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Introduction. Optical fibers are widely used for high-bandwidth transmitting communication signals over long distances. The key feature enabling this performance is signal low attenuation, that is signals experience minimal power loss propagating along the optical fiber. One of the factors influencing power loss during information transmission is the fiber bending. Bending can increase the signal transmission power loss of an optical fiber because of both macrobending and microbending. Studying the dependence of signal power losses when bending on waveguide parameters makes it possible to control the signal power losses of an optical fiber during information transmission. Aim of the Study. The study ia aimed at evaluating the effect of microbending on the field and energy of a weakly guiding optical fiber with a gradient refractive index profile in a single-mode regime. Materials and Methods. From the equations for the fields of straight and curved sections of weakly guiding fiber for an arbitrary gradient profile of the refractive index with the help of the subsequent solution of inhomogeneous Helmholtz equations by the Green’s function method, there were obtained expressions for relative energy: the ratio of the field energy of the fiber curved section to the field energy of the fiber straight section (in the first approximation for a single-mode regime). Results. The obtained expression for the relative energy depends on two parameters: the waveguide parameter and the ratio of the optical fiber radius to the radius of curvature. For the quadratic case of a power-law profile, as the closest to the actually used one, numerical calculations were used to construct the dependences of the relative energy on the parameter characterizing the bending for different values of the waveguide parameter. Discussion and Conclusion. It has been shown that in the case of microbending, the longer the wavelength or the smaller the fiber radius, the lower the losses. The results obtained can be used in calculating optical fiber profiles designed to operate in a bent state and eliminate expensive experimental modeling of light guides and in designing waveguides to solve specific applications, in particular, to increase energy efficiency, reliability and performance of the measuring instruments.

Purpose: Wheelchair athletes experience a reduction in fat-free mass due to the underlying condition and/or muscle disuse. This leads to a lower resting energy expenditure (REE), as well as a lower energy expenditure during exercise or daily activities. Traditional markers of low energy availability (LEA), including amenorrhea and low bone mineral density, are often inconclusive in wheelchair athletes. This case study provides data from a professional female wheelchair badminton player with multiple sclerosis who presented with a reduced measured-to-predicted REE ratio (REEratio), a common indicator of LEA in able-bodied athletes. Furthermore, a nutrition and exercise intervention was conducted to restore REE. Methods: REE and body composition were measured using indirect calorimetry and dual-energy X-ray absorptiometry, respectively. The predicted REE of the REEratio was calculated using 2 separate approaches. An REEratio <0.9 was considered an indicator for LEA. A nutrition and exercise intervention was implemented to normalize REE and induce weight loss through increased meal frequency, a 200- to 400-kcal/d increase in energy intake, and added endurance exercise. Results: The athlete (33 y, 78 kg, 154 cm) initiallly showed an REEratio of 0.65 to 0.70, which increased to 1.00 to 1.09 after 1 year. The athlete lost 11.8 kg, almost exclusively (11 kg) in the form of fat mass. The athlete reported reduced fatigue and higher perceived fitness. Conclusion: The nutrition and exercise intervention successfully restored energy status, induced sustainable weight loss, and reduced fatigue in a wheelchair athlete with multiple sclerosis with presumed LEA. Methods to assess LEA in this population require further validation. [ABSTRACT FROM AUTHOR]

We consider a set of bipolar Euler–Poisson equations and study two asymptotic limiting processes. The first is the zero-electron-mass limit, which formally results in a nonlinear adiabatic electron system. In a second step, we analyze the combined zero-electron-mass and quasi-neutral limits, which together lead to the compressible Euler equations. Using the relative energy method, we rigorously justify these limiting processes for weak solutions of the two-species Euler–Poisson equations that dissipate energy, as well as for strong solutions of the limit systems that are bounded away from vacuum. This justification is valid in the regime of initial data for which strong solutions exist. To deal with the electric potential, in the first case we use elliptic theory, whereas in the second case we employ the theory of Riesz potentials and properties of the Neumann function. [ABSTRACT FROM AUTHOR]

A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier–Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, which triggers the migration of the endothelial cells and the blood vessel formation. The coupling of the equations is realized by the chemotaxis force in the momentum balance equation. The global existence of finite energy weak solutions is shown for adiabatic pressure coefficients γ > 8 / 5 . The solutions satisfy a relative energy inequality, which allows for the proof of the weak–strong uniqueness property. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence rate of a finite volume approximation of the compressible Navier–Stokes–Fourier system. To this end we first show the local existence of a regular unique strong solution and analyse its global extension in time as far as the density and temperature remain bounded. We make a physically reasonable assumption that the numerical density and temperature are uniformly bounded from above and below. The relative energy provides us an elegant way to derive a priori error estimates between finite volume solutions and the strong solution. [ABSTRACT FROM AUTHOR]

The syndrome of relative energy deficiency in sports (RED-S) is the result of a prolonged period of low energy availability in athletes and leads to the deterioration of health and physical performance. Our study aimed to investigate the prevalence of RED-S-related health and performance problems in young Slovenian athletes, comparing middle (14–17 years) with late (18–21 years) adolescents.

The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end, we apply the relative energy concept provided by [7]. We consider the case of regular polynomial-type potentials and positive mobilities, as well as the degenerate case with logarithmic potential and vanishing mobility. [ABSTRACT FROM AUTHOR]

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For arbitrary large initial data and the periodic boundary conditions, we prove the existence of global-in-time measure-valued solutions. We also show, using the relative energy technique, that the measure-valued solutions coincide with the classical solutions as long as the latter exist. [ABSTRACT FROM AUTHOR]

Mental task categorization using single/limited channel(s) electroencephalogram (EEG) signals is crucial for designing portable brain–computer interface and neurofeedback systems. However, EEG signals are corrupted with ocular artifacts and muscle artifacts, which degrade the robustness of existing features resulting inaccurate categorization of mental tasks. Therefore, in this paper, we propose a real-time mental task categorization method using stationary wavelet transform (SWT)-based novel discriminant features and different classifiers. It consists of four major stages: EEG signal decomposition and reconstruction using SWT into subbands; computation of proposed relative subband energy features (i.e., total energy of all subbands( E t ), relative energy of each subband k ( E r (k) ) and sum of relative energy pair ratio and difference); significant feature selection; classification using seven classifiers. The robustness of the proposed method is evaluated using two publicly available datasets and in-house dataset recorded using single-channel EEG headset. Performance evaluation results show that the proposed method with support vector machine classifier achieves the highest average subject-dependent accuracy of 98% for classification of mental/mental and baseline/mental tasks. Extensive comparative performance analysis depicts the superiority of the proposed method as compared to existing techniques in terms of accurate categorization of mental tasks, computational complexity, EEG processing length and robustness under artifact-contaminated EEG signals. [ABSTRACT FROM AUTHOR]

Cross section for dissociation of 6Li into α + d in the field of 209Bi target nucleus has been measured at an energy about 20% below the Coulomb barrier by detecting α and d in coincidence using a segmented Si-Strip detector array. Measured distribution of relative energy ' E α d ' suggests that the dissociation of the projectile at present beam energy proceeds dominantly through direct breakup and by a small fraction through sequential breakup via 3+ resonance state. The Q-value distribution shows that the events are accompanied by the residual target nuclei remaining at the ground state. Measured angular distributions of direct breakup cross-section are analyzed within the framework of Continuum Discretized Coupled Channel (CDCC) calculations. Asymptotic Normalization Coefficient (ANC) describing the amplitude of the tail of the bound state wave function in α +dis obtained from the variation of spectroscopic amplitude with the Single particle asymptotic normalization coefficient. The estimated ANC parameter (2.581 ± 0.212 fm−1/2) is in excellent agreement with the values previously found in the literature. [ABSTRACT FROM AUTHOR]

We derive a priori error estimates of the Godunov method for the multidimensional compressible Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance between the numerical solution and the strong solution. This yields also the estimates of the L 2 -norms of the errors in density, momentum and entropy. Under the assumption, that the numerical density is uniformly bounded from below by a positive constant and that the energy is uniformly bounded from above and stays positive, we obtain a convergence rate of 1/2 for the relative energy in the L 1 -norm, that is to say, a convergence rate of 1/4 for the L 2 -error of the numerical solution. Further, under the assumption—the total variation of the numerical solution is uniformly bounded, we obtain the first order convergence rate for the relative energy in the L 1 -norm, consequently, the numerical solution converges in the L 2 -norm with the convergence rate of 1/2. The numerical results presented are consistent with our theoretical analysis. [ABSTRACT FROM AUTHOR]

One of the most important roles of water system supply is piping networking. Performance of water supply sistem service is determined not only by a capacity from the source, but also by water volume which must also be up to the vertices with high flow and adequate pressure as needed. Besides, the effectiveness of a pipline is measured from the cost of investment and operational cost over life of specified order. In order to achieve adequate pressure and flow conditions it must be analyzed the size carefully. Linear programming represents the completion of operations research techniques that can solve optimization problems. Linear prograsmming is used to minimize cost size of pipe. On this research, a sample informartion taken by a clean water distributin network in PDAM Tirta Khuripan, Bogor, West Java. By using the method of linear programing the result of optimization in PDAM Tirta Khuripan, Bogor, West Java diameter on each pipe in with the selection of the main pipe diameter between 8 inch to 22 inch and pressure energy or relative energy is 2 metes into 7 metes by license set.

In this paper, a model that was recently derived in Reinken et al. to describe the dynamics of microswimmer suspensions is studied. In particular, the global existence of weak solutions, their weak–strong uniqueness, and a connection to a different model that was proposed in Wensink et al. is shown. [ABSTRACT FROM AUTHOR]

Near-infrared (NIR) light has been shown to produce a range of physiological effects in humans, however, there is still no agreement on whether and how a single parameter, like the flicker frequency of NIR light, affects the brain. An 810nm NIR LED was used as the stimulator. Fifty subjects participated in this experiment. Forty subjects were randomly divided into four groups. Each group underwent a 30-minute NIR LED radiation with four different frequencies (i.e., 0Hz, 5Hz, 10Hz and 20Hz, respectively) on the forehead. The remaining 10 subjects formed the control group, in which they underwent a 30-minute rest period without light radiation. EEG signals of all subjects during each test were recorded. Gravity frequency (GF), relative energy change, and sample entropy were analyzed. The experimental groups had larger GF values compared to the control group. Higher stimulation frequency would cause larger growth of GF (F=14.75, P

Near-infrared (NIR) light has been shown to produce a range of physiological effects in humans, however, there is still no agreement on whether and how a single parameter, like the flicker frequency of NIR light, affects the brain. An 810 nm NIR LED was used as the stimulator. Fifty subjects participated in this experiment. Forty subjects were randomly divided into four groups. Each group underwent a 30-minute NIR LED radiation with four different frequencies (i.e., 0 Hz, 5 Hz, 10 Hz and 20 Hz, respectively) on the forehead. The remaining 10 subjects formed the control group, in which they underwent a 30-minute rest period without light radiation. EEG signals of all subjects during each test were recorded. Gravity frequency (GF), relative energy change, and sample entropy were analyzed. The experimental groups had larger GF values compared to the control group. Higher stimulation frequency would cause larger growth of GF (F = 1 4. 7 5 , P < 0. 0 0 1). The amplitude of alpha waves relative energy increased, while theta waves decreased remarkably in the experimental groups (p < 0. 0 2), and the extent of increase/decrease was larger at higher stimulation frequency, compared to that of the control. Sample entropy of electrodes in the frontal areas were much larger than those in other brain areas in the experimental groups (p < 0. 0 0 1). Larger frequency of the NIR LED light would cause more distinct brain activities in the stimulated areas. It indicates that NIR LED light may have a positive effect on modulating brain activity. These results may help improve the design of photobiomodulation treatments in the future. [ABSTRACT FROM AUTHOR]

Theoretical analyses are valuable for the exploration of the effects of unnatural amino acids on enzyme functions; however, many necessary parameters for unnatural amino acids remain lacking. In this study, we developed and tested force field parameters compatible with Amber ff14SB for 18 phenylalanine and tyrosine derivatives. The charge parameters were derived from ab initio calculations using the RESP fitting approach and then adjusted to reproduce the benchmark relative energies (at the MP2/TZ level) of the α- and β-backbones for each unnatural amino acid dipeptide. The structures optimized under the proposed force field parameters for the 18 unnatural amino acid dipeptides in both the α- and β-backbone forms were in good agreement with their QM structures, as the average RMSD was as small as 0.1 Å. The force field parameters were then tested in their application to seven proteins containing unnatural amino acids. The RMSDs of the simulated configurations of these unnatural amino acids were approximately 1.0 Å compared with those of the crystal structures. The vital interactions between proteins and unnatural amino acids in five protein–ligand complexes were also predicted using MM/PBSA analysis, and they were largely consistent with experimental observations. This work will provide theoretical aid for drug design involving unnatural amino acids.

Structures and relative stabilities of neutral acetonitrile clusters up to decamer have been investigated. We used the ABCluster code to thoroughly explore the potential energy surfaces (PESs) of the acetonitrile clusters and to generate initial geometries, which are further fully optimized at the MN15/6‐31++G(d,p) level of theory. Our exploration yielded several new local and global minima structures of the acetonitrile clusters. We located new global minimum structures of the acetonitrile pentamer to decamer. The results show that the PESs of the acetonitrile clusters are very flat, yielding several isoenergetic structures. Our investigations also revealed that the stability of the acetonitrile clusters is due both to CH⋯N and dipole–dipole interactions. Structures stabilized by the latter are found to be more stable than those stabilized by the former at low temperatures. Furthermore, we examined the effect of temperature on the stability of the structures of the acetonitrile clusters for temperatures in the range 20 to 400 K. We found that several structures contribute to the population of the clusters at high temperatures, and also that a significant contribution to the population comes from isomers that lie within 2.0 kcal/mol from the most stable one. In addition, we used the most stable structures to compute the binding energies of the acetonitrile clusters and to assess the performance of some DFT functionals (MN15, ωB97XD, PW6B95D3, and B2PLYP) in comparison with the MP2 method associated to the aug‐cc‐pVTZ basis set in calculating the binding energies. We found that the MN15 functional performs better than ωB97XD and PW6B95D3, and that MN15 is less sensitive to the basis set change. We also used an extrapolation scheme to calculate the binding energies of the acetonitrile clusters at the highly accurate W1BD, CBS‐QB3, and G4MP2 levels of theory. The resulting binding energies are recommended for future benchmarking of the acetonitrile clusters. [ABSTRACT FROM AUTHOR]

We identify a large class of objects|dissipative measure-valued (DMV) solutions to the Navier-Stokes-Fourier system|in which the strong solutions are stable. More precisely, a DMV solution coincides with the strong solution emanating from the same initial data as long as the latter exists. The DMV solutions are represented by parameterized families of measures satisfying certain compatibility conditions. They can be seen as an analogue to the dissipative measure-valued solutions introduced earlier in the context of the (inviscid) Euler system. [ABSTRACT FROM AUTHOR]

We investigate a version of one velocity Baer-Nunziato type system with dissipation describing the motion of a mixture of two compressible fluids. We define for this system weak solutions on one hand and dissipative weak solutions on the other hand, and recall the theorem about their existence on a large time interval. We investigate strong solutions and show their existence on a short time interval. Finally, we prove that any weak solution satisfies a relative energy inequality and prove for this system the weak-strong uniqueness principle. This is the main result of the paper. [ABSTRACT FROM AUTHOR]

Aim. Theoretical substantiation of directions of the cyclization reaction in different solvents by means of quantum-chemical calculations of thermodynamic parameters of three tautomers of the initial N-ethyl-N'-[4-(6,7,8,9-tetrahydro-5H-[1,2,4]triazol[4,3-a]azepin-3-yl) phenyl]thiourea. Methods. Quantum-chemical calculations of relative energies, interconversion barriers, structural and thermodynamic parameters of tautomers of thiourea in dioxane, ethanol, dimethylformamide (DMFA) and tetrachlormethane were performed on the basis of the density functional theory applying the GAUSSIAN 09W software. The influence of the solvent was taken into account within the framework of the continuum polarized model. Results. In all the solvents under study, the cyclization reaction must proceed in one direction to form the N-ethyl-4-phenyl-N'-[4-(6,7,8,9-tetrahydro-5H-[1,2,4]triazol[4,3- a]azepin-3-yl) phenyl]-1,3-thiazole-2(3H)-imine. The smallest barrier of initial thiourea tautomers interconversion was observed in the presence of dioxane as a solvent; this fact indicated the advantage of synthesis conducting in this solvent precisely in comparison to ethanol, water, tetrachlormethane and DMFA. Conclusions. Dioxane is the most suitable solvent for cyclization. [ABSTRACT FROM AUTHOR]

The structure-dependent energies of organic compounds reflect the energies arising from all of their different structural elements. The value of the contribution of an element, for example a double bond differs from C=C, to C=O or C=S. In this article, the energies of structural elements occurring in different classes of compounds are compared. [ABSTRACT FROM AUTHOR]

In order to study the change features of infrasonic waves in coal sample loading, we collect coal samples from the research area, conduct both lab test and theoretic analysis, and based on filtered and de-noised signals, establish the characteristic parameter of infrasonic waves -- relative energy, and analyze the changes in the energy parameter of infrasonic waves in the loading process. The analysis shows: in the loading process, the energy of infrasonic waves changes in stages, including the slow increase, rapid increase towards the peak and slow decrease stages, which are consistent with the deformation stages of coal samples, and when the coal samples enter the plastic deformation stage from the elastic deformation stage, the infrasonic waves show an obvious abnormal change. Therefore, we can predict the deformation and failures of coal samples according to the changes in the energy of infrasonic waves. At the same time, due to advantages like non-coupled contact and small attenuation, the infrasonic wave prediction method is very useful in the coal sample failure prediction. This is of great significance to improving the accuracy of coal sample failure prediction and reducing coal mine accidents. [ABSTRACT FROM AUTHOR]

The structure-dependent energies of organic radicals, cations, and anions are deduced from their calculated relative enthalpies and are compared to the relative enthalpies of their parent compounds. The use of relative enthalpies to express the relative energies of organic radicals, cations, and anions proved to be as fruitful as in the case of their parent organic compounds. The same energy-determining structural factors may have stronger, weaker, or even opposite effects in the radicals, cations, or anions than those in their parent molecules. [ABSTRACT FROM AUTHOR]

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler–Poisson system with friction to the Keller–Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler–Korteweg theory with monotone pressure laws to the Cahn–Hilliard equation. [ABSTRACT FROM PUBLISHER]

To study the precursory failure infrasonic characteristics of coal samples, coal rock stress loading system and infrasonic wave acquisition system were adopted, and infrasonic tests in uniaxial loading process were made for the coal samples in the studied area. Wavelet filtering, fast Fourier transform, and relative infrasonic energy methods were used to analyze the characteristics of the infrasonic waves in the loading process, including time domain characteristics, and relative energy. The analysis results demonstrated that the frequencies of the infrasonic signals in the loading process mainly distribute within 5–10 Hz, which are significantly different from noise signals. The changes of the infrasonic signals show clear periodic characters in time domain. Meanwhile, the relative energy changes of the infrasonic wave also show periodic characters, which are divided into two stages by the yield limit of coal samples, and are clear and easy to be recognized, so that they can be used as the precursory characteristics for recognizing coal sample failures. Moreover, the infrasonic waves generated by coal samples have low frequency and low attenuation, which can be collected without coupling and transmitted in long distance. This study provides an important support for the further in-situ prediction of coal rock failures. [ABSTRACT FROM AUTHOR]