Errors In Numerical Calculations Research Articles

Evaluation of prompt engineering strategies for pharmacokinetic data analysis with the ChatGPT large language model.

To systematically assess the ChatGPT large language model on diverse tasks relevant to pharmacokinetic data analysis. ChatGPT was evaluated with prototypical tasks related to report writing, code generation, non-compartmental analysis, and pharmacokinetic word problems. The writing task consisted of writing an introduction for this paper from a draft title. The coding tasks consisted of generating R code for semi-logarithmic graphing of concentration-time profiles and calculating area under the curve and area under the moment curve from time zero to infinity. Pharmacokinetics word problems on single intravenous, extravascular bolus, and multiple dosing were taken from a pharmacokinetics textbook. Chain-of-thought and problem separation were assessed as prompt engineering strategies when errors occurred. ChatGPT showed satisfactory performance on the report writing, code generation tasks and provided accurate information on the principles and methods underlying pharmacokinetic data analysis. However, ChatGPT had high error rates in numerical calculations involving exponential functions. The outputs generated by ChatGPT were not reproducible: the precise content of the output was variable albeit not necessarily erroneous for different instances of the same prompt. Incorporation of prompt engineering strategies reduced but did not eliminate errors in numerical calculations. ChatGPT has the potential to become a powerful productivity tool for writing, knowledge encapsulation, and coding tasks in pharmacokinetic data analysis. The poor accuracy of ChatGPT in numerical calculations require resolution before it can be reliably used for PK and pharmacometrics data analysis.

Mass gap for a monopole interacting with different nonlinear spinor fields

We study the properties of the mass gap for monopole solutions in SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a spinor field described by the nonlinear Dirac equation. Different types of nonlinearities parameterized by the parameter λ are under consideration. It is shown that for the range of values of this parameter studied in the present paper the value of the mass gap depends monotonically on this parameter, and the position of the mass gap does not practically depend on λ. In the present paper we study the dependence of the size of a mass gap, its position, etc., on the value of a parameter describing the nonlinear self-interaction potential of the spinor field. By the term a position of the mass gap, we mean the value of the frequency E, for which the energy spectrum has a minimum. It is of interest to note that the position of the mass gap E,  does not practically depend on the nonlinearity parameter λ. One can assume that in fact this is the case, and deviations from this value are related to errors in numerical calculations. It is of interest that the position of the mass gap does not practically depend on the value of the nonlinearity parameter, at least in the range of values of the spinor field nonlinearity parameter considered here.

Study on Truncation and Roundoff Errors in Numerical Methods

History is full of many examples where errors in numerical calculation have played important role or sometimes proved fatal also. (e.g. The Patriot and the Scud [6], The short flight of the Ariane 5 [7], The Vancouver Stock Exchange [8,9,10], Parliamentary elections in Schleswig-Holstein [11]). So in this paper we review two types of errors occurred while performing calculations: first is truncation error and second is round off error . Examples are given in support of the theory part.

Air Pollution in Moscow Megacity: Data Fusion of the Chemical Transport Model and Observational Network

Comparisons of observational data obtained at the Moscow Ecological Monitoring network (MEM) with numerical simulations using a chemical transformation and transport model (SILAM—System for Integrated modeLling of Atmospheric coMposition) showed that the errors in determining the gaseous pollutant concentrations in the urban atmosphere have a more complex structure than those assumed under the conventional algorithms of data assimilation. These errors are statistically nonstationary; they show a pronounced diurnal cycle and a significant lifetime. The statistical features of errors in numerical calculations also depend upon the type of pollutants, i.e., the chemical reactions in which they participate. Our analysis showed that the simulation errors are not small: the ratios of calculated and measured concentrations (even for daily averages at all measuring stations) may vary in a wide range. For the chemically active pollutants, the intradiurnal error variations may reach 100%. The diurnal cycle of such errors was found to vary according to seasons (in our case, summer and winter). The analysis of statistical properties of the errors, including their temporal and spatial variability, allows one to correct and adequately forecast the air pollution in the metropolis area at lead times up to three days in advance.

Designing megastable systems with multidimensional lattice of chaotic attractors

Multistable systems and their dynamic properties are interesting topics in nonlinear dynamics. Small differences in the initial conditions (for example, due to rounding errors in numerical calculations) lead to completely different results for such dynamic systems, which makes a long-term prediction of their behavior practically impossible. This happens even if such systems are deterministic, that is, their future behavior is completely determined by the choice of initial conditions without the participation of random elements. In other words, the deterministic nature of these systems does not make them predictable. The behavior of the solutions of a dynamic system depends both on the choice of their initial conditions and on the values of the system parameters. The coexistence of several attractors, or multistability, corresponds to the simultaneous existence of more than one nontrivial attractor for the same set of system parameters. This phenomenon was discovered in almost all natural sciences, including electronics, optics, biology. In recent years, the efforts of many researchers have been aimed at creating so-called megastable systems, that is, systems that, at constant values of their parameters, have a countable number of coexisting attractors. Interest in such systems is due to a wide range of applications, for example, for hiding information in communication systems and audio encryption schemes, biomedical engineering and fuzzy control. The article proposes methods for the synthesis of megastable systems using systems in Lurie form. Megastable systems containing a 1-D lattice of chaotic attractors can be obtained by replacing the nonlinearity in the original system with a periodic function. By replacing some variables with periodic functions in the original system of order n, one can construct a megastable system containing an n-D lattice of chaotic attractors. As one example, a fourth-order system with a 4-D lattice of chaotic attractors is constructed for the first time. The Lyapunov exponents and Kaplan – Yorke dimension are calculated for attractors belonging to lattices

Intercomparison of Calculated Incident Power Density and Temperature Rise for Exposure From Different Antennas at 10–90 GHz

Recently, international exposure guidelines/standards for human protection from electromagnetic fields were revised. For frequencies between 6–300 GHz, the permissible incident power density is defined as the reference level, which is derived from a new metric “absorbed/epithelial power density” based on thermal modeling. However, only a few groups computed the power density and the resultant temperature rise at frequencies greater than 6 GHz, where their exposure conditions were different. This study presents the first intercomparison study of the incident power density and the resultant temperature rise in a human body exposed to different frequency sources ranging from 10 to 90 GHz. This intercomparison aims to clarify the main causes of numerical calculation errors in dosimetry analyses through objective comparison of computation results from six organizations using their numerical methods with various body and antenna models. The intercomparison results indicate that the maximum relative standard deviation (RSD) of peak spatially averaged incident power densities for dipole and dipole array antennas is less than 22.1% and 6.3%, respectively. The maximum RSD of the heating factor, which is defined as the ratio of the peak temperature elevation at the skin surface to the peak spatially averaged incident power density in free space, for dipole and dipole array antennas is less than 43.2% and 41.2%, respectively. The deviations in the heating factors caused by different body models and dielectric/thermal parameters are within 33.1% and 19.6% at 10 and 30 GHz, respectively, when the antenna-to-skin model distance is greater than 5 mm. Under this condition (>5 mm), the deviation in the heating factors caused by different antenna models at 30 GHz does not exceed 26.3%. The fair agreement among the intercomparison results demonstrates that numerical calculation errors of dosimetry analyses caused by the definition of spatially averaged incident power density are marginal.

Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation

In a previous paper, a calculation system for a high-accuracy, high-speed calculation of a one-dimensional (1D) Poisson equation based on the interpolation finite difference method was shown. Spatial high-order finite difference (FD) schemes, including a usual second-order accurate centered space FD scheme, are instantaneously derived on the equally spaced/unequally spaced grid points based on the definition of the Lagrange polynomial function. The upper limit of the higher order FD scheme is not theoretically limited but is studied up to the tenth order, following the previous paper. In the numerical analyses of the 1D Poisson equation published in the previous paper, the FD scheme setting method, SAPI (m), m = 2, 4, …, 10, was defined. Due to specifying the value of m, the setting of FD schemes is uniquely defined. This concept is extended to the numerical analysis of two-dimensional Poisson equations. In this paper, we focus on Poiseuille flows passing through arbitrary cross sections as numerical calculation examples. Over regular and irregular domains, three types of FD methods—(i) forward time explicit method, (ii) time marching successive displacement method, and (iii) alternative direction implicit method—are formulated, and their characteristics of convergence and numerical calculation errors are investigated. The numerical calculation system of the 2D Poisson equation formulated in this paper enables high-accuracy and high-speed calculation by the high-order difference in an arbitrary domain. Especially in the alternative direction implicit method using the band diagonal matrix algorithm, convergence is remarkably accelerated, and high-speed calculation becomes possible.

ВЛИЯНИЕ РАДИАЦИОННОГО ТЕПЛООБМЕНА НА ИНТЕНСИФИКАЦИЮ ТЕПЛОПЕРЕНОСА В ТОНКОПЛЕНОЧНОЙ ТЕПЛОВОЙ ИЗОЛЯЦИИ

Актуальность исследования обусловлена тем, что тепловая защита оборудования и трубопроводов играет важную роль при проведении энергосберегающих мероприятий на энергетических объектах различного назначения, а рост уровня потерь тепла или холода при транспортировке энергоносителей является причиной создания новых подходов к энергосберегающим мероприятиям при выполнении теплоизоляционных работ. Известно, что основным методом снижения потерь тепловой энергии при ее транспортировке и хранении является применение высокоэффективных теплоизоляционных материалов. Таким материалом является тонкопленочная тепловая изоляция. Уникальные теплофизические характеристики тонкопленочных теплоизоляционных покрытий позволяют использовать их в различных энергетических системах и оборудовании. Несмотря на это технологии применения тонкопленочных теплоизоляционных покрытий к настоящему моменту времени не получили развития. Это объясняется рядом причин, основными из которых являются: недостаток знаний о физических свойствах и механизмах процессов тепломассопереноса в тонкопленочных теплоизоляционных покрытиях. Цель: исследование кондуктивно-конвективно-радиационного теплопереноса в слое тонкопленочной тепловой изоляции с учетом разнородности свойств микросфер и связующих веществ. Объект: цилиндрический слой тонкопленочного теплоизоляционного покрытия. На внутренней и внешней поверхностях теплоизоляционного покрытия поддерживаются постоянные температуры. Геометрия тонкопленочного теплоизоляционного покрытия представляла собой связующее вещество и полые микросферы. Исследования проводились для слоя теплоизоляции толщиной 0,33 мм. Температура на внутренней и внешней поверхностях изоляции принималась в соответствии с экспериментальными данными. Предполагалось, что слой тонкопленочной теплоизоляции на 62 % состоит из микросфер диаметром 50 мкм и на 38 % из связующего вещества. Рассматривались два типа полых микросфер с толщинами стенок: 5 и 2 мкм. Методы. Решение поставленной задачи получено методом конечных элементов. Использовалась аппроксимация Галеркина, неравномерная конечно-элементная сетка. Параметры элементов сетки выбирались из условий сходимости решения. Увеличение числа элементов расчетной сетки проводилось с использованием метода Делоне. Результаты. Установлены величины тепловых потоков в слое тонкопленочной тепловой изоляции при наличии радиационного теплообмена. На основании сопоставления результатов численного моделирования теплопереноса в слое тонкопленочной тепловой изоляции, выполненного с использованием кондуктивно-конвективной модели теплопереноса, с результатами для кондуктивно-конвективно-радиационной модели установлено, что расхождение между ними не превышает 0,1 % и объясняется погрешностями численных расчетов. По этой причине в практических расчетах можно использовать более простую кондуктивную модель теплопереноса.

КОНДУКТИВНО-КОНВЕКТИВНЫЙ ТЕПЛОПЕРЕНОС В ТОНКОПЛЕНОЧНОЙ ТЕПЛОВОЙ ИЗОЛЯЦИИ

Актуальность исследованияобусловлена тем, что тепловая защита оборудования и трубопроводов играет важную роль при проведении энергосберегающих мероприятий на объектах различного назначения, а рост уровня потерь теплоты или холода при транспортировке энергоносителей является причиной создания новых подходов к энергосберегающим мероприятиям при выполнении теплоизоляционных работ. Известно, что основным методом снижения потерь тепловой энергии при ее транспортировке и хранении является применение высокоэффективных теплоизоляционных материалов. Таким материалом является тонкопленочная тепловая изоляция. Уникальные теплофизические характеристики тонкопленочных теплоизоляционных покрытийпозволяют использовать их в различных энергетических системах и оборудовании. Несмотря на это технологии применения тонкопленочных теплоизоляционных покрытий к настоящему моменту времени не получили развития. Это объясняется рядом причин, основными из которых являются: недостаток знаний о физических свойствах и механизмах процессов тепломассопереноса в тонкопленочных теплоизоляционных покрытиях. Цель: исследование кондуктивно-конвективного теплопереноса в слое тонкопленочных теплоизоляционных покрытий с учетом разнородности свойств микросфер и связующих веществ. Объект: цилиндрическийслойтонкопленочных теплоизоляционных покрытий. На внутренней и внешней поверхностях тонкопленочных теплоизоляционных покрытий поддерживаются постоянные температуры. Геометриятонкопленочных теплоизоляционных покрытий представляла собой связующее вещество и полые микросферы. Исследования проводились для слоя тонкопленочных теплоизоляционных покрытий толщиной 0,33 мм. Температуры на внутренней и внешней поверхностях тонкопленочных теплоизоляционных покрытий принималась в соответствии с экспериментальными данными. Предполагалось, что слой тонкопленочных теплоизоляционных покрытий на 62 % состоит из микросфер диаметром 50 мкм и на 38 % из связующего вещества. Рассматривались два типа полых микросфер с толщинами стенок 5 и 2 мкм. Методы. Решение поставленной задачи получено методом конечных элементов. Использовалась аппроксимация Галеркина, неравномерная конечно-элементная сетка. Параметры элементов сетки выбирались из условий сходимости решения. Увеличение числа элементов расчетной сетки проводилось с использованием метода Делоне. Результаты.Выявлено влияние на тепловые потери вида связующего вещества и характеристик микросфер, толщины стенки микросферы и газовой фазы, содержащейся в полости микросферы. Для рассматриваемого случая отклонение от экспериментальных данных составило до 90 % в зависимости от состава тонкопленочных теплоизоляционных покрытий.Анализ результатов численного моделирования теплопереноса в слое тонкопленочных теплоизоляционных покрытий для кондуктивно-конвективной и кондуктивной моделей показал, что расхождение между ними не превышает 3 %и объясняется погрешностями численных расчетов. По этой причине в практических расчетах можно использовать более простую кондуктивную модель теплопереноса.

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

This paper provides critical insights into the rigorous formulation of moderately rarefied gas transport through narrow channels in naturally and induced fractured porous media, such as gas shale rocks, approximated as round (cylindrical) and flat (slit) types. This formulation considers critical improvements over the previous attempts by proper implementation of the effective equivalent mean hydraulic radius of tight flow channels, the wall-slip effect accommodation of Maxwell (Philos Trans R Soc Lond A 170:231–256, 1879), the variable cross-section hard sphere model of gas molecules and the modified bulk mean free-path of Bird (Phys Fluids 26(11):3222–3223, 1983. https://doi.org/10.1063/1.864095), the apparent viscosity and mean free path for the confined-state gas behavior modification, the flow through narrow capillary tubes represented by a Hagen–Poiseuille-type equation, the Knudsen diffusivity, and an improved relationship between the apparent permeability and the intrinsic permeability. The description of gas transport through extremely tight channels is accomplished by superposition of the Poiseuille bulk flow (convection) and the Knudsen transport (diffusion) mechanisms. This approach is applied to investigate the accuracy of several previous studies on the modeling of gas transport through extremely tight narrow channels of round and flat types under moderately rarefied conditions. Although the simulation results reported by the previous studies of Roy et al. (J Appl Phys 93(8):4870–4879, 2003), Javadpour (J Can Pet Technol 48(8):16–21, 2009), and Veltzke and Thoming (J Gas Mech 698:406–422, 2012) appear to follow the trends observed in the experimental studies of Roy et al. (2003) flowing argon gas through a round channel (tube) and Ewart et al. (J Gas Mech 584:337–356, 2007. https://doi.org/10.1017/S0022112007006374) flowing helium gas through a single straight flat narrow channel, it is concluded that these results are not actually accurate for several reasons. The accuracy of the basic model presented by Javadpour (2009) suffers from some formulation issues and the low-order accuracy of the numerical approximations. The complicated model presented by Veltzke and Thoming (2012) is impractical and difficult because of the two-dimensional solutions of the Navier–Stokes equations with no-slip boundary condition and produces inaccurate solutions because of the improper definition of the effective radius of the straight flat narrow channel. The improved pressure equation of the compressible rarefied gas flow in tight channels developed in the present paper is highly nonlinear. The possibility of numerical calculation errors associated with the solution of the differential pressure equation was eliminated completely by an application of an integral transformation by facilitating a pseudo-transfer or flow potential function, and the solution of this equation was obtained accurately and fully analytically. It is shown that the proper formulation and accurate analytical solution developed in this paper can indeed lead to significantly accurate matches of the same experimental data than those reported by the previous studies. Thus, the deviation of the previous simulation results from the experimental data cannot be attributed simply to possible experimental errors associated with the laboratory tests but also to the limitations in formulation and inaccuracies in numerical solution. The exercises presented in this paper reveal that the previous modeling efforts certainly involve various types of errors and the experimental data cannot be matched by the gas transport models simply by adjusting the values of the unknown model parameters unless the models and their parameters are theoretically meaningful.

Comprehensive Validation of Transient Stability Calculations in Electric Power Systems and Hardware-Software Tool for Its Implementation

Reliability and survivability of electric power systems (EPS) depend on transient stability assessment (TSA). One of the most effective way to TSA is time-domain simulation. However, large-scale EPS mathematical model contains a stiff nonlinear system of high-order differential equations. Such system cannot be solved analytically. At the same time, numerical methods are imperfectly applied for such system due to limitation conditions. To make it appropriate, the EPS mathematical model is simplified and additional limitations are used. These simplifications and limitations reduce reliability of simulation results. Consequently, their validation is needed. The most reliable approach to provide it is to compare the simulation results with the field data. However, in practice, there are not enough data for such validation. This paper proposes an alternative approach for validation - the application of a reference model instead of field data. A hardware-software system HRTSim was used as a reference model. This power system simulator has all the necessary properties and capabilities to obtain reliable information required for comprehensive validation of transient stability calculations in EPSs. Main disturbances leading to instability in EPSs are investigated to conduct the validation (processes in cases of faults, single-phase auto-reclosing operation and power system interconnection). Fragments of corresponding experimental studies illustrate the efficiency of the proposed approach. Obtained results confirmed the possibility of the developed approach to identify the causes of numerical calculation errors and to determine disturbances calculated with the significant error. In addition, experimental studies have revealed that numerical calculations error depends on disturbances intensity.

On the volume conservation of emulsion drops in boundary integral simulations

Boundary Integral simulations are very common to study the microhydrodynamics of viscous drops and predict the rheology of emulsions. The standard boundary integral formulation for the velocity field at the drop surface is given by surface integrals of singular Green’s functions in space and depends on geometric quantities of the mesh, as the local mean curvature and the unitary exterior normal vector. Typically, the drops deform and rotate under the flow action, which leads to a great distortion of the computational mesh and, therefore, might produce several numerical errors in the surface velocity calculation. In this work, we investigate the numerical errors in the calculation of the surface velocity in boundary integral simulations of a viscous drop in simple shear flows. Assuming that the flow is incompressible, such that the total volume of the drops must remain constant, we use the net flow rate across the drop surface as a measure of the numerical errors in the simulations. For both small and moderate regimes of drop surface deformation, we show that the net mass flow rate across the drop surface is positive, and strongly depends on the drop-to-basis fluid viscosity ratio, capillary number of the flow, and mesh refinement. These results indicate that the volume of the drops increases continuously during the simulations. To remove the spurious mass flow rate from the simulations, we present a mesh convergence study based on an extrapolation procedure to an almost continuous mesh, so that the results become independent of mesh refinement and recover the theoretical prediction of a null net flow rate and constant drop volume in incompressible flows. The extrapolation method proposed here can be straightforwardly implemented to improve the accuracy of BI simulations used to study drop microhydrodynamics and emulsion rheology. As a matter of example, we applied the method to predict the surface deformation of a high-viscosity emulsion drop, and the result is compared in very good agreement with asymptotic theories available in the related literature.

Spurious Current Suppression in VOF-CSF Simulation of Slug Flow through Small Channels

A numerical treatment is proposed to minimize the creation of unphysical, spurious currents in modeling liquid–gas slug flow using the volume of fluid-continuum surface force (VOF-CSF) method. An elongated gas slug drawn into a small circular channel initially filled with liquid is considered. To suppress spurious currents formed by numerical errors in calculation of the surface tension force at small capillary numbers (Ca < 0.01), an artificial relative reference frame is specified with motion in a direction opposite to the flow. An increase in the local relative velocity magnitude near the interface is demonstrated to be the key mechanism for spurious current suppression. A comparison of simulations performed with and without this treatment shows that spurious currents are eliminated at Ca = 0.0029; liquid film thickness, gas slug velocity, and liquid-phase circulation near the leading slug interface are preserved and the computed values agree with the literature. This demonstrates that the proposed moving reference frame method does not influence the computed physical phenomena of interest while suppressing unphysical spurious velocities.

A Surface Parameter-Based Method for Accurate and Efficient Tool Path Generation

Along with the increasing need for multi-axis and multi-tasking machining tools for the machining of complex free surfaces, the importance of CAM applications related to the accuracy of the free surfaces has increased dramatically. The machining accuracy and surface integrity of a product depends not only on the performance of the machining tool itself but also on the tool path generated by CAM. At present, there is a trade off between numerical calculation errors and cost in CAM. There is no calculation method that satisfies both sides. Of particular importance is the fact that the cost increases exponentially with the rank of the free surface. Therefore, this paper proposes a new method of generating tool paths efficiently; it generates tool paths directly from 2-dimensional parametric space by using the parametric surface defined as a polynomial. We confirm that this method can reduce the cost and that the tool path can be generated by means of a simple calculation process, without considering singular points. Moreover, since commercial CAM kernels cannot accommodate to our method, we design and implement a new CAM kernel that can access the parametric surface directly in order to develop this method.

Methodology and verification of calculations for contact stresses in a wheel–rail system

The distribution of contact stresses in the wheel–rail system is a decisive factor for the wear of elements and the safety of rail transport. Analytical calculations of stresses based on the Hertz theory can only be applied to elastic deformation of materials. High dynamic loads leading to plastic deformation (not considered in the Hertz theory) are a predominant cause of problems in the contact vicinity. These problems can be successfully resolved by applying the finite-elements method. Two- and three-dimensional test models were generated to estimate an error in numerical calculations in the MSC.MARC program. We compared the results of numerical calculations with analytical calculations. Based on the obtained results we defined the effect of parameters describing the finite-elements mesh on the calculation error for contact stresses, and adjusted mesh parameters appropriately to achieve as low as possible error in numerical calculations. We also defined the effect of material characteristics on the value of contact stresses on the wheel–rail interface.

Adaptive particle shape setting and normal calculation methods in fluid rendering

In this paper, we present an adaptive particle shape setting method in Lagrangian-approach based screen space splatting algorithm in real-time fluid rendering. The particle radius will be adjusted according to its Weber number and local density in the rendering process so that a large radius of peaceful fluid particle can help to eliminate a bumpy surface artifact, and a small radius can prevent the obviously spherical shape of particles in splash. The shape of fluid particle will be controlled adaptively on the basis of Weber number too, so that fast moving particles could have an ellipsoidal appearance which describes the splash particle shape in turbulent flow persuasively. We also propose an adaptive normal calculation method to avoid the numerical calculation errors in the normal computation process. The sampling interval will be set in accordance with the viewing distance from camera to the fluid so that fuzzy edges or double image effect in a fixed sampling interval normal computation process could be prevented. Both of the two approaches introduced in this paper take only small amount of computing time and will have little impact on the time consuming property of a real-time fluid rendering application.

FINITE FLIESS FUNCTIONAL EXPANSION AND ITS APPLICATION TO FLIGHT CONTROL OF MISSILES

This paper addresses output tracking of nonlinear systems via state feedback and Fliess expansion. Under the full row rank assumption on the “decoupling matrix,� it is shown that a suitable state feedback can be designed such that the Fliess expansion of the closed-loop system contains only finite terms. A significant advantage of this form is that it avoids the truncation error in numerical calculation of Fliess expansions. As an application, this expansion is invoked to solve the problem of attitude control of missiles. Piecewise constant control is designed on each sampling interval to realize tracking optimization. Numerical simulations demonstrate the efficacy of the proposed control scheme.

Electron-hole duality during band-to-band tunneling process in graphene-nanoribbon tunnel-field-effect-transistors

This letter provides clear insight into the interplay between electron and hole characteristics of carriers within the forbidden gap during the band-to-band tunneling process, taking graphene-nanoribbons as an example. Accurate numerical models are presented and analytical formulas for tunneling probabilities are derived for both source/drain to channel and direct source-drain tunneling based on the Wentzel–Kramers–Brillouin (WKB) method. It is shown that not considering the electron-hole duality can lead to significant errors in numerical calculations, and more importantly, lack of proper understanding of the phenomenon gives rise to seriously misleading conclusions. Furthermore, the regime of validity of the WKB approximation for graphene-nanoribbon tunnel-field-effect-transistors is discussed in light of the electron-hole duality concept.

Analysis of stress and strain in tension cylindrical sample

AbstractOne of the basic engineering problem occurring during the numerical analysis is to define the function of yield stress of material in the real conditions of a technological process. These properties are necessary to calculate the deformation and the state of stress and strain in the surface layer of an object. An inappropriate selection of the mechanical properties of the material is the reason of the occurrence of errors in numerical calculations of a continuous object, considered as a boundary and initial problem. Scientific investigations are being conducted with the aim to develop a database concerning yield stresses for different metals, depends on complex conditions of thermo‐dynamical loads, e.g. temperature, the equivalent of the strain and the strain rate. The article presents a method of the determination of this dependence while using an experimental and numerical analysis. During the model investigations on the INSTRON testing machine, the force of elongation of the sample is measured and then calculations are made of the displacement of nodes of finite elements, plotted on outside surface of sample. The process is considered as a multi nonlinear problem. For this reason, an incremental method of motion and deformation of solid in an updated Lagrange formulation is used. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Chaotic behavior in piecewise linear Linz–Sprott equations

This paper presents the first rigorous proof of the chaotic behavior in a piecewise linear Linz-Sprott system, which is the algebraically simplest continuous three-dimensional dynamical system with chaotic behavior. The proof is computer assisted and relies on the estimation of the numerical calculation errors. The mathematical part of the proof uses topological hyperbolicity and information on the whereabouts of the periodic trajectories.