Balance Of Total Energy Research Articles

ВРАЩЕНИЯ ТОРОВ В СТРУКТУРЕ ЖИДКОГО КРИСТАЛЛА

Liquid crystals are a collection of flattened molecules. On the one hand, they have a welldefined structure, on the other hand, this structure is deformable, since its elements can change their position in space. In columnar structures, consisting of disks, plates, and tori, the fluid lines and cords are distinguished. In the case of tori and circular disks, a hexagonal structure of the arrangement of molecules is observed in a combination of the cord. The aim of this work is to obtain the stability of tori positions in an elementary fragment of a liquid crystal and to analyze their rotations in a self-consistent field of the surrounding toroidal molecules. To solve this problem, the method of mathematical modeling was used, based on classical models of molecular dynamics. The calculation is carried out on the basis of the model of cross-atom-atom interactions for molecular tori. The minimal fragment of the cord is selected, which makes it possible to determine the characteristic dynamic state of the central torus in the fragment. To describe the motion of the molecular tori, the equations of motion for their centers of mass and the Euler equations for their angular displacements are used. The minimal fragment of the material contains twenty-nine tori. The equations for displacements of the centers of mass of the tori are initially represented as ordinary differential equations of the second order. However, by introducing fictitious points into the consideration of velocities, they can be reduced to a system of first-order equations with a doubled number of lower-order equations. The resulting system of the first-order differential equations is integrated numerically using a highorder accuracy step-by-step scheme. All calculations are performed with a constant time step. The accuracy of the obtained numerical results is verified in terms of the balance of total energy of the system. Calculations show that the central torus of the presented fragment executes angular oscillations around its main axis with amplitude of more than one revolution. Thus, the performed calculations show that a representative fragment of the liquid crystal structure of molecular tori can be used as a generator of high-frequency mechanical vibrations.

Efficient implementation of energy conservation for higher order finite elements with variational integrators

In this paper, we introduce a variational integrator for higher order finite element models. The solution quality of finite element simulation strongly depends on the approximation in time and space. A variational integrator is robust due to conservation of both the balance of total linear momentum and the balance of total angular momentum. It also binds the error in the balance of total energy. We extend the variational integrator to an integrator that conserves the balance of total energy as well. However, the approximation in time cannot mend the approximation error in space. Therefore, we use a higher order approximation in space to obtain a better solution compared to the real live model that should be simulated. We show different numerical examples with Dirichlet and Neumann boundaries. For the Dirichlet boundaries we use the Lagrange multiplier method and for the Neumann boundaries we introduce the forces on the nodes by constant pressure.

Conservation properties of higher order time stepping schemes based on variational integrators

AbstractThis paper deals with higher order accurate variational integrators for finite element systems. The variational integrator (VI) is based on higher order LAGRANGE polynomials as shape functions and a higher order GAUSSIAN quadrature rule. The goals of this paper are to implement a discrete gradient to preserve the balance of total energy and fulfill the constraints with the LAGRANGE multiplier method and a NEWTON‐COTÊS quadrature rule. We show the calculation of bearing forces from the LAGRANGE multipliers, which are essential for the balance of total linear momentum and the balance of total angular momentum. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Determining a set of suspicious electricity customers using statistical ACL Tukey’s control charts method

Estimation a set of suspicious electricity customers is the first stage for detecting fraud of electricity. This paper deals with this stage. Based on historical data about monthly measurements of electricity, customers’ time series are formed and then analysis of these series is performed using Tukey’s control charts as one of the statistical method. The asymmetric control limit (ACL) Tukey’s control charts are chosen due to a rather expressed asymmetry and dominantly presented right distribution of time series data. As usual, the choice of upper (UCL) and lower (LCL) control limits is not based on allowed number of observations outside of the control limits. The choice of these limits is based on the balance of total energy, registered energy and energy losses. The essence of this approach is the simultaneous observation all customers’ time series of the controlled set with the same control limits and the same percentage of total and normalized energy losses in the observed distribution network. The criterion for finding the number of suspicious customers and their addresses is allowed error between the number of registered customers with one or more data (observations) outside the control limits for given losses and the number of suspicious customers’ indicators based on certain balance of energy and the estimated total percentage of losses in distribution network.

Alteration of the flexible loop in 1-deoxy-D-xylulose-5-phosphate reductoisomerase boosts enthalpy-driven inhibition by fosmidomycin.

1-Deoxy-d-xylulose-5-phosphate reductoisomerase (DXR), which catalyzes the first committed step in the 2-C-methyl-d-erythritol 4-phosphate pathway of isoprenoid biosynthesis used by Mycobacterium tuberculosis and other infectious microorganisms, is absent in humans and therefore an attractive drug target. Fosmidomycin is a nanomolar inhibitor of DXR, but despite great efforts, few analogues with comparable potency have been developed. DXR contains a strictly conserved residue, Trp203, within a flexible loop that closes over and interacts with the bound inhibitor. We report that while mutation to Ala or Gly abolishes activity, mutation to Phe and Tyr only modestly impacts kcat and Km. Moreover, pre-steady-state kinetics and primary deuterium kinetic isotope effects indicate that while turnover is largely limited by product release for the wild-type enzyme, chemistry is significantly more rate-limiting for W203F and W203Y. Surprisingly, these mutants are more sensitive to inhibition by fosmidomycin, resulting in Km/Ki ratios up to 19-fold higher than that of wild-type DXR. In agreement, isothermal titration calorimetry revealed that fosmidomycin binds up to 11-fold more tightly to these mutants. Most strikingly, mutation strongly tips the entropy–enthalpy balance of total binding energy from 50% to 75% and 91% enthalpy in W203F and W203Y, respectively. X-ray crystal structures suggest that these enthalpy differences may be linked to differences in hydrogen bond interactions involving a water network connecting fosmidomycin’s phosphonate group to the protein. These results confirm the importance of the flexible loop, in particular Trp203, in ligand binding and suggest that improved inhibitor affinity may be obtained against the wild-type protein by introducing interactions with this loop and/or the surrounding structured water network.

Steady compressible Navier–Stokes–Fourier system for monoatomic gas and its generalizations

We consider steady compressible Navier–Stokes–Fourier system for a gas with pressure p and internal energy e related by the constitutive law p = ( γ − 1 ) ϱ e , γ > 1 . We show that for any γ > 3 2 there exists a variational entropy solution (i.e. solution satisfying the weak formulation of balance of mass and momentum, entropy inequality and global balance of total energy). This result includes the model for monoatomic gas ( γ = 5 3 ). If γ > 5 3 , these solutions also fulfill the weak formulation of the pointwise total energy balance.

Weak and Variational Solutions to Steady Equations for Compressible Heat Conducting Fluids

We study a steady compressible Navier–Stokes–Fourier system in a bounded three-dimensional domain. We consider a general pressure law of the form $p=(\gamma-1)\varrho e$ which includes in particular the case $p=a_1\varrho\vartheta+a_2\varrho^\gamma$. We show the existence of a variational entropy solution (i.e., a solution satisfying balance of mass, momentum, entropy inequality, and global balance of total energy) for $\gamma>\frac{3+\sqrt{41}}{8}$ which is a weak solution (i.e., also the weak formulation of total energy balance is satisfied), provided $\gamma>\frac{4}{3}$. These results cover at least two physically reasonable cases, namely, $\gamma=\frac{5}{3}$ (monoatomic gas) and $\gamma=\frac{4}{3}$ (relativistic gas).

On rational treatments of the general laws of balance and jump, with emphasis on configurational formulations

The present contribution intends to provide a rational framework for manipulating the general differential laws of balance and jump of continuum mechanics. At first, multiplications of the latter laws by proper physical fields are introduced, together with identical expansions. We then point out that the results of these mathematical manipulations, while being of the form of the general differential balance law again, are characterized by a possible lack of integrability with respect to volume production terms in the presence of a singular surface, the production terms being necessary for consistency. Lack of integrability is not to be expected when the general law is specified to the fundamental laws of balance of mass, momentum, total energy and entropy. When it must be supposed that integrability could be missing, however, the integral form of the general law of balance cannot be written down for a region containing a singular surface, and the so-called pillbox procedure fails for deriving the general relation of jump at the singular surface. The specific relations of balance and jump then have to be derived from proper relations that follow from consistent mathematical manipulations of the general differential law of balance and the general law of jump. In the present paper, these general relations are listed explicitly for balance of scalar and vectorial entities, multiplied and expanded by scalar, vector or tensor fields, respectively. Based on this rationale, various important formulations on configurational forces known from the literature on the mechanics in material space are recalled: The specific relation of balance of pseudomomentum, the configurational forces and the driving force at an interface are derived from the above general relations by involving the fundamental laws of balance and jump of linear momentum. The driving traction at an interface is then set into connection with the derived relations of balance and jump of kinetic, internal and free energy, respectively. The latter relations follow from the general relations by involving the fundamental laws of balance of linear momentum, total energy and entropy. As a result, we present relations between the driving traction at an interface and the surface production terms that appear in the various relations of jump, which should allow new interpretations of configurational formulations.

Weak Solutions for the Vlasov-Poisson Initial-Boundary Value Problem with Bounded Electric Field

The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main ingredient consists of estimating the change in momentum along characteristics of regular electric fields inside bounded spatial domains. As direct consequences, the propagation of the momentum moments and the existence of weak solution satisfying the balance of totalenergy are obtained.

Analysis of Joint Clearances in Multibody Systems

A methodology for the study of typical smooth joint clearances in multibody systems is presented. The proposed approach takes advantage of the analytical definition of the material surfaces defining the clearance, resulting in a formulation where the gap does not play a central role, as it happens in standard contact models. The contact forces are formulated in conserving form, such that the balance of total energy during the intermittent contact is exactly established in the discrete time integration scheme. Some numerical applications are presented, showing that the proposed methodology is very stable in long-term simulations with relatively large time step sizes. Therefore, it appears to be promising in terms of efficiency and robustness for the numerical analysis of real joints with clearances.

On the necessity of surface growth terms for the consistency of jump relations at a singular surface

When a singular surface is present in the region under consideration, the local forms of the equations of balance must be accompanied by jump relations in order to connect the different values of the discontinuous entities at the two sides of the singular surface. The classical general form of these jump relations is provided by the Kotchine relation. In the present contribution, we exemplary deal with balance of mass, momentum and kinetic energy, as well as with balance of total energy, denoted as the first law of thermodynamics, and with balance of internal energy. We first derive an extension of the Kotchine relation with respect to surface growth terms. By a surface growth term we mean an entity which equivalently describes the balance of some quantity associated with the material that is instantaneously located at or in the vicinity of the singular surface. In a more detailed modelling, a singular surface is often described by a thin shell-type region or layer of transition. Surface growth terms may represent a non-vanishing rate of change of the respective quantity, or they may characterise some sources of this quantity. As a main result of the present paper, we show that surface growth terms are needed in order to ensure consistency between the jump relations for balance of mass, momentum and kinetic energy, and between the jump relations for balance of total energy and balance of internal energy. Even when surface growth terms for mass, balance of momentum and total energy are absent, one generally must take into account surface growth terms for balance of kinetic energy and balance of internal energy. The presented results refer to both, a singular surface, as well as to a thin region of transition. The jump relations in the latter case are referred to an equivalent singular surface, replacing the region of transition. The uni-axial flow of a fluid in a diffusor is used to demonstrate that the present results may be used even in cases in which the region of transition is not thin.

On spatial and material settings of thermo-hyperelastodynamics for open systems

The present treatise aims at deriving a general framework for the thermodynamics of open systems typically encountered in chemo- or biomechanical applications. Due to the fact that an open system is allowed to constantly gain or lose mass, the classical conservation law of mass has to be recast into a balance equation balancing the rate of change of the current mass with a possible in- or outflux of matter and an additional volume source term. The influence of the generalized mass balance on the balance of momentum, kinetic energy, total energy and entropy is highlighted. Thereby, special focus is dedicated to the strict distinction between a volume specific and a mass specific format of the balance equations which is of no particular relevance in classical thermodynamics of closed systems. The change in density furnishes a typical example of a local rearrangement of material inhomogeneities which can be characterized most elegantly in the material setting. The set of balance equations for open systems will thus be derived for both, the spatial and the material motion problem. Thereby, we focus on the one hand on highlighting the remarkable duality between both approaches. On the other hand, special emphasis is placed on deriving appropriate relations between the spatial and the material motion quantities.

The Balance of Kinetic and Total Energy Simulated by the OSU Two-Level Atmospheric General Circulation Model for January and July

A three-year simulation which prescribes seasonally varying solar radiation and sea surface temperature is the basis of the present study of the horizontal structure of the balances of kinetic and total energy simulated by Oregon State University's two-level atmospheric general circulation model. Mechanisms responsible for the local energy changes are identified, and the energy balance requirement's fulfilment is examined. In January, the vertical integral of the total energy shows large amounts of external heating over the North Pacific and Atlantic, together with cooling over most of the land area of the Northern Hemisphere. In July, an overall seasonal reversal is found. Both seasons are also characterized by strong energy flux divergence in the tropics, in association with the poleward transport of heat and momentum.

The dynamics of the harmonic space slider-crank mechanism

This paper deals with the distribution of mass in the links of the simple harmonic space slider-crank mechanism to achieve the desirable features of inertia balance and constancy of total kinetic energy during the cycle.