Formula For Energy Research Articles

Coulson-type integral formulas for the general energy of a vertex

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently Arizmendi and Juárez-Romero proposed the concept of vertex energy and Arizmendi et al. further obtained a Coulson-type integral formula for the vertex energy of a graph. In this paper, we will introduce the concept of the general energy of a vertex, and give some Coulson-type integral formulas for the general energy of a vertex.

A Spectro-geometric solution of dynamic characteristics of submarine-like structures

In this paper, the Spectro-geometric method is used to study the vibration behaviors of the submarine-like structure. The substructures of the geometric model include: cylindrical shell, conical shell, spherical shell, annular plate and rectangular plate. The energy formula of the sub-structure is deduced by the principle of first-order shear deformation. In order to satisfy the continuity conditions between the sub-structures and the related boundary conditions, the artificial spring technology is introduced in this paper. The Lagrange energy functional for the entire model is established. For efficient modeling, the displacement functions used here is the two-dimensional spectral geometric functions. Substitute the displacement function into the energy functional and solve it by the Ritz method to obtain the displacement coefficient and natural frequency of the structure. Through the convergence analysis and the comparative studies for the substructures and the whole structure under different boundary conditions, it is verified that the method in this paper is feasible. The effects of coupling parameters, material parameters, and molecular structure dimensions on the free and forced vibrations of the submarine-like structure are also investigated.

RETRACTED ARTICLE: Simulation of hybridized nanofluids flowing and heat transfer enhancement via 3-D vertical heated plate using finite element technique

The present study probed the creation of heat energy and concentrating into Newtonian liquids across vertical 3D-heated plates. The role of the Soret and Dufour theories in concentrating and energy formulas is discussed. The role of hybrid nanoparticles is introduced to illustrate particle efficiency in terms of solute and thermal energy. It is removed a viscous dissipation process and a changing magnetic field. The proposed approach is motivated by the need to maximize solute and thermal energy uses in biological and industrial domains. The constructed system of (partial differential equations) PDEs includes concentration, momentum, and thermal energy equations within various thermal characteristics. Transformations are used to formulate the system of (ordinary differential equations) ODEs for solution. To assess various features vs various variables, a Galerkin finite element approach is used. Motion into nanoscale components is shown to be smaller than motion into hybrid nanoparticles. Furthermore, fluctuations in heat energy and solute particle counts are seen in relation to changes in Soret, Eckert, magnetic, and Dufour numbers. The basic finding is that the generation of thermal energy for hybridized nanomaterials is much higher.

Verwendung von diätetischen Lebensmitteln für besondere medizinische Zwecke („bilanzierte Diäten“) für Säuglinge, Aktualisierung 2022

Foods for special medical purposes (FSMP) are intended for the dietary treatment of infants with special medical and nutritional needs. These products should only be used on medical advice and under medical supervision. Marketing for and over the counter sales of these products do not ensure appropriate medical guidance and supervision. The use of special nutrient solutions for the first postnatal days in healthy neonates to supplement breastfeeding and the use of special dietary products for infants with colic and/or constipation are not recommended due to a lack of clinical evidence. The use of infant formulas based on soya protein is only recommended for infants with galactosemia or hereditary lactose intolerance but not as first choice for infants with cow’s milk protein allergy. Marketing of these formulas has to follow the general legal restrictions for infant formulas in order to protect and support breastfeeding. Homemade and industrially thickened formulas, so-called antireflux formulas, may be considered in selected cases of regurgitation. The use of energy and nutrient-enriched infant formulas may be considered for non-breastfed infants with disease-associated growth faltering or malnutrition.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework, the Modal Electromechanical Coupling Factor (MEMCF) is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures. It is also an important tool to guide the piezoelectric damping design of linear structures. Advanced aircraft often fly in maneuvers, and the variable working conditions induce drastic changes in the load level on structures. Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated. To achieve a good vibration reduction effect covering all working conditions, one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures. Therefore, this paper defines the Nonlinear Modal Electromechanical Coupling Factor (NMEMCF) and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures. Three candidate definitions of the NMEMCF are given, including two frequency definitions and one energy definition. The energy definition is the most promising one. It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF. In addition, based on the energy formula, the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state. The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities. A strong correlation among the NMEMCF, geometric parameters, and energy dissipation is observed. The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping, especially for variable working conditions.

Test method for fracture toughness GIC based on ubiquitiform theory

A new fracture toughness test method for obtaining the crack initiation fracture toughness GIC and crack propagation fracture toughness GC was proposed. This method was based on the basic idea of ubiquitiform geometry and experimental results showing that material fracture surfaces possess ubiquitiform characteristics. A uniaxial tensile test was performed on plate specimens with cracks made by ductilecast iron to generate Mode I fracture failure. Loading–displacement curves were recorded in accordance with the experimental process, and the crack-initiation work W1 and the crack propagation work W2 were recorded. The morphology of the fracture surface was observed through electron microscopy, and the ubiquitiformal complexity D of the fracture surface was calculated on the basis of ubiquitiform theory. The ubiquitiform fracture area of the fracture surface was further obtained. The formula for ubiquitiform fracture energy was provided and used to calculate the ubiquitiform fracture energies Guf1 and Guf2 of the tested material. By analyzing the relationship between the above ubiquitiform fracture energy and fracture toughness GIC, a test method for determining fracture toughness based on ubiquitiform fracture energy was proposed. The experimental fracture toughness test results for several cracks of different sizes were consistent within a certain range of crack lengths.

Thermodynamic analysis of nucleation of alcohol molecules with the varied alkyl chain length in nanoconfined solution

Combining the molecular dynamics (MD) simulations and the free-energy-based thermodynamic analysis, we analyze the role of alkyl chain length on the nucleation of alcohol molecules with the mono-hydroxyl in nanoconfined solution. The free energy formulae and thermodynamic equilibrium equation are parameterized by fitting the theoretical equilibrium equation to MD simulation results. We find that alcohol molecules with the varied alkyl chain length show different nucleation states, i.e., dispersion, reversible and aggregation states, corresponding to the total free energy Gconfine(n, N) with a single minimum at n∼ 1, two minima at n∼ 1 and N separated by a maximum, and a local minimum at n∼N, respectively. The alcohol molecule with a longer alkyl chain tends to aggregate into a cluster at a lower solute number in nanoconfined solution. Besides, the free energy of cluster formation in nanoconfined solution Gcluster(n) also depends on the alkyl chain length, and three regions can be identified: For the shorter alkyl chain, such as ethanol, there is no local maximum on Gcluster(n), indicating that alcohol molecules tend to be dispersed in water; For the intermediate alkyl chain length, such as 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol, the critical nucleation number nc and nucleation barrier Gb monotonically decrease with the increase of alkyl chain length; For the longer alkyl chain, nc∼ 1 and Gb∼0kBT suggest that alcohol molecules, such as 1-heptanol, can aggregate into clusters easily. Our work deepens the understanding of the alkyl chain length effect on the nucleation behavior of alcohol molecules in nanoconfined solution.

Shell-model study on properties of proton dripline nuclides with Z, N = 30–50 including uncertainty analysis * *Supported by the National Natural Science Foundation of China (11775316, 11825504, 11961141004), the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2016TQ03N575), the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006)

The binding and proton separation energies of nuclides with are investigated based on the shell model, with an uncertainty analysis via statistical methods. Several formulas are used to obtain the binding and proton separation energies according to shell-model calculations. The non-parametric bootstrap method is applied to establish an uncertainty decomposition and recomposition framework. Moreover, this is used to estimate the stability of proton(s) emission for each nuclide. Two formulas for calculating the binding energies with a systematic uncertainty of MeV are proposed, and a reliable extrapolation ability is examined. These binding energy formulas deduce similar forms for their respective and energies, which predict the extension of the nuclear boundary of this region. A good description of the binding and proton separation energies is provided. The one- and two-proton separation energies and partial half-lives of proton emission are predicted, thus revealing a new dripline. Furthermore, there are 30 unstable nuclides predicted to be bound against proton(s)-emission. These nuclear properties will be useful in nuclear astrophysics.

Semi-empirical Formula for X-rays Interaction Cross Sections and Energies with Atoms

Semi-empirical Formula for X-rays Interaction Cross Sections and Energies with Atoms

Hydrogen-bond mediated and concentrate-dependent NaHCO3 crystal morphology in NaHCO3–Na2CO3 aqueous solution: Experiments and computer simulations

Adding Na2CO3 to the NaHCO3 cooling crystallizer, using the common ion effect to promote crystallization and improve product morphology, is a new process recently proposed in the literature. However, the mechanism of the impact of Na2CO3 on the crystal morphology is still indeterminate. In this work, the crystallization of NaHCO3 in water and Na2CO3–NaHCO3 aqueous solution was investigated by experiments and molecular dynamics simulations (MD). The crystallization results demonstrate that the morphology of NaHCO3 crystal changed gradually from needle-like to flake structure with the addition of Na2CO3. The simulation results indicate that the layer docking model and the modified attachment energy formula without considering the roughness of crystal surface can obtain the crystal morphology in agreement with the experimental results, but the lower molecules of the crystal layer have to be fixed during MD. Thermodynamic calculation of the NaHCO3 crystallization process verifies that the common ion effect from Na+ and the ionization equilibrium transformation from CO32– jointly promote the precipitation of NaHCO3 crystal. The radial distribution function analysis indicates that the oxygen atoms of Na2CO3 formed strong hydrogen bonds with the hydrogen atoms of the (0 1 1) face, which weakened the hydration of water molecules at the crystal surface, resulting in a significant change in the attachment energy of this crystal surface. In addition, Na+ and CO32– are more likely to accumulate on the (0 1 1) face, resulting in the fastest growth rate on this crystal surface, which eventually leads to a change in crystal morphology from needle-like to flake-like.

Energy formulae for fractional Schrödinger-Poisson system

Via a geometric-capacity-theoretic approach, this note discovers two brand-new formulae for the fractional energy ∫Rn(−Δ)swdν of a quantum particle arising from the fractional Schrödinger-Poisson system(−Δ)sv+(V+w)v=f(⋅,v)&(−Δ)sw=(Γ(s)πn2Γ(n2−s))v2 which models the behavior of a quantum particle within an unknown electrostatic field.

A Remark on the Spherical Bipartite Spin Glass

Auffinger and Chen (J Stat Phys 157:40–59, 2014) proved a variational formula for the free energy of the spherical bipartite spin glass in terms of a global minimum over the overlaps. We show that a different optimisation procedure leads to a saddle point, similar to the one achieved for models on the vertices of the hypercube.

Energy-efficient virtual machine placement in data centres via an accelerated Genetic Algorithm with improved fitness computation

Energy efficiency is a critical issue in data centre management, which is the foundation for cloud computing. The VM placement has a considerable impact on a data centre's energy efficiency and resource utilisation. The assignment of VMs to PMs is an NP-hard problem without an easy way to find an optimal solution, particularly in large-scale data centres. In this study, the VM placement problem is formulated as a constrained optimisation problem. The Genetic Algorithm (GA) is a suitable method for solving this problem in terms of the quality of the solution. However, GA is time-consuming to obtain an optimal solution in the large scale optimisation problem. Therefore, this paper focuses on accelerated GA for energy-efficient VM placement. As the most time-consuming element of the GA is the calculation of its fitness function, this paper simplifies this calculation through a new fitness function in GA. Simulation results of small-, medium-, and large-scale data centres demonstrate that our accelerated GA is faster than the standard GA and gives better quality of solution than the First Fit Decreasing (FFD) algorithm, respectively. The findings of our GA with the new fitness function reveal an 8% energy saving for our GA compared to FFD and a 66% reduction in our GA execution time compared to the standard GA with standard energy formula as a fitness function. The number of generations in our GA is reduced by about 50% in comparison with the standard GA. Moreover, we started with 3000 PMs in the large-scale dataset, and only 1086 PMs were actually used after running our GA. Therefore, we may switch off far more PMs for energy savings from our GA results than those from the standard GA.

Energy Conservation for Fluids and Radiation Beams Using Pressure Notion to Account for Thermal, Mechanical, and Frictional Collisional Energy

One of the most challenging problems is energy conservation for systems which consist of aggregates of particles, such as fluids and radiation beams, as well as their interaction through collision and friction. The lack of a usable energy expression for this system that accounts for mechanical and thermal interactions makes it challenging to describe. The effect of thermal, mechanical, collision, and friction processes on the system energy was taken into consideration using the fluid momentum equation in this study. We can incorporate all of these processes using the concept of pressure, which is analogous to the concept of potential. We have found a conserved expression for energy using this viewpoint. This equation also includes thermal, mechanical (sound), and frictional pressures besides the frenetic and potential terms. It reduces to newton ordinary energy formula in the absence of pressure. We have also generalized the ordinary gas low to account for non-thermal mechanical pressures.

Strong Replica Symmetry in High-Dimensional Optimal Bayesian Inference

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how replica symmetry in the strong sense of concentration of all multioverlaps can be established as a consequence of the Franz–de Sanctis identities; the identities themselves in the current setting are obtained via a novel perturbation coming from exponentially distributed “side-observations” of the signal. Concentration of multioverlaps means that asymptotically the posterior distribution has a particularly simple structure encoded by a random probability measure (or, in the case of binary signal, a non-random probability measure). We believe that such strong control of the model should be key in the study of inference problems with underlying sparse graphical structure (error correcting codes, block models, etc) and, in particular, in the rigorous derivation of replica symmetric formulas for the free energy and mutual information in this context.

Pre-Lithiation Strategies and Energy Density Theory of Lithium-Ion and Beyond Lithium-Ion Batteries

Pre-lithiation is the most effective method to overcome the initial capacity loss of high-capacity electrodes and has the potential to be used in beyond-conventional lithium-ion batteries. In this article we focus on two types of pre-lithiation: the first type can be applied to batteries in which the cathode has been fully lithiated but the anode has a large initial capacity loss, such as batteries made with lithium metal oxide cathode and silicon-carbon anode. The second type can be applied to batteries in which both electrodes are initially lithium-free and suffer a loss of lithium during the initial cycles, such as batteries made with sulfurized-polyacrylonitrile cathode and silicon-carbon anode. We describe the pre-lithiation procedures and electrode potential profiles during pre-lithiation corresponding to different pre-lithiation sources for both types of pre-lithiation. We also derive formulas for the theoretical specific energy and energy density that are based entirely on measurable parameters such as specific capacities, porosities, mass densities of two electrodes and extra lithium source, Coulombic efficiencies of electrodes, and the voltage of the cell. These formulas can be applied to different pre-lithiation sources to predict the specific energy of conventional and beyond-conventional lithium-ion batteries as a function of the type of pre-lithiation.

Practical formulae for predicting the ballistic limit velocity of armour perforation by ductile hole growth

Previous comparisons to vast amount of experimental data have shown that the specific cavitation energy of target material, which takes into account the hole slenderness ratio effect, is essential in predicting ballistic limit velocity for perforation by ductile hole growth. In the present study, a concise summary of available formulae for the specific cavitation energy of monolithic targets is provided in a practical and accessible way. New analytical expressions are derived for specific cavitation energies and effective yield stresses of targets with linear-hardening response and combined (multi-terms) Ludwik-Voce hardening rule, with Ludwik and Voce laws as special cases. Four (and in two cases five) analytical predictions of ballistic limit velocities, which consider the hole slenderness ratio effect, are compared with experimental data for perforation of aluminium and steel targets. The accuracy of these analytical predictions is compared, in several Tables and Figures, with predictions by cylindrical plane-strain, cavitation model and finite element numerical simulations.

Tidal energy potential in coastal Vietnam

Tidal energy is a renewable energy source produced by the rise and fall of ocean tides. Tidal energy can be exploited using a special type of generator that converts tidal energy into electricity. Tidal power generation has the potential to open up many prospects for energy field and minimize carbon dioxide emissions that cause the greenhouse effect. To evaluate the possibility of tidal power, it is necessary to have documents and data on average annual tidal amplitude, tidal regime, and main tidal waves in the study area. To calculate the tidal power potential for the east coast of Vietnam, this article applies the calculation formula of tidal power energy by Russian scientist L.B. Bernstein. The annual mean tidal amplitude and the K1, O1, and M2 wave amplitude data at nearly 2000 calculation points along the coast of Vietnam were extracted from the TPOX8-Atlas harmonic constant set. Research results showed that Vietnam has great potential for tidal energy along the Hai Phong - Quang Ninh coastal area and the southeast region with a prospective 41.6 GWh/km2/y.

On a Class of Orthogonal-Invariant Quantum Spin Systems on the Complete Graph

AbstractWe study a two-parameter family of quantum spin systems on the complete graph, which is the most general model invariant under the complex orthogonal group. In spin $S=\frac {1}{2}$ it is equivalent to the XXZ model, and in spin $S=1$ to the bilinear-biquadratic Heisenberg model. The paper is motivated by the work of Björnberg, whose model is invariant under the (larger) complex general linear group. In spin $S=\frac {1}{2}$ and $S=1$ we give an explicit formula for the free energy for all values of the two parameters, and for spin $S>1$ for when one of the parameters is non-negative. This allows us to draw phase diagrams and determine critical temperatures. For spin $S=\frac {1}{2}$ and $S=1$, we give the left and right derivatives as the strength parameter of a certain magnetisation term tends to zero, and we give a formula for a certain total spin observable, and heuristics for the set of extremal Gibbs states in several regions of the phase diagrams, in the style of a recent paper of Björnberg, Fröhlich, and Ueltschi. The key technical tool is expressing the partition function in terms of the irreducible characters of the symmetric group and the Brauer algebra. The parameters considered include, and go beyond, those for which the systems have probabilistic representations as interchange processes.

A novel computational method of the free energy for an Ising model on Cayley tree of order three

In this paper, we consider the Ising-Vannimenus model on a Cayley tree of order three. We provide an efficient approach to give some explicit formulas for the free energies and the entropies corresponding to the boundary conditions (b.c.) for Ising-Vannimenus model including compatible and translation-invariant boundary conditions.