Use Of Analytical Expressions Research Articles

A Closed-Form Expression for Analysis of Dark State Exchange Saturation Transfer (DEST) NMR Experiments.

Closed-form expressions for the analysis of Dark state Exchange Saturation Transfer (DEST) NMR experiments, a powerful experimental tool for characterizing exchange processes involving the interaction of NMR visible species with very high molecular weight partners, is presented. Essentially identical exchange and relaxation parameters are derived from the analytical and numerical best fits of the DEST profiles obtained for a protein construct derived from huntingtin exon-1, comprising the N-terminal amphiphilic sequence followed by a seven-residue glutamine repeat, httNTQ7, in the presence of small (SUV) and large (LUV) unilamellar lipid vesicles. The use of analytical expressions significantly speeds up the fitting of experimental DEST profiles to a two-state exchange model and simplifies the analysis of the DEST effects.

A simplified approach for predicting last ply failure load of VO-notched laminated composite components

In this study, the last ply failure (LPF) load of composite laminates with VO-notches under pure mode I and mixed mode I/II was investigated experimentally, analytically, and numerically. The efficiency of the virtual isotropic material concept (VIMC) in combination with a new combined failure criterion was also evaluated. The J-integral and average strain energy density failure criteria were combined with VIMC. Using analytical expressions for the J-integral and the average strain energy density (ASED), the prediction of the fracture load of notched components was simplified and expedited. The experimental fracture loads of notched specimens were determined for quasi-isotropic and cross-ply laminates under mode I and mixed mode I/II. The fracture loads were predicted using analytical expressions for the J-integral and ASED, combined with VIMC. The VIMC-ASED and VIMC-J-integral failure criteria demonstrated good accuracy in predicting the LPF, with the highest accuracy for mode I, slightly reduced accuracy for mixed mode I/II. VIMC, in combination with energy-based failure criteria, effectively predicts the fracture load. The use of analytical expressions further simplified and expedited the prediction process without losing accuracy, making it a practical approach for engineering applications. Additionally, this approach significantly reduces the time and cost associated with extensive experimental testing.

Assessment methodology for security of an automated control system of critical information infrastructure against DDoS attacks based on Monte Carlo simulation

Objective. The purpose of the study is to develop a methodology for assessing the security of an automated control system of critical information infrastructure from DDoS attacks. The purpose of the methodology development is to provide the decision–maker with a scientifically sound tool for assessing the risk of implementing a DDoS attack.Method. To achieve the stated goal of the study, simulation modeling based on the Monte Carlo method was used.Result. The expediency of using Monte Carlo simulation to assess the probability of server failure under DDoS attacks is confirmed. It was concluded that the server can be considered as a queuing system, however, the flow of incoming applications under DDoS attacks is not Poisson, so the use of analytical expressions to assess the probability of failure is considered incorrect. The simulation results allow the decision-maker to assess the probability of server failure and make organizational and technical decisions to increase the level of security. Analysis of the simulation results showed the effectiveness of improving server performance by increasing service channels.Conclusion. Thus, the developed methodology will be useful in conducting an information security audit of an organization to justify the amount of its insurance premium in the framework of cyber risk insurance. A possible direction for further research is to study the issue of computer network security, taking into account the features of a specific topology.

Statistical Characterization of Strain-Controlled Low-Cycle Fatigue Behavior of Structural Steels and Aluminium Material.

Probabilistic evaluation of the resistance to low-cycle deformation and failure of the critical components in the equipment used in the energy, engineering, metallurgy, chemical, shipbuilding, and other industries is of primary importance with the view towards their secure operation, in particular, given the high level of cyclic loading acting on the equipment during its operation. Until recently, systematic probabilistic evaluation has been generally applied to the results of statistical and fatigue investigations. Very few investigations applying this approach to the low-cycle domain. The present study aims to substantiate the use of probabilistic calculation in the low-cycle domain by systematic probabilistic evaluation of the diagrams of cyclic elastoplastic deformation and durability of the materials representing the major types of cyclic properties (hardening, softening, stabilization) and investigation of the correlation relationships between mechanical properties and cyclic deformation and failure parameters. The experimental methodology that includes the calculated design of the probabilistic fatigue curves is also developed and the curves are compared to the results of the experiment. Probabilistic values of mechanical characteristics were determined and calculated low-cycle fatigue curves corresponding to different failure probabilities, to assess them from the probabilistic perspective. A comparison of low-cycle fatigue curves has shown that the durability curves generated for some materials using analytical expressions are not accurate. According to the analysis of the relative values of experimental probabilities of low-cycle fatigue curves, the use of analytical expressions to build the curves can lead to a significant error. The results obtained allow for the revision of the load bearing capacity and life of the structural elements subjected to cyclic elastoplastic loading in view of the potential scattering of mechanical properties and resistance parameters to low-cycle deformation and failure. In addition, the results enable determination of the scatter tolerances, depending on the criticality of the part or structure.

High-cycle fatigue behavior of type 4340 steel pressurized blocks including mean stress effect

Mean stress effects in pressurized steel blocks were examined under constant amplitude fatigue loading. The tests were performed to provide experimental data needed to study the effect of mean stress on fatigue lives of subject specimen, and to substantiate the use of analytical expressions to account for the mean stress. The mean stress was the result of subjecting the specimens to an autofrettage pressure which induced compressive residual stresses at the crossbore intersection of the specimens. Fatigue tests were carried out under both tensile and compressive mean stress levels. Test results were compared to several mean stress accounting relationships such as the Smith-Watson Topper, Bergmann and Seeger, modified Goodman, Gerber and Soderberg. Test results indicated that the modified Goodman equation is favorable in accounting for the effect of both tensile and compressive mean stresses on fatigue life (up to a compressive mean stress to ultimate stress ratio of −0.2). The behavior under compressive mean stress to ultimate stress ratio of less than −0.2 indicated that a linear correction relationship was required.

Push-forward method for piecewise deterministic biochemical simulations

A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well-stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some molecular species are in small numbers and reactions changing them are infrequent. In this case, discrete stochastic events trigger changes of the smooth deterministic dynamics of the biochemical network. Piecewise-deterministic Markov processes (PDMP) are well adapted for describing such situations. Although PDMP models are now well established in biology, these models remain computationally challenging. Previously we have introduced the push-forward method to compute how the probability measure is spread by the deterministic ODE flow of PDMPs, through the use of analytic expressions of the corresponding semigroup. In this paper we provide a more general simulation algorithm that works also for non-integrable systems. The method can be used for biochemical simulations with applications in fundamental biology, biotechnology and biocomputing. This work is an extended version of the work presented at the conference CMSB2019.

Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems

The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement.

Super-Eddington accretion in the Q2237+0305 quasar?

The interband time lags between the flux variations of the Q2237+0305 quasar have been determined from light curves in the Johnson-Cousins V, R, and I spectral bands. The values of the time lags for filter pairs R − V, I − R, and I − V are significantly higher than those predicted by the standard accretion disk model by Shakura and Sunyaev. To explain the discrepancy, the idea of a supercritical accretion regime in quasars considered in 1973 by Shakura and Sunyaev is applied. This regime has been shown by them to cause an extended scattering envelope around the accretion disk. The envelope efficiently scatters and re-emits the radiation from the accretion disk and thus increases the apparent disk size. We made use of analytical expressions for the envelope radius and temperature derived by Shakura and Sunyaev in their analysis of super-Eddington accretion and show that our results are consistent with the existence of such an envelope. The corresponding parameters of the accretion regime were calculated. They provide the radii of the envelope in the V, R, and I spectral bands consistent with the inter-band time lags determined in our work.

The Optimal Distribution of Income Revisited

This paper revisits the optimal distribution of income model in Fair (1971). This model is the same as in Mirrlees (1971) except that education is also a decision variable and tax rates are restricted to lie on a tax function. In the current paper the tax-rate restriction is relaxed. As in Fair (1971), a numerical method is used. The current method uses the DFP algorithm with numeric derivatives. Because no analytic derivatives have to be taken, it is easy to change assumptions and functional forms and run alternative experiments. Gini coefficients are computed, which provides a metric for comparing the redistributive effects under different assumptions. Ten optimal marginal tax rates are computed per experiment corresponding to ten tax brackets.The sensitivity of the results to the four main assumptions of the model are examined: 1) the form of the social welfare function that the government maximizes, 2) the form of the utility function that each individual maximizes, 3) the distribution of ability across individuals, and 4) the rate of return to education. The changes in the Gini coefficient from before-tax income to after-tax income for the experiments are compared to actual changes from various countries. Experiments using a lognormal distribution of ability match the data better than those using a lognormal distribution with a Pareto tail --- there is less actual redistribution than a Pareto tail implies. The numerical approach in this paper has advantages over the use of analytic expressions. When functional forms are changed, it may be easier to run a new numerical experiment then use an analytic expression, which can be complicated. Also, although not done in this paper, individual heterogeneity is straightforward to handle. The coding can have a different utility function for each individual. And different assumptions about education can be easily incorporated. The approach also shows the problematic nature of assuming a quasi-linear utility function --- a utility function with no income effects.

Quantitative assessment of the identifiability of pipeline systems★The research was carried out within the project III.17.4.3 of the Fundamental research program of SB RAS (AAAA-A17-117030310437-4)

The article is devoted to the issues of quantitative assessment of the identifiability of the pipeline systems (heat, water, gas supply systems etc.). Identifiability is first considered as a complex property, including such particular properties as observability and parametric identifiability. A brief description of the topic relevance and a review of available development in this sphere allow giving the structuring of identifiability analysis problems. The technique of differentiate quantitative analysis of this property is disclosed. It based on the use of analytical expressions for covariance matrices of parameters. New concepts of experimental matrices, parametric identifiability and observability of pipeline systems are introduced. Analytic expressions for these matrices are given. The substantiation of the integral indicators of the pipeline systems identifiability is presented, including the covariance matrix determinant for the estimated parameters and the relative variance of the prediction for non-measurable state parameters. The analytical interrelation of these indicators is opened. These indicators can be accepted in a role of criteria at decision of synthesis problems for optimal measurements composition.

Design of a wide-angle, polarization-insensitive, dual-band metamaterial-inspired absorber with the aid of equivalent circuit model

We present the design of a wide-angle, polarization-insensitive, dual-band, low-profile metamaterial-inspired absorber for operation at two wireless local area network channels, related to 2.45 and 5 GHz industrial, scientific and medical frequencies. The design synthesis methodology involves equivalent circuit model calculations with the use of analytical expressions of capacitive and inductive elements prior to full-wave electromagnetic optimization, for easily acquiring of very high absorption conditions at the targeted frequencies. The unit cell of the metamaterial-inspired absorber consists of a joint metallic Jerusalem cross resonator with interdigital capacitors and a tetra-arrow resonator printed on top of a grounded 1-mm-thick lossy FR-4 substrate. The proposed absorber shows almost unity absorptivity at the targeted frequencies and a robust absorption characteristic under changes in incidence angle and polarization. The proposed structure can be used for protection of the systems from electromagnetic interference with existing wireless local area network frequencies.

Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured Plus Gaussian Interference Via Invariance

This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions.

ANALYTICAL SOLUTIONS FOR RADIATION-DRIVEN WINDS IN MASSIVE STARS. I. THE FAST REGIME

Accurate massloss rate estimates are crucial keys to study wind properties of massive stars and test different evolutionary scenarios. From a theoretical point of view, this implies to solve a complex set of differential equations in which the radiation field and the hydrodynamics are strong coupled. The use of analytical expression to represent the radiation force and the solution of the equation of motion have many advantages over numerical integrations. Therefore, in this work, we present an analytical expression as solution of the equation of motion for radiation driven winds, in terms of the force multipliers parameters. This analytical expression is obtained by employing the line acceleration expression given by Villata (1992) and the methodology proposed by Mueller and Vink (2008). On the other hand, we find useful relationships to determine the parameters for the line acceleration given by Mueller and Vink (2008) in terms of the force multiplier parameters.

Migration of tungsten dust in tokamaks: role of dust–wall collisions

The modelling of a controlled tungsten dust injection experiment in TEXTOR by the dust dynamics code MIGRAINe is reported. The code, in addition to the standard dust–plasma interaction processes, also encompasses major mechanical aspects of dust–surface collisions. The use of analytical expressions for the restitution coefficients as functions of the dust radius and impact velocity allows us to account for the sticking and rebound phenomena that define which parts of the dust size distribution can migrate efficiently. The experiment provided unambiguous evidence of long-distance dust migration; artificially introduced tungsten dust particles were collected 120° toroidally away from the injection point, but also a selectivity in the permissible size of transported grains was observed. The main experimental results are reproduced by modelling.

Real Time Analytical Linearization of Turbofan Engine Model

This paper presents a methodology for developing a control oriented analytical linear model of a turbofan engine at both equilibrium and nonequilibrium conditions. This scheme provides improved accuracy over the commonly used linearization method based on numerical perturbation and piecewise linear interpolation. Linear coefficients are obtained by evaluating at current conditions analytical expressions, which result from differentiation of simplified nonlinear expressions. Residualization of the fast dynamics states are utilized since the fast dynamics are outside of the primary control bandwidth. Analytical expressions based on the physics of the aerothermodynamic processes of a gas turbine engine facilitate a systematic approach to the analysis and synthesis of model based controllers. In addition, the use of analytical expressions reduces the computational effort, enabling linearization in real time at both equilibrium and nonequilibrium conditions to enable more accurate capture of system dynamics during aggressive transient maneuvers. The methodology is formulated and applied to a separate flow twin spool turbofan engine model in the numerical propulsion system simulation (NPSS) platform. The derived linear model is validated against the full nonlinear engine model.

Stress of drawing solid rectangular profiles

The process of drawing rectangular sections is conveniently designed with the use of analytical expressions that make it possible to operatively evaluate different manufacturing factors. The application of a drawing tool with optimum angles makes it possible to cut down power inputs and reduce the failure and unsoundness of a blank. A design procedure for the drawing stress of the rectangular section is advanced. Formulas for calculating the drawing stress and determining the optimum angles of a channel of the drawing tool are derived. It is shown that the optimum angles depend on the friction coefficient and the reduction ratio.

An Analytical Step-by-Step Procedure to Derive the Flexural Response of RC Sections in Compression

This paper proposes an analysis procedure able to determine the flexural response of rectangular symmetrically reinforced concrete sections subjected to axial load and uniaxial bending. With respect to the usual numerical approaches, based on the fibre decomposition method, this procedure is based on the use of analytical expressions of the contributions to the equilibrium given by the longitudinal reinforcement and the concrete region in compression, which depend on the neutral axis depth and the curvature at each analysis step. The formulation is developed in dimensionless terms, after a preliminary definition of the geometrical and mechanical parameters involved, so that the results are valid for classes of RC sections. The constitutive laws of the materials include confinement effect on the concrete and postyielding behaviour of the steel reinforcement, which can be assumed to be softening behaviour for buckled reinforcing bars. The strength and curvature domains at the first yielding of the reinforcement in tension and at the ultimate state are derived in the form of analytical curves depending on the compression level; therefore, the role of a single parameter on the shape of these curves can easily be deduced. The procedure is validated by comparing some results with those numerically obtained by other authors.

Computational Modeling of Columnar to Equiaxed Transition in Alloy Solidification

AbstractThe columnar to equiaxed transition (CET) provides a challenging simulation goal for computational models of alloy solidification, in addition to being an important technological feature of many casting processes. CET thus provides an industrially relevant test‐case for those developing numerical models across a range of scales. Whether or not CET occurs depends on numerous experimental parameters such as cooling rate, speed of columnar growth, thermal gradient in the liquid, and level of grain refiner in the alloy. Information on columnar and equiaxed grain structure, and the transition between the two, is very useful for foundry engineers, at the macroscopic scale of the casting. The detailed microstructure within each grain is determined by typically dendritic growth and local transport of solute and heat. This paper presents a review of recent progress on modeling CET at multiple length scales. It is evident that, whilst micro‐models can provide simulations of physical phenomena, such as the evolution of dendrite morphology, at scales 10−3 to 10−5 m, finite computational resources preclude this resolution over the length scale of castings which is in the 10−2–100 m range. Instead, reasonably accurate models of CET formation in castings can be achieved by meso‐scale modeling featuring 10−3–10−2 m phenomena. Such meso‐scale models make use of analytical expressions to simulate dendrite growth in undercooled melts. Recent progress in modeling of CET, at both macro/meso‐ and micro‐scales is reviewed, and computational challenges yet to be met are summarized.

Energy dissipation in the presence of sub-harmonic excitation in dynamic atomic force microscopy

Amplitude modulation atomic force microscopy allows quantifying energy dissipation in the nanoscale with great accuracy with the use of analytical expressions that account for the fundamental frequency and higher harmonics. Here, we focus on the effects of sub-harmonic excitation on energy dissipation and its quantification. While there might be several mechanisms inducing sub-harmonics, a general analytical expression to quantify energy dissipation whenever sub-harmonics are excited is provided. The expression is a generalization of previous findings. We validate the expression via numerical integration by considering capillary forces and provide experimental evidence of sub-harmonic excitation for a range of operational parameters.

Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems

The heat transfer coefficient of convection from the wall to the flow depends on flow type, on surface temperature distribution in a stream-wise direction, and in transient cases also on time. In so-called conjugated problems, the surface temperature distribution of the wall and flow are coupled together. Thus, the simultaneous solution of convection between the flow and wall, and conduction in the wall are required because heat transfer coefficients are not known. For external and internal flows, very accurate approximate analytical expressions have been derived for heat transfer in different kinds of boundary conditions which change in flow direction. Due to the linearity of the energy equation, the superposition principle can be adopted to couple with these expressions the surface temperature and heat flux distributions in conjugated problems. In the paper, this type of approach is adopted and applied to a number of industrial applications ranging from flat plates of electroluminecence displays to the optimization of heat transfer in fins, fin arrays and mobile phones.