Sharif Digital Repository

In Chaps. 16 – 21 we address a central question in the field of complex systems: Given a fluctuating (in time or space), sequentially uni- or multi-variant measured set of experimental data (even noisy data), how should one analyse the data non-parametrically, assess their underlying trends, discover the characteristics of the fluctuations, including diffusion and jump parts, and construct stochastic evolution equation for the data? © 2019, Springer Nature Switzerland AG  

In Chaps. 16 – 21 we address a central question in the field of complex systems: Given a fluctuating (in time or space), sequentially uni- or multi-variant measured set of experimental data (even noisy data), how should one analyse the data non-parametrically, assess their underlying trends, discover the characteristics of the fluctuations, including diffusion and jump parts, and construct stochastic evolution equation for the data? © 2019, Springer Nature Switzerland AG  

In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some celebrated functional responses such as Holling type-II (or Michaelis-Menten), Holling type-III, Ivlev, mx (Holling type I), sigmoidal [e.g., Real and mx2/((A + x)(B +x))] and some other monotone functions, has always at least one ω-periodic solution. Besides, for some well-known functional responses... 

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zliang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time tc. The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale tc and the singularity time scale tc,v→0 of the KPZ equation with an infinitesimal surface tension is investigated. © 2004 Springer Science+Business Media, Inc  

We investigate short-term non-linearity of solar irradiance fluctuations using the multifractal detrended fluctuation analysis (MFDFA). The MFDFA shows that time series of solar irradiance have a long range correlation function with a multifractal behavior. We apply this method to solar irradiance time series from several regions around the world with resolutions of seconds and minutes. The obtained generalized Hurst and Renyi exponents h(q) and τ(q) suggest the non-linear and non-stationary essence of measured irradiance time series. Also, we analyze shuffled, random phase, and rank-wised surrogated data to reveal the nature of the multifractality and conclude that linear and non-linear... 

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number,... 

In most applications of antenna arrays, side lobe levels (SLLs) are commonly unwanted. Especially, the first side lobe level which determines maximum SLL is the main source of electromagnetic interference (EMI), and hence, it should be lowered. A procedure of finding the optimum side lobe-minimizing weights for an arbitrary linear equally spaced array is derived, which holds for any scan direction, beam width, and type of antenna element used. In this science article, the use of convolution procedure and the time scaling property reduces the side lobe level for any type of linear equally spaced array. Results show that by this procedure, the side lobe level is reduced about two times or even... 

We present a scheme for achieving macroscopic quantum superpositions in optomechanical systems by using single photon postselection and detecting them with nested interferometers. This method relieves many of the challenges associated with previous optical schemes for measuring macroscopic superpositions and only requires the devices to be in the weak coupling regime. It requires only small improvements on currently achievable device parameters and allows the observation of decoherence on a time scale unconstrained by the system's optical decay time. Prospects for observing novel decoherence mechanisms are discussed  

The level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, να+, where Tα=1να+ is the average waiting time for observing the level α again. We estimate the probability P(K,α), which provides us the probability of observing K times of the level α with positive slope, in time scale Tα. For analyzed time series, we found that maximum K is about ≈6. We show that by using the level crossing analysis one can estimate how the DAX and oil time series will develop. We carry out the same analysis for the increments of DAX and oil price log-returns (which is known as inverse statistics), and provide the... 

This paper deals with the question of existence of periodic solutions of nonautonomous predator-prey dynamical systems with Beddington-DeAngelis functional response. We explore the periodicity of this system on time scales. New sufficient conditions are derived for the existence of periodic solutions. These conditions extend previous results presented in [M. Bohner, M. Fan, J. Zhang, Existence of periodic solutions in predator-prey and competition dynamic systems, Nonlinear. Anal.: Real World Appl. 7 (2006) 1193-1204; M. Fan, Y. Kuang, Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelies functional response, J. Math. Anal. Appl. 295 (2004) 15-39; J. Zhang, J. Wang,... 

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold's number in inertial range. Further, we... 

Improvement of microcantilever-based sensors and actuators chiefly depends on how comprehensively they are modeled and precisely formulated. Atomic Force Microscopy (AFM) is the most widespread application of microcantilever beam as a sensor, which is usually influenced by the tip-sample interaction force. For this, vibration of AFM microcantilever probe is analyzed in this paper, along with analytical, numerical and experimental investigation of the influence of the sample interaction force on the microcantilever vibration. Nonlinear integro-partial equation of microcantilever vibration subject to the tip-sample interaction is then derived and numerically simulated. Moreover, multiple time... 

Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the... 

Molecular dynamics simulations were used to propose a closed-form expression for the mobility of the [Formula presented] edge dislocation in low-carbon α-Fe (up to 0.1 at.% C) at temperatures of 300, 400 and 500 K and applied shear stresses of 10–100 MPa. Considering this parameter helps us to understand the effect of damage cascade on the dislocation mobility. The results confirmed that the point defect clusters at the thermal spike stage of the cascade (that they can be considered as an unstable precipitation-like phase), the distance of damage cascade relative to the center of the dislocation core and forming carbon-vacancy (C–V) complexes are some rather stronger obstacles for movement... 

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothesis and show that it is valid up to time scales smaller than the correlation time scale of temporal velocity correlation function. We support the analytical calculation by performing numerical simulation of the periodically kicked Burgers equation. © 2008 The American Physical Society  

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number,... 

Computational methods to understand interactions in bio-complex systems are however limited to time-scales typically much shorter than in Nature. For example, on the nanoscale level, interactions between nanoparticles (NPs)/molecules/peptides and membranes are central in complex biomolecular processes such as membrane-coated NPs or cellular uptake. This can be remedied by the application of e.g. Jarzynski's equality where thermodynamic properties are extracted from non-equilibrium simulations. Although, the out of equilibrium work leads to non-conservative forces. We here propose a correction Pair Forces method, that removes these forces. Our proposed method is based on the calculation of... 

The dynamics of droplet detachment from a surface is a fundamental topic studied in coating engineering, fluid mechanics, and subsurface engineering applications. This topic has direct relevance to wettability alteration using the modified ionic composition of water in contact with oil droplet, low salinity waterflooding (LSWF). Previous experimental studies of LSWF have shown a very long timescale in wettability alteration which cannot be explained using bulk diffusion coefficient. In the present study, we address both the time scale of detachment, as well as the impact of buoyancy and interfacial forces (referred to as Bond number) on droplet detachment by proposing an advanced...