Search results for: generalized differential quadrature

Authors: Abhijith Asok

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This paper presents a generalized approach for the simple linear data transformation, Y=bX, through an integration of multidimensional coordinate geometry, vector space theory and polygonal geometry. The scaling is performed by adding an additional ’Dummy Dimension’ to the n-dimensional data, which helps plot two dimensional component-wise straight lines on pairs of dimensions. The end result is a set of scaled extensions of observations in any of the 2n spatial divisions, where n is the total number of applicable dimensions/dataset variables, created by shifting the n-dimensional plane along the ’Dummy Axis’. The derived scaling factor was found to be dependent on the coordinates of the common point of origin for diverging straight lines and the plane of extension, chosen on and perpendicular to the ’Dummy Axis’, respectively. This result indicates the geometrical interpretation of a linear data transformation and hence, opportunities for a more informed choice of the factor ’b’, based on a better choice of these coordinate values. The paper follows on to identify the effect of this transformation on certain popular distance metrics, wherein for many, the distance metric retained the same scaling factor as that of the features.

Keywords: data transformation, dummy dimension, linear transformation, scaling

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Authors: Angelis P. Barlampas

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Theoretical background Disorders of fixation and rotation of the large intestine, result in the existence of its parts in ectopic anatomical positions. In case of symptomatology, the clinical picture is complicated by the possible symptomatology of the neighboring anatomical structures and a differential diagnostic problem arises. Target The purpose of this work is to demonstrate the difficulty of revealing the real cause of abdominal pain, in cases of anatomical variants and the decisive contribution of imaging and especially that of computed tomography. Methods A patient came to the emergency room, because of acute pain in the right hypochondrium. Clinical examination revealed tenderness in the gallbladder area and a positive Murphy's sign. An ultrasound exam depicted a normal gallbladder and the patient was referred for a CT scan. Results Flexible, unfixed ascending colon and cecum, located in the anatomical region of the right mesentery. Opacities of the surrounding peritoneal fat and a small linear concentration of fluid can be seen. There was an appendix of normal anteroposterior diameter with the presence of air in its lumen and without clear signs of inflammation. There was an impression of possible inflammatory swelling at the base of the appendix, (DD phenomenon of partial volume; e.t.c.). Linear opacities of the peritoneal fat in the region of the second loop of the duodenum. Multiple diverticula throughout the colon. Differential Diagnosis The differential diagnosis includes the following: Inflammation of the base of the appendix, diverticulitis of the cecum-ascending colon, a rare case of second duodenal loop ulcer, tuberculosis, terminal ileitis, pancreatitis, torsion of unfixed cecum-ascending colon, embolism or thrombosis of a vascular intestinal branch. Final Diagnosis There is an unfixed cecum-ascending colon, which is exhibiting diverticulitis.

Keywords: unfixed cecum-ascending colon, abdominal pain, malrotation, abdominal CT, congenital anomalies

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Authors: Tahseen Saad, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A new concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. To control the coordination problem, which depends on offset selection and to estimate uniform delay based on the offset choice in a traffic signal network. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and are compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show new model minimizes the total uniform delay to almost half compared to conventional models. The mathematical objective function is robust. The algorithm convergence time is fast.

Keywords: area traffic control, traffic flow, differential evolution, sinusoidal periodic function, uniform delay, offset variable

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Pranitha Janapatla, Venkata Suman Gontla

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The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Marcelo Jesus Kato Avila, Joao Da Costa Pantoja

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Differential settlement of foundations is a serious pathology in buildings that put at risk lives and property. A common reason for the occurrence of this specific pathology in central Brazil is the presence of collapsible clay, a typical soil in the region. In this study, the foundation of a condemned building erected above this soil is analyzed. The aim is to prevent problems in new constructions, to predict which buildings may be subjected to damages, and to make possible a more precise treatment in less advanced differential settlements observed in the buildings of the vicinity, which includes a hospital, a Military School, an indoor sporting arena, the Police Academy, and the Military Police Headquarters. The methodology consists of visual inspection, photographic report of the main pathologies, analysis of the existing foundations, determination of the soil properties, the study of the cracking level and assessment of structural failure risk of the building. The findings show that the presence of water weaken the soil structure on which the foundation rest, being the main cause of the pathologic settlement, indicating that even in a one store building it was necessary to consider deeper digging, other categories of foundations, and more elaborated and detailed foundation plans when the soil presents this behavior.

Keywords: building cracks, collapsible clay, differential settlement, structural failure risk

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Authors: Evans Iyamu

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Genes encoding hydrophobins play distinct roles at different stages of the life cycle of fungi, and they foster hyphal attachment to surfaces. The hydrophobin Sc4 is known to provide a hydrophobic membrane lining of the gas channels within Schizophyllum commune fruiting bodies. Here, we cultivated non-fruiting, monokaryotic S. commune 12-43 on glass surfaces that could be verified by micrography. Differential gene expression profiling of nine hydrophobin genes and the hydrophobin-like sc15 gene by quantitative PCR showed significant up-regulation of sc4 when S. commune was attached to glass surfaces, also confirmed with RNA-Seq data analysis. Another silicate, namely quartz sand, was investigated, and induction of sc4 was seen as well. The up-regulation of the hydrophobin gene sc4 may indicate involvement in S. commune hyphal attachment to glass as well as quartz surfaces. We propose that the covering of hyphae by Sc4 allows for direct interaction with the hydrophobic surfaces of silicates and that differential functions of specific hydrophobin genes depend on the surface interface involved. This study could help with the clarification of the biological functions of hydrophobins in natural surroundings, including hydrophobic surface attachment. Therefore, the analysis of growth on glass serves as a basis for understanding S. commune interaction with glass surfaces while providing the possibility to visualize the interaction microscopically.

Keywords: hydrophobin, structured glass surfaces, differential gene expression, quartz sand

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Longqing Li

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The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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Authors: V. S. Klimash, Ye Min Thu

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Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model

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Authors: Muhammad Faraz, Talat Rafique, Jang Min Park

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In this article, rotational flow above a permeable surface with a variable free stream angular velocity is considered. Main interest is to solve the associated heat/mass transport equations under different situations. Firstly, heat transport phenomena occurring in generalized vortex flow are analyzed under two altered heating processes, namely, the (i) prescribed surface temperature and (ii) prescribed heat flux. The vortex motion imposed at infinity is assumed to follow a power-law form 〖(r/r_0)〗^((2n-1)) where r denotes the radial coordinate, r_0 the disk radius, and n is a power-law parameter. Assuming a similar solution, the governing Navier-Stokes equations transform into a set of coupled ODEs which are treated numerically for the aforementioned thermal conditions. Secondly, mass transport phenomena accompanied by activation energy are incorporated into the generalized vortex flow situation. After finding self-similar equations, a numerical solution is furnished by using MATLAB's built-in function bvp4c.

Keywords: bödewadt flow, vortex flow, rotating flows, prescribed heat flux, permeable surface, activation energy

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Xuezhang Hou

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A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Kehinde Peter Oyeduntan, Kayode Oshinubi

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Nigeria is referred as the ‘Giant of Africa’ due to high population, land mass and large economy. However, it still trails far behind many smaller economies in the continent in terms of maritime operations. As we have seen that the maritime industry is the spark plug for national growth, because it houses the most crucial infrastructure that generates wealth for a nation, it is worrisome that a nation with six seaports lag in maritime activities. In this research, we have studied how the Gross Domestic Product (GDP) of the maritime transport influences the Nigerian economy. To do this, we applied Simple Linear Regression (SLR), Support Vector Machine (SVM), Polynomial Regression Model (PRM), Generalized Additive Model (GAM) and Generalized Linear Mixed Model (GLMM) to model the relationship between the nation’s Total GDP (TGDP) and the Maritime Transport GDP (MGDP) using a time series data of 20 years. The result showed that the MGDP is statistically significant to the Nigerian economy. Amongst the statistical tool applied, the PRM of order 4 describes the relationship better when compared to other methods. The recommendations presented in this study will guide policy makers and help improve the economy of Nigeria in terms of its GDP.

Keywords: maritime transport, economy, GDP, regression, port

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Authors: M. Salmanzadeh

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In paper, we will deal with incompressible Couette flow, which represents an exact analytical solution of the Navier-Stokes equations. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. The numerical technique that we will employ for the solution of the Couette flow is the Crank-Nicolson implicit method. Parabolic partial differential equations lend themselves to a marching solution; in addition, the use of an implicit technique allows a much larger marching step size than would be the case for an explicit solution. Hence, in the present paper we will have the opportunity to explore some aspects of CFD different from those discussed in the other papers.

Keywords: incompressible couette flow, numerical method, partial differential equation, Crank-Nicolson implicit

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Authors: Benniche Omar

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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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Authors: M. O. Durojaye, J. T. Agee

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This paper is on the one-dimensional, positive temperature coefficient (PTC) thermistor model with a hyperbolic tangent function approximation for the electrical conductivity. The method of asymptotic expansion was adopted to obtain the steady state solution and the unsteady-state response was obtained using the method of lines (MOL) which is a well-established numerical technique. The approach is to reduce the partial differential equation to a vector system of ordinary differential equations and solve numerically. Our analysis shows that the hyperbolic tangent approximation introduced is well suitable for the electrical conductivity. Numerical solutions obtained also exhibit correct physical characteristics of the thermistor and are in good agreement with the exact steady state solutions.

Keywords: electrical conductivity, hyperbolic tangent function, PTC thermistor, method of lines

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Joon Ho Kim, Tae Kwon Ha

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Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by Differential Speed Rolling (DSR) process were studied by Electron Back Scattered Diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100°C with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400°C for 30 to 120 min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: aluminium/copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: Dmitry Yu. Korulkin, Raissa A. Muzychkina

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In review the generalized data about biosynthetic routs formation anthraquinone molecules in natural cells. The basic possibilities of various ways of biosynthesis of different quinoid substances are shown.

Keywords: anthraquinones, biochemical evolution, biosynthesis, metabolism

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Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

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The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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Authors: Sumara Khursheed, Jitendra Sharma

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The present work reports synthesis of nanocomposites (NCs) of phosphor (KCaVO4:Sm3+) embedded poly(methylmethacrylate) (PMMA) using solution casting method and their optical properties measurements for their possible application in making flexible luminescent films. X-ray diffraction analyses were employed to obtain the structural parameters as crystallinity, shape and size of the obtained NCs. The emission and excitation spectra were obtained using Photoluminescence spectroscopy to quantify the spectral properties of these fluorescent polymer/phosphor films. Optical energy gap has been estimated using UV-VIS spectroscopy while differential scanning calorimetry (DSC) was exploited to measure the thermal properties of the NC films in terms of their thermal stability, glass transition temperature and degree of crystallinity etc.

Keywords: nanocomposites, luminescence, XRD, differential scanning calorimetry, PMMA

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Authors: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

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In this paper, quantitative structure-retention relationships (QSRR) analysis was applied in order to correlate in silico biological and lipophilicity molecular descriptors with retention values for the set of selected s-triazine herbicides. In silico generated biological and lipophilicity descriptors were discriminated using generalized pair correlation method (GPCM). According to this method, the significant difference between independent variables can be noticed regardless almost equal correlation with dependent variable. Using established multiple linear regression (MLR) models some biological characteristics could be predicted. Established MLR models were evaluated statistically and the most suitable models were selected and ranked using sum of ranking differences (SRD) method. In this method, as reference values, average experimentally obtained values are used. Additionally, using SRD method, similarities among investigated s-triazine herbicides can be noticed. These analysis were conducted in order to characterize selected s-triazine herbicides for future investigations regarding their biodegradability. This study is financially supported by COST action TD1305.

Keywords: descriptors, generalized pair correlation method, pesticides, sum of ranking differences

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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