Ordinary Form Research Articles

Bifurcation of Rupture Path-Linear and Nonlinear Damping

Bifurcation of rupture path is studied for the effect of linear and nonlinear cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the method separation of variables. Analytical solutions yield the bifurcation of linear and nonlinear cubic damping was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible due to lower cubic damping. Amplitude attenuated during the seismic moment. Imaginary parts of the solutions illustrate the intersection or collision of soliton, for which, the bifurcation of rupture path is initiated. Intersection is not visible if the energy is well dispersed. Wave profile illustrates the existing of linear exciting and nonlinear damping effect during seismic moment.

Post-Critical Behavior of Suspension Bridges Under Nonlinear Aerodynamic Loading

Abstract The limit cycle oscillations (LCOs) exhibited by long-span suspension bridges in post-flutter condition are investigated. A parametric dynamic model of prestressed long-span suspension bridges is coupled with a nonlinear quasi-steady aerodynamic formulation to obtain the governing aeroelastic partial differential equations adopted herewith. By employing the Faedo–Galerkin method, the aeroelastic nonlinear equations are reduced to their state-space ordinary differential form. Convergence analysis for the reduction process is first carried out and time-domain simulations are performed to investigate LCOs while continuation tools are employed to path follow the post-critical LCOs. A supercritical Hopf bifurcation behavior, confirmed by a stable LCO, is found past the critical flutter condition. The analysis shows that the LCO amplitude increases with the wind speed up to a secondary critical speed where it terminates with a fold bifurcation. The stability of the LCOs within the range bracketed by the Hopf and fold bifurcations is evaluated by performing parametric analyses regarding the main design parameters that can be affected by uncertainties, primarily the structural damping and the initial wind angle of attack.

Social Media Services and Technologies Towards Web 3.0

Daily growth of the social media, together with numbers of service and application, reveals a significant change on information sharing. Unlike a conventional push-n-receive scenario, the social media offers a more attractive environment where the user acts as information transmitter and receiver—they create, comment, and remix new or existing information—and in other way adds extra value to the content in its ordinary form. Although social media is a relatively new phenomenon, its roots can be traced to wellestablished and mature technologies and social behaviors that have underpinned information exchanges. What distinguishes social media, setting it apart from existing forms of online communication and interactions, is the ability of users to easily create and share information with their networks in real time, using not just computers, but also smart devices (e.g., mobile, sensors, etc.). This leads to a dramatic implication as information can reach wider audiences much faster, capturing their attention even when they are away from their computer screen. The success of online services such as Facebook, Twitter, and YouTube are testimony to the importance of social media and the impact they have had on both individuals and businesses. Giving a quick glance to the history of Web, the fundamentals of information service explosion today was laid with Web 1.0, which is the read-only Web. The initial system created a constantly growing library for the publishing of information on static websites where users Multimed Tools Appl (2015) 74:5007–5013 DOI 10.1007/s11042-015-2461-4

Calculation of equation of state of a material mixture

The problem of calculating the equation of state (EOS) of a material mixture often comes from fluid-dynamical system containing multiple materials. Generally, the EOS of a material mixture is a system of nonlinear equations which are usually solved by the tabular method and the Newton iterative method. However, the former has poor accuracy, and the later has a finite radius of convergence and hence will converge only if the initial guess is sufficiently close to the final solution. So, a procedure different from the above two method is presented for calculating the EOS of a material mixture whose constituents are in pressure equilibrium and temperature equilibrium. An imbedding method is used to determine the constituent partial thermodynamic variables subjected to the constraints that the total volume and energy of mixture and the constituent mass fractions are specified. The imbedding method has a large radius of convergence, introducing a parameter defined in the interval [0, 1] and a system of imbedding equations which is linearly composed of the to-be-solved EOS of a material mixture and the easy-to-solve EOS of a material mixture. While the parameter changes continuously from 0 to 1, the imbedding method continuously changes the solution of the to-be-solved EOS which the easy-to-solve EOS of a material mixture is continuously converted into. The system of imbedding equations can be changed into a system of ordinary differential form by taking the parameter as independent variable, easily solved by a matured computational method such as trapezoidal rule. By using thermodynamic formulae, two equations in the generalized Maxwellian form are obtained, relating respectively the pressure rate and temperature rate to the strain rate and the constituent mass fraction rate. Finally, the computational method is verified by calculating the EOS of various mass fractions of lead and tin mixture.

Reduced order finite element modelling of a nonlinear system: an application to induction heating system

In this paper, a fully dynamic three dimensional induction heating system having axial symmetry is considered. The model is described by nonlinear partial differential equations and nonlinearities are due to dependence of specific heat, thermal and electrical conductivities on temperatures. A mathematical model in nonlinear ordinary differential form is obtained. A reduction technique is applied to obtain a reduced model for further use. Error due to the reduction is obtained and it has been observed that the error is quite small thus illustrating the validity of this model. Numerical results and possible extensions are given.

Transverse magnetic field on Jeffery–Hamel problem with Cu–water nanofluid between two non parallel plane walls by using collocation method

An analysis has been performed to study the problem of magneto-hydrodynamic (MHD) Jeffery–Hamel flow with nanoparticles. The governing equations for this problem are reduced to an ordinary form and is solved using collocation method (CM) and numerically by fourth order Runge–Kutta technique. Also, Velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of the semi angles between the plates, Reynolds number, magnetic field strength and nanoparticles volume fraction on the velocity field. As an important outcome, Increasing Reynolds numbers leads to reduce velocity and excluded backflow in convergent channel.

Aeroelastic behavior of long-span suspension bridges under arbitrary wind profiles

The aeroelastic behavior of suspension bridges under generic temporal and space wind distributions is studied employing a parametric one-dimensional structural model coupled with a strip-based indicial representation of the unsteady aerodynamic loads. The aeroelastic response to spatially nonuniform gusts is also investigated. The equations of motion linearized about the prestressed aerostatic equilibrium are expressed in terms of incremental kinematic variables. The aerodynamic loading characteristics of the deck cross sections of the Runyang Suspension Bridge (over the Yangtze river in China) are evaluated by means of computational fluid dynamics simulations performed to extract the aeroelastic derivatives from which the indicial aerodynamic representation is obtained. The aeroelastic equations of motion are then reduced to the state-space ordinary differential form by using the Faedo–Galerkin approach. The reduced-order bridge dynamics and the description of the aerodynamic loading via the added aerodynamic states are solved simultaneously by using a time-integration numerical scheme. Dependence of the flutter condition and the transient response to gusts is shown through systematic parametric studies.

CNT suspended nanofluid analysis in a flexible tube with ciliated walls

Abstract: The current investigation is carried out to analyze the effect of heat transfer in a flexible tube with ciliated walls and carbon nanotubes. The problem has been formulated in the form of non-linear partial differential equations, which are then reduced to ordinary differential equation form using the dimensionless variables and the conditions of low Reynolds number and long wavelength. Exact solutions have been obtained for velocity, temperature and pressure gradient and graphs for velocity, temperature and pressure gradient have been plotted for a better analysis of the solution.

Limit periodic travelling wave solution of a model for biological invasions

Abstract In this paper, we consider a class of biological invasion model with density-dependent migrations and Allee effect, which is reduced to one ordinary differential form via the travelling wave solution ansatz. For the corresponding planar system, we firstly obtain the first several weak focal values of its one equilibrium by computing the singular point quantities, then determine the existence of one stable limit cycle from its Hopf bifurcation. Thus a special periodic travelling wave solution which is isolate as a limit is obtained, and it corresponds to the particular real patterns of spread during biological invasions, which is an interesting discovery.

Strongly modified four-wave mixing in a coupled semiconductor quantum dot-metal nanoparticle system

We study the four-wave mixing effect in a coupled semiconductor quantum dot-spherical metal nanoparticle structure. Depending on the values of the pump field intensity and frequency, we find that there is a critical distance that changes the form of the spectrum. Above this distance, the four-wave mixing spectrum shows an ordinary three-peaked form and the effect of controlling its magnitude by changing the interparticle distance can be obtained. Below this critical distance, the four-wave mixing spectrum becomes single-peaked; and as the interparticle distance decreases, the spectrum is strongly suppressed. The behavior of the system is explained using the effective Rabi frequency that creates plasmonic metaresonances in the hybrid structure. In addition, the behavior of the effective Rabi frequency is explained via an analytical solution of the density matrix equations.

Mock modular forms and d-distinct partitions

The generating function for partitions into (d+1)-distinct parts (d+1∈N) may be expressed as the q-hypergeometric seriesRd+1(1;q):=∑n⩾0qd+1(n)qn=∑n⩾0q(d+1)(n2)+n(q;q)n, where qd+1(n):=p(n|parts differ by at least d+1). Within combinatorial number theory, this function has long since been of historical importance: a famous identity of Euler and Sylvester implies that the distinct parts function q1/24R1(1;q) is an ordinary modular form, and the celebrated Rogers–Ramanujan identities imply that the 2-distinct parts function q−1/60R2(1;q) is an ordinary modular form. More recently Alder–Andrews, Zagier, and others have studied the general series Rd+1(1;q) for d∈N0. In particular, Zagier has proved for d>1 that these series are never ordinary modular forms; however, other than the cases d=0 (Euler) and d=1 (Rogers–Ramanujan), the precise modular properties of these combinatorial series remain unknown. Here, we prove for integers d⩾1, that the combinatorial q-series Rd+1(1;q), and relevant generalizations, are natural denominators of a new class of mixed mock modular forms. As such, we also obtain many new results as corollaries, including new expressions for Zwegersʼs lauded μ-function, and many of the well-known combinatorial q-series in the subject, confirming the central role that the q-hypergeometric series Rd+1(1;q) play within the theory. Once armed with this realization, we also obtain general theorems on the analytic behavior of Rd+1(1;q) and related series near the unit disk, a priori an impenetrable barrier littered with exponential singularities.

A new numerical algorithm based on the first kind of modified Bessel function to solve population growth in a closed system

Volterra's model for population growth in a closed system includes an integral term to indicate accumulated toxicity in addition to the usual terms of the logistic equation. In this research, a new numerical algorithm is introduced for solving this model. The proposed numerical approach is based on the modified Bessel function of the first kind and the collocation method. In this method, we aim to solve the problems on the semi-infinite domain without any domain truncation, variable transformation in basis functions and shifting the problem to a finite domain. Accordingly, we employ two different collocation approaches, one by computing through Volterra's population model in the integro-differential form and the other by computing by converting this model to an ordinary differential form. These methods reduce the solution of a problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of these methods, we compare the numerical results of the present methods with some well-known results in other to show that the new methods are efficient and applicable.

一阶微分电路构成的混沌

混沌是有界非线性函数最一般的普遍形式，它普遍的存在于自然界的各个学科领域。混沌是各种各样有界非线性振荡的统一术语。本文证明三个频率不同谐波源混频构成的一阶微分电路，也可以产生混沌。它充分说明混沌函数存在的广泛性。该微分方程能够用谐波分析法和功率平衡定理求出它的主谐波解。并用仿真软件画出相图，验证求解结果的正确性。在上世纪混沌理论刚刚出现时，很多文献认为是奇异吸引子，这种认识显然是片面的。事实上，人们也可以做出一个完全相反的结论，相点的运动轨道既不发散趋于无穷，也不收敛为稳定极限环。相点自由任意的游荡在相空间不是随机的，是正常一般的运动形式。轨线不重复的混沌相图是无处不在的普遍现象，轨线不断重复的等周期振荡才是特殊的个别现象。 Chaos is the most universally common form of bounded nonlinear function. It commonly exists in the various subject areas of nature. Chaos is the universal term of variously bounded nonlinear aperiodic oscillation. This paper proves that the first order differential circuit which is constituted by mixing of three harmonic sources with different frequency also can produce chaos. It sufficiently explains that the extensiveness of chaotic functions exists in nature. The main harmonic components in the differential equations can be solved by using the harmonic balance principle and power balance theorem. Their correctness of solving results can be verified by phase portrait plotted by simulation. In last century, the era when chaos theory was first published, chaos was considered as a singular attractor in a lot of literatures. The recognition is obviously unilateral and wrong. In fact, people can also make a completely opposite conclusion, the motional trajectory of phase point will neither diverge to be infinite nor converge to stable limit cycle. The phase point freely and arbitrarily wandering in phase space is ordinary and universal motional form, but it is non-random. Chaotic phase portraits on which trajectories are not repeated are pervasive phe-nomenon. The constant periodic oscillation which continuously repeats original orbit is an indi-vidual and special motion form.

Migration, Participation, and Taxation in Rural China

In this paper, I analyze an ordinary form of political participation under an authoritarian regime in rural China. I present a game-theoretic model that reformulates and extends Albert Hirschman’s Exit, Voice, and Loyalty argument to analyze politics in rural China. I explore how rural-to-urban migration and the petition system may strengthen ordinary people’s power vis-a-vis China’s authoritarian regime. My model shows that allowing rural residents to migrate from their local villages and to petition against their local governments would not necessarily give local officials incentives to provide public goods, but would strengthen the central government’s authority to control the local governments. My model’s argument suggests that contrary to Tiebout’s argument, internal migration would not necessarily motivate local governments to provide public goods unless democratic institutions get local officials responsive to popular preferences. Moreover, without further institutionalization of the petition system, this seemingly democratic system would not strengthen villagers’ power vis-a-vis local governments but hurt it.

Wach modules and critical slope p-adic L-functions

Abstract We study Kato and Perrin-Riou's critical slope p-adic L-function attached to an ordinary modular form using the methods of A. Lei, D. Loeffler and S. L. Zerbes, Wach modules and Iwasawa theory for modular forms, Asian J. Math. 14 (2010), 475–528. We show that it may be decomposed as a sum of two bounded measures multiplied by explicit distributions depending only on the local properties of the modular form at p. We use this decomposition to prove results on the zeros of the p-adic L-function, and we show that our results match the behaviour observed in examples calculated by Pollack and Stevens in “Overconvergent modular symbols and p-adic L-functions”, Ann. Sci. Éc. Norm. Supér. (4) 44 (2011), no. 1, 1–42.

Semi-computational simulation of magneto-hemodynamic flow in a semi-porous channel using optimal homotopy and differential transform methods

In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field. The two-dimensional momentum conservation partial differential equations are reduced to ordinary form incorporating Lorentizian magnetohydrodynamic body force terms. These ordinary differential equations are solved by the homotopy analysis method, the differential transform method and also a numerical method (fourth-order Runge–Kutta quadrature with a shooting method), under physically realistic boundary conditions. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. The differential transform method (DTM) does not require an auxiliary parameter and is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the velocity profiles in the channel are studied in detail. Interesting fluid dynamic characteristics are revealed and addressed. The HAM and DTM solutions are shown to both correlate well with numerical quadrature solutions, testifying to the accuracy of both HAM and DTM in nonlinear magneto-hemodynamics problems. Both these semi-numerical techniques hold excellent potential in modeling nonlinear viscous flows in biological systems.

Side-effect analysis of sunitinib (S) in patients treated with metastatic renal cell cancer (mRCC): Single center experience in the National Institute of Oncology, Hungary—Influence of dose reduction/modification and application schedule on the efficacy of S.

e15530 Background: S, an active and relatively well tolerated treatment for mRCC, based on the result of a global phase III study. Methods: Retrospectively, 383 patient’s data with clear cell mRCC were collected, who were treated with S in our department between 01/nov/2005 and 31/dec/2012. S was used in 1st or 2 nd line setting. The first few dozen subjects were involved in a clinal trial after progression on first line INF therapy. In Hungary S became reimbursed by the public health insurence from 01/jan/2008 in second line, and from 01/feb/2010 in first line. All patients had definitely favorable or intermediate risk based on MSKCC risk group criteria. The starting dose of S was mostly 50 mg (schedule 4 weeks on followed by 2 weeks off). Results: We investigated the prevalence of necessity of dose reduction/modification or pretence to follow an out of ordinary application form. We registered the frequency and modality of the different types of side effects, we also studied the outcome of patients. Incidence of grade 3+4 side effects was nearly 60%. The most common side effects were fatigue (63%), mucositis/stomatitis (40,2%), hand-foot syndome (16,1%), diarrhea (34%), hypertension (34%), nausea (2%), anaemia (8,6%), leukopenia (4,6%), thrombopenia (20%) and hypothyreosis (20%). Objective response rate based on RECIST and progression-free survival (PFS) were also recorded. The efficacy of treatment was nearly similar to the global clinical trial results. CR was rare (4,2%), most of our patients had PR (31,1%) or SD (51,2%) as best response. In first line setting the results were even better (CR 10,5%, PR 44% and SD 57,5). Conclusions: S is effective and safe agent to treat patients with mRCC. Due to side effects, dose reduction / modification is often needed but rarely requires treatment discontinuation. The early detection and right management of side effects is crucial to maintain the patients on the treatment. Unfortunately the deviation from the standard care may bias the efficacy.

Mirroring Activity in the Brain and Movement Determinant in the Rorschach Test

Human movement (M) responses to the Rorschach are related to cognitive sophistication, creativity, and empathy. Recent studies also link Ms to EEG-mu suppression, an index of mirroring activity in the brain. In this article, we further investigate the link between Ms and mu suppression by testing some clinical interpretative distinctions. Previously collected EEG data recorded during the administration of the Rorschach were reanalyzed. We hypothesized that (a) among several responses investigated, only M would be associated with mu suppression, and (b) Ms with active movement, ordinary form quality, or whole human figures would be most strongly associated with mu suppression. Hypothesis 1 was fully confirmed, thus supporting that the traditional interpretation of M has a neurobiological foundation. Hypothesis 2 was partially confirmed; that is, active Ms were associated with mu suppression more strongly than passive Ms (p < .05), but no other significant differences emerged. Clinical implications are discussed.

Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field

Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1－αt)1/2 and a magnetic field proportional to B0(1－αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.

Numerical Solution for Accelerated Rotating Disk in a Viscous Fluid

The problem of a disk rotating in a viscous fluid has been investigated. The disk is accelerated with angular velocity proportional to time. Employing suitable similarity transformations the governing partial differential equations are transformed in to ordinary differential form. The resulting equations are solved numerically using SOR method and Simpson’s (1/3) rule. The results have been improved by using Richardson’s extrapolation. The effect of the non-dimensional parameter s which measures unsteadiness is observed on velocity components, skin friction coefficient and torque of the disk.