to the expansion given by the Variable Moment of Inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values. The same formalism is found to give very good results for superdeformed nuclear bands, which are closer to the classical SU(2) limit, as well as for rotational bands of diatomic molecules, in which a partial summation of the Dunham expansion for rotation-vibration spectra is achieved. Vibrational spectra of diatomic molecules can be described by the q-deformed anhannonic oscillator, having the symmetry Uq(2)>Oq(2). An alternative de- scription is obtained in terms of the quantum algebra SUq(1,1). In both cases the energy formula obtained is equivalent to an expansion in terms of powers of (v+½) , where ν is the vibrational quantum number, while in the classical ST(1,1) case only the first two powers appear. In all cases the improved description of the empirical data is obtained with q being a phase (and not a real number). Further applications of quantum algebraic symmetries in nuclei and molecules are discussed.

Dual output from unitary input for a hybrid coaxial triboelectric nanogenerator inspired by a crank engine

Energy conversion cannot be sufficiently achieved from a single output device having a single input. Energy conversion efficiency and output power of triboelectric nanogenerator (TENG) can be enhanced by increasing the contact area or the number of devices. Especially, combining two or more of the four operational mode (contact-separation, lateral sliding, single electrode, freestanding) of triboelectric nanogenerator would be more efficient to harvest mechanical energy than with singleharvesting mode. In this paper, a hybrid coaxial triboelectric nanogenerator (HC-TENG) can generate electrical output from dual outputs. This HC-TENG consists of a disk-TENG and LS-TENG so that a large current can be harvested from the rotating movement of disk-TENG at a high frequency input and an additional output can be generated from the LS-TENG by adding one axis. The structure of device with one axis was inspired by the structure of crank engine, which can convert linear motion into rotational motion. When applying the structure of HC-TENG to an application, the input-output efficiency was calculated by using the rotational kinetic energy formula with the value of 16.66%. Moreover, the efficiency of HC-TENG was verified by comparing experimental values with theoretical calculations for the presence of the dual outputs. This combination of multiple TENGs can be adopted for enhancing efficiency from every ambient rotational movement in real life.

A systematic review of UK-based long-term nonsurgical interventions for people with severe obesity (BMI ≥35kgm-2 ).

IntroductionThe aim of this project was to systematically review UK evidence on the effectiveness of long‐term (≥12 months) weight management services (WMSs) for weight loss and weight maintenance for adults (≥16 years) with severe obesity (body mass index ≥35 kg m−2), who would generally be eligible for Tier 3 services.MethodsFour data sources were searched from 1999 to October 2018. ResultsOur searches identified 20 studies, mostly noncomparative studies: 10 primary care interventions, nine in secondary care specialist weight management clinics and one commercial setting intervention. A programme including a phase of low energy formula diet (810–833 kcal day−1) showed the largest mean (SD) weight change at 12 months of –12.4 (11.4) kg for complete cases, with 25.3% dropout. Limitations or differences in evaluation and reporting (particularly for denominators), unclear dropout rates, and differences between participant groups in terms of comorbidities and psychological characteristics, made comparisons between WMSs and inferences challenging.ConclusionsThere is a persistent and clear need for guidance on long‐term weight data collection and reporting methods to allow comparisons across studies and services for participants with severe obesity. Data could also include quality of life, clinical outcomes, adverse events, costs and economic outcomes. A randomised trial comparison of National Health Service Tier 3 services with commercial WMSs would be of value.

Gibbs free energy based representation formula within the context of implicit constitutive relations for elastic solids

We derive a representation formula for a class of solids described by implicit constitutive relations between the Cauchy stress tensor and the Hencky strain tensor. Using a thermodynamic framework, we show that the Hencky strain tensor can be obtained as the derivative of the specific Gibbs free energy with respect to a stress tensor related to the Cauchy stress tensor. Unlike previous studies that have considered implicit relations between the Cauchy stress tensor and the Hencky strain we work with quantities that allow us to split the deformation into two parts. One part is connected to deformations that change the volume and the other to deformations where volume is preserved. Such a decomposition allows us to clearly characterise the interplay between the corresponding parts of the stress tensor, and to identify additional restrictions regarding the admissible formulae for the Gibbs free energy. We also show that if the constitutive relations of this type are linearised under the small strain assumption, then one can transparently obtain linearised models with density/pressure/stress dependent elastic moduli in a natural manner.

Phase Diagram of the Quantum Random Energy Model

We prove Goldschmidt’s formula (Goldschmidt in Phys Rev B 47:4858–4861, 1990) for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is based on a combination of variational methods on the one hand, and bounds on the size of percolation clusters of large-deviation configurations in combination with simple spectral bounds on the hypercube’s adjacency matrix on the other hand.

The Second-Order Correction to the Ground State Energy of the Dilute Bose Gas

We establish the Lee-Huang-Yang formula for the ground state energy of a dilute Bose gas for a broad class of repulsive pair-interactions in 3D as a lower bound. Our result is valid in an appropriate parameter regime of soft potentials and confirms that the Bogolubov approximation captures the right second order correction to the ground state energy.

A Simple Theory of Asymmetric Linear Elasticity

Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined as the transpose of the deformation gradient tensor to involve rotation as well as symmetric strain. The new theory basically differs from the prevailing micropolar theory or couple stress theory in that it maintains the same basis as the classical theory of linear elasticity and does not need extra concepts, such as “microrotation” and “couple stresses”. The constitutive relation of the new theory, the three-parameter Hooke’s law, comes from the theorem about isotropic asymmetric linear elastic materials. Concise differential equations of translational motion are derived consequently giving the same velocity formula for P-wave and a different one for S-wave. Differential equations of rotational motion are derived with the introduction of spin, which has an intrinsic connection with rotation. According to the new theory, S-wave essentially has rotation as large as deviatoric strain and should be referred to as “shear wave” in the context of asymmetric strain. There are nine partial differential equations for the deformation harmony condition in the new theory; these are given with the first spatial differentiations of asymmetric strain. Formulas for rotation energy, in addition to those for (symmetric) strain energy, are derived to form a complete set of formulas for the total mechanical energy.

Nuclear statistical equilibrium equation of state with a parametrized Dirac–Brückner Hartree–Fock calculation

Abstract We calculate new equations of state (EOSs) for astrophysical simulations in the framework of the extended nuclear statistical equilibrium, in which we minimize the free energy density for the full ensemble of nuclei in a hot and dense stellar environment. To evaluate bulk and surface energies of heavy nuclei and free energies of uniformly distributed nucleons, we use fitting formulae for the interaction energies and single-nucleon potentials at zero temperature of a Dirac–Brückner Hartree–Fock (DBHF) theory, one of the modern approaches to describe homogeneous nuclear matter. We find that the DBHF EOS exhibits larger mass fractions for medium-mass nuclei and smaller mass fractions for the other nuclei than the EOS obtained using the variational method (VM), another modern model for homogeneous nuclear matter. This effect is due to the more deeply bound energy for symmetric nuclear matter and the larger symmetry energy encoded in the DBHF EOS. At supra-nuclear densities, the DBHF EOS exhibits characteristics of a larger free energy, a higher pressure, and a larger neutron chemical potential of neutron-rich matter, which lead to a larger radius of cold neutron stars than that obtained by the VM EOS.

ПОВНА ЕНЕРГІЯ ГАРМОНІЧНОГО ОСЦИЛЯТОРА З ІМПУЛЬСНОЮ ДІЄЮ

The problem of finding the total energy of a harmonic oscillator with pulsed action at fixed moments of time is considered. Both for the case of the homogeneous equation of harmonic oscillations and for the case of the equation of harmonic oscillations in the presence of external perturbation, formulas for the total energy of the oscillatory system are obtained. The case of periodic impulse effects is analyzed. The conditions under which in this oscillatory system there are periodic modes are specified. It is shown that under the fulfillment of these conditions on the values of impulse action and external perturbation, the total energy of the vibrational system is also a periodic function of the time variable.