Browsing by Subject "Brownian motion"

Now showing 1 - 12 of 12

Open Access
A continuous review replenishment-disposal policy for an inventory system with autonomous supply and fixed disposal costs
(Elsevier, 2008) Pinçe, Ç.; Gürler, Ü.; Berk, E.
In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment-disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability.
Open Access
Dynamical effects of noise on nonlinear systems
(2014) Duman, Özer
Randomness and nonlinear dynamics consitute the most essential part of many events in nature. Therefore, a better and comprehensive understanding of them is a crucial step in describing natural phenomena as well as the prospect of predicting their future outcome. Besides the interest from a fundamental point of view, it is also useful in a wide variety of applications requiring delicate and careful use of energy. Especially recent advances in micro- and nano-scale technology requires harnessing the underlying noise itself as it is relatively hard to exert forces without damaging the system at that scale. The main aim of this work is to study the effects of noise on nonlinear dynamics. We show that the interplay between noise, nonlinearity and nonequilibrium conditions leads to a finite drift with the potential to change the dynamics of the system completely in a predictable and tunable fashion. We report that the noise-induced drift disrupts the phase space of a 2-D nonlinear system by shifting the fixed point by a finite amount which may result in dramatic alterations over the temporal behavior of the system. We track such alterations to several multi-dimensional model systems from ecology, soft matter and statistical physics. In a 2-D ecological model describing two species competing for the same resource, it is found that the system switches between coexistence and extinction states depending on the shift due to the noise-induced drift whereas for an aggregate of Brownian particles, it is shown that noise-induced drift selectively shifts the probability distribution in certain geometries which can be used in the realization of a microparticle sorter in the mould of Feynman ratchets. In the case of the aggregate consisting of microswimmers, tunable anomalous diffusion depending on the confinement length is reported.
Open Access
Engineering particle trajectories in microfluidic flows using speckle light fields
(SPIE, 2014) Volpe, G.; Volpe, Giovanni; Gigan, S.
Optical tweezers have been widely used in physics, chemistry and biology to manipulate and trap microscopic and nanoscopic objects. Current optical trapping techniques rely on carefully engineered setups to manipulate nanoscopic and microscopic objects at the focus of a laser beam. Since the quality of the trapping is strongly dependent on the focus quality, these systems have to be very carefully aligned and optimized, thus limiting their practical applicability in complex environments. One major challenge for current optical manipulation techniques is the light scattering occurring in optically complex media, such as biological tissues, turbid liquids and rough surfaces, which give rise to apparently random light fields known as speckles. Here, we discuss an experimental implementation to perform optical manipulation based on speckles. In particular, we show how to take advantage of the statistical properties of speckle patterns in order to realize a setup based on a multimode optical fiber to perform basic optical manipulation tasks such as trapping, guiding and sorting. We anticipate that the simplicity of these "speckle optical tweezers" will greatly broaden the perspectives of optical manipulation for real-life applications. © 2014 SPIE.
Open Access
Feedback fluid queues with multiple tresholds
(2006) Kankaya, Hüseyin Emre
Unlike discrete or continuous time queuing systems fed with point processes, workload in fluid queues arrives at the system as a fluid flow rather than jobs or packets. The rate of the fluid flow is governed by a continuous time Markov chain in Markov fluid queues. In first order fluid queues, rates are deterministically determined by a background Markov chain whereas in second order fluid queues, a Brownian motion is additionally inserted to the queue content process. Each of those queues can either accommodate a single regime or multiple regimes (equivalently multiple thresholds) in which the rates and the infinitesimal generator might be different in different regimes but they should be fixed within a single regime. In this thesis, we first generalize the existing solution of first order feedback fluid queues with multiple thresholds for the steady state distribution function of queue occupancy by also allowing the existence of repulsive type boundaries and states with zero rates. Secondly, we complete the boundary conditions for not only the transient but also the steady state solution of second order feedback fluid queues with multiple thresholds. Finally, we apply the theory of feedback fluid queues with multiple thresholds as an effective approximation to the Markov modulated discrete time queueing model that arises in the performance evaluation of an adaptive MPEG video streaming system in UMTS environment. By doing so, we eliminate the state space explosion problem that arises in the original discrete model.
Open Access
Forces and torques on the nanoscale: from measurement to applications
(SPIE, 2012) Volpe,Giovanni
The possibility of measuring microscopic forces down to the femtonewton range has opened new possibilities in fields such as biophysics and nanophotonics. I will review some of the techniques most often employed, namely the photonic force microscope (PFM) and the total internal reflection microscope (TIRM), which are able to measure tiny forces acting on optically trapped particles. I will then discuss several applications of such nanoscopic forces: from plasmonic optical manipulation, to self-propelled microswimmers, to self-organization in large ensembles of particles.
Open Access
An inventory model for recyclable goods with a disposal option
(2002-09) Çerağ, Pinçe
Open Access
Nanomechanical measurement of the Brownian force noise in a viscous liquid
(American Chemical Society, 2020) Arı, A. B.; Hanay, Mehmet Selim; Paul, M. R.; Ekinci, K. L.
We study the frequency spectrum of the thermal force giving rise to Brownian motion of a nanomechanical beam resonator in a viscous liquid. In the first set of experiments, we measure the power spectral density (PSD) of the position fluctuations of the resonator around its fundamental mode at its center. Then, we measure the frequency-dependent linear response of the resonator, again at its center, by driving it with a harmonic force that couples well to the fundamental mode. These two measurements allow us to determine the PSD of the Brownian force noise acting on the structure in its fundamental mode. The PSD of the force noise from multiple resonators spanning a broad frequency range displays a “colored spectrum” and follows the dissipation of a blade oscillating in a viscous liquid—by virtue of the fluctuation–dissipation theorem of statistical mechanics.
Open Access
Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the smoluchowski-kramers limit
(Springer, 2012) Hottovy, S.; Volpe, G.; Wehr, J.
We consider the dynamics of systems with arbitrary friction and diffusion. These include, as a special case, systems for which friction and diffusion are connected by Einstein fluctuation-dissipation relation, e. g. Brownian motion. We study the limit where friction effects dominate the inertia, i. e. where the mass goes to zero (Smoluchowski-Kramers limit). Using the Itô stochastic integral convention, we show that the limiting effective Langevin equations has different drift fields depending on the relation between friction and diffusion. Alternatively, our results can be cast as different interpretations of stochastic integration in the limiting equation, which can be parametrized by α∈ℝ. Interestingly, in addition to the classical Itô (α=0), Stratonovich (α=0. 5) and anti-Itô (α=1) integrals, we show that position-dependent α=α(x), and even stochastic integrals with α∉[0,1] arise. Our findings are supported by numerical simulations. © 2012 Springer Science+Business Media, LLC.
Open Access
Numerical simulation of Brownian particles in optical force fields
(SPIE, 2013) Volpe, G.; Volpe, Giovanni
Optical forces can affect the motion of a Brownian particle. For example, optical tweezers use optical forces to trap a particle at a desirable position. Using more complex force fields it is possible to generate more complex configurations. For example, by using two optical traps placed next to each other, it is possible to obtain a bistable potential where a particle can jump between the two potentials with a characteristic time scale. In this proceeding, we discuss a simple finite difference algorithm that can be used to simulate the motion of a Brownian particle in a one-dimensional field of optical forces.
Open Access
Numerical simulation of optically trapped particles
(SPIE, 2014) Volpe, G.; Volpe, Giovanni
Some randomness is present in most phenomena, ranging from biomolecules and nanodevices to financial markets and human organizations. However, it is not easy to gain an intuitive understanding of such stochastic phenomena, because their modeling requires advanced mathematical tools, such as sigma algebras, the Itô formula and martingales. Here, we discuss a simple finite difference algorithm that can be used to gain understanding of such complex physical phenomena. In particular, we simulate the motion of an optically trapped particle that is typically used as a model system in statistical physics and has a wide range of applications in physics and biophysics, for example, to measure nanoscopic forces and torques.
Open Access
Simulation of active Brownian particles in optical potentials
(SPIE, 2014) Volpe, G.; Gigan, S.; Volpe, Giovanni
Optical forces can affect the motion of a Brownian particle. For example, optical tweezers use optical forces to trap a particle at a desirable position. Unlike passive Brownian particles, active Brownian particles, also known as microswimmers, propel themselves with directed motion and thus drive themselves out of equilibrium. Understanding their motion in a confined potential can provide insight into out-of-equilibrium phenomena associated with biological examples such as bacteria, as well as with artificial microswimmers. We discuss how to mathematically model their motion in an optical potential using a set of stochastic differential equations and how to numerically simulate it using the corresponding set of finite difference equations.
Open Access
Spatial measurement of spurious forces with optical tweezers
(SPIE, 2013) Bordeu, I.; Volpe, Giovanni; Staforelli, J. P.
The study of diffusion in a crowded and complex environment, such as inside a cell or within a porous medium, is of fundamental importance for science and technology. Combining blinking holographic optical tweezers and sub-pixel video microscopy permits one to study Brownian motion in confined geometries. In this work, in particular, we have studied the Brownian motion of two colloidal particles interacting hydrodynamically with each other. The proximity between the two microspheres induces a space-dependence in the particles diffusion coefficient and, therefore, a spurious drift. We measure this drift and evaluate the magnitude of the spurious force associated with it. We present the optoelectronic tools employed in the experiment and we discuss the experimental results.