Sharif Digital Repository

Cone penetration tests have long been used to characterize snowpack stratigraphy. With the development of sophisticated digital penetrometers such as the SnowMicroPen, vertical profiles of snow hardness can now be measured at a spatial resolution of a few micrometers. By using small penetrometer tips at this high vertical resolution, further details of the penetration process are resolved, leading to many more stochastic signals. An accurate interpretation of these signals regarding snow characteristics requires advanced data analysis. Here, the failure of ice connections and the pushing aside of separated snow grains during cone penetration lead to a combination of (a) diffusive noise, as... 

In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication... 

In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication... 

The present study aims to investigate the impact of nanoparticle migration due to Brownian motion and thermophoresis on Ag-MgO/Water hybrid nanofluid natural convection. An enclosure with sinusoidal wavy walls is considered for this investigation; right and cold walls of this enclosure are in constant temperature while the upper and bottom walls are insulated. This simulation follows Buongiorno's mathematical model; Brownian and thermophoresis diffusion of Ag occurs in MgO-Water nanofluid while the diffusion of MgO happens in Ag-water nanofluid. The result indicates that Nu number increments up to 11% by increasing thermophoresis diffusion for both nanoparticles. Also, increasing Brownian... 

The method outlined in the Chaps. 15 – 21 has been used for revealing nonlinear deterministic and stochastic behaviors in a variety of problems, ranging from physics, to neuroscience, biology and medicine. In most cases, alternative procedures with strong emphasis on deterministic features have been only partly successful, due to their inappropriate treatment of the dynamical fluctuations [1]. In this chapter, we provide a list of the investigated phenomena using the introduced reconstruction method. In the “outlook” possible research directions for future are discussed. © 2019, Springer Nature Switzerland AG  

The method outlined in the Chaps. 15 – 21 has been used for revealing nonlinear deterministic and stochastic behaviors in a variety of problems, ranging from physics, to neuroscience, biology and medicine. In most cases, alternative procedures with strong emphasis on deterministic features have been only partly successful, due to their inappropriate treatment of the dynamical fluctuations [1]. In this chapter, we provide a list of the investigated phenomena using the introduced reconstruction method. In the “outlook” possible research directions for future are discussed. © 2019, Springer Nature Switzerland AG  

The prediction of flow behavior in porous media can provide useful insights into the mechanisms involved in CO2 sequestration, petroleum engineering and hydrology. The multi-phase flow is usually simulated by solving the governing equations over an efficient model. The geostatistical (or fine grid) models are rarely used for simulation purposes because they have too many cells. A common approach is to coarsen a fine gird realization by an upscaling method. Although upscaling can speed up the flow simulation, it neglects the fine scale heterogeneity. The heterogeneity loss reduces the accuracy of simulation results. In this paper, the relation between heterogeneity loss during upscaling and... 

Just a few investigations have been conducted to study the mixed nanofluids(MNs), which contain more than one type of nanoparticles, despite considerable advances in the field of nanofluids thermal conductivity. In present research, by combining different volume fractions of various nanoparticles, the variation of mixed nanofluids thermal conductivity was considered. The mentioned nanofluids have different fabrication cost. First, the effect of each specific nanoparticle presence in the base fluid on the thermal conductivity of nanofluid was surveyed both experimentally and theoretically. Then, the thermal conductivities of two MNs, one consisted of a metallic nanoparticle (high thermal... 

Both experimental and numerical studies are unanimous for enhancing Nusselt number for forced convection of nanofluids with slight difference, but there is inconsistency for natural convection heat transfer of nanofluids. In this paper attempt is made to study the effects of nanoparticles migration on the natural convection behavior of nanofluids. For analysis, a mixture model is used by including important phenomena such as Brownian motion and thermophoresis effects. These two mechanisms are taken into account to compute the slip velocities between the base fluid and nanoparticles. The governing equations are solved numerically and good agreements are observed in comparison with... 

Numerical investigation on the application of nanofluids in Micro-Pin-Fin Heat Sinks (MPFHSs) has been presented in this paper. To investigate flow and heat transfer behavior in MPFHS the three-dimensional steady Navier-Stokes and energy equations were discretized using a finite volume approach and have been solved iteratively, using the SIMPLE algorithm. DI-water is used as a base coolant fluid while the nanoparticles used in the present study are CuO nanoparticles with mean diameters of 28.6 and 29 nm and Al 2O 3 nanoparticles with mean diameters of 38.4 and 47 nm. The results show that (i) a significant enhancement of heat transfer in the MPFHS due to suspension of CuO orAl 2O 3... 

We investigate the stability of the pressure-driven, low-Reynolds-number flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and antisymmetric patterns; (ii) single modes that are either symmetric or antisymmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable... 

A deterministic energy supply model with bottom-up structure has limited capability in handling the uncertainties. To enhance the applicability of such a model in an uncertain environment two main issues have been investigated in the present paper. First, a binomial lattice is generated based on the stochastic nature of the source of uncertainty. Second, an energy system model (ESM) has been reformulated as a multistage stochastic problem. The result of the application of the modified energy model encompasses all uncertain outcomes together and enables optimal timing of capacity expansion. The performance of the model has been demonstrated with the help of a case study. The case study has... 

We study the first-passage-time processes of the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time of the fractional Brownian motion and subordinated walk on the different fractal curves (loop-erased random walk, harmonic explorer, and percolation front) are derived. We also define natural parametrized subordinated Schramm-Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean-square displacement and mean first passage time for NS-SLE are obtained by numerical means  

In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot (WM) function as the drift of the Loewner equation we introduce a large class of fractal curves with discrete scale invariance (DSI). We show that the fractal dimension of the curves can be extracted from the diffusion coefficient of the trend of the variance of the WM function. We argue that, up to the fractal dimension calculations, all the WM functions follow the behavior of the corresponding Brownian motion. Our study opens a way to classify all the... 

A reaction-diffusion equation on [0, 1]d with the heat conductivity k > 0, a polynomial drift term and an additive noise, fractional in time with H > 1/2, and colored in space, is considered. We have shown the existence, uniqueness and uniform boundedness of solution with respect to k Also we show that if k tends to infinity, then the corresponding solutions of the equation converge to a process satisfying a stochastic ordinary differential equation  

Here, the existence and measurability of solutions for stochastic differential equations driven by fractional Brownian noise with Hurst parameter greater than 1 2 is proved. Our method is based on approximating the main equation by delayed equations as in Peano's method in ODEs. This method makes the proofs easier and needs weaker assumptions for the existence part, compared with the previous works as in [25]. In addition the constructive nature of the proofs helps to develop some numerical methods for solving such SDEs. © 2009 Iranian Mathematical Society