The purpose of this paper is to discuss a class of stochastic differential equations with delay driven by G-Brownian motion (G-SDDEs, in short). The asymptotical boundedness and exponential stability ...of the equations are obtained by means of G-Lyapunov function. An example is proposed to illustrate the theory obtained.
In this work, the continuity with respect to the Hurst parameter of solutions to stochastic evolution equations is studied. Compared with recent studies on such continuity property, the model here is ...considered in a different point of view in which the equations are of SPDEs type, the solution and the fractional Brownian motion take value on a Hilbert space. The main contribution is to investigate the existence and stability of the solution with respect to the Hurst index in the space C(0,T;L2(Ω,H)).
•Combines nanoparticles with fins in a triplex-tube PCM energy storage system.•The melting in triplex-tube TES system was modeled, validated and investigated.•Fins alone was found to be better than ...nanoparticles or nanoparticle-fin combination.•Enhancement with nanoparticles increased with length and reduced thickness of fins.
Latent thermal energy storage based on Phase Change materials (PCMs) offers a promising solution for correcting the problem of availability of intermittent energy from renewable sources like solar, wind, etc. PCMs have the potential to store large amounts of energy in relatively small volumes and within nearly isothermal processes. However, a major drawback of today's PCMs is that their low thermal conductivity values critically limit their energy storage applications. Also, this grossly reduces the melting/solidification rates, thus making the system response time to be too long. In this study, three enhancement techniques: fins, nanoparticles and a combination of both were investigated with the aim of correcting this limitation. A numerical study based on enthalpy method was used to comparably examine the effects of these techniques on the PCM melting rate in triplex-tube latent heat storage system. A mathematical model that takes into account the natural convection and the Brownian motion of nanoparticles was formulated and successfully validated against previous experimental data. The influence of using different dimensions of fin and different nanoparticle volume fractions on evolution of the solid-liquid interfaces, distribution of isotherms, and temporal profile of liquid fraction over the whole melting process was studied and reported. The results indicate that PCM melting is improved by using these techniques studied. Also it was found that the use of fins alone is better than using either nanoparticles alone or a combination of fins and nanoparticles. The use of longer fins with smaller thicknesses is recommended so as to improve phase-change heat transfer and minimize the volume occupied in the energy storage space.
Guaranteed Lifetime Withdrawal Benefits (GLWBs) are an increasingly popular add-on to Variable Annuities, offering a guaranteed stream of payments for the remainder of the policyholder's life. GLWBs ...have typically been priced using numerical methods such as finite difference schemes or Monte Carlo simulations; obtaining accurate and precise solutions using these methods can be very computationally expensive. In this paper, we extend an existing method for analytic pricing of these policies to a more general fee structure. We introduce a novel variation on the commonly offered ratchet rider that more directly addresses policyholder motivation around lapse-and-reentry behaviour. We then modify our pricing method to accommodate this new rider and compare it to the existing annual ratchet with respect to a policyholder's incentive to lapse such a policy.
Optimizing Brownian escape rates by potential shaping Chupeau, Marie; Gladrow, Jannes; Chepelianskii, Alexei ...
Proceedings of the National Academy of Sciences - PNAS,
01/2020, Letnik:
117, Številka:
3
Journal Article
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Brownian escape is key to a wealth of physico-chemical processes, including polymer folding and information storage. The frequency of thermally activated energy barrier crossings is assumed to ...generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates, in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under 2 different regularizations and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.
•Our method is an attractive and easy idea using moving least squares (MLS) and the spectral collocation method to estimate the solution of nonlinear stochastic Volterra integro-differential ...equations.•An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Therefore, this method is independent of the geometry of the domains.•A significant advantage of our approach is that it provided acceptable results with a small number of points and basis functions.•This method can be used to solve problems with smooth and nonsmoth solution.
In this paper, an attractive idea using moving least squares (MLS) and spectral collocation method is extended to estimate the solution of nonlinear stochastic Volterra integro-differential equations (NSVIDEs) that arise in mathematical modeling of natural systems in financial mathematics, physics, and engineering. An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Another advantage that may be appealing to the readers of this article is that acceptable results can be obtained using a small number of points and basis functions, so the calculations are reduced. Applying the proposed scheme leads to the conversion of the problem into a system of algebraic equations. An error bound is presented to ensure the convergence and reliability of the method. Some illustrative examples are presented to reveal the efficiency and applicability of this technique.
Using the method of Brownian dynamics, we investigate the dynamic properties of a 2d suspension of active disks at high Péclet numbers using active microrheology. In our simulations the tracer ...particle is driven either by a constant or an oscillatory external force. In the first case, we find that the mobility of the tracer initially appreciably decreases with the external force and then becomes approximately constant for larger forces. For an oscillatory driving force we find that the dynamic mobility shows a quite complex behavior-it displays a highly nonlinear behavior on both the amplitude and frequency of the driving force. In the range of forces studied, we do not observe a linear regime. This result is important because it reveals that a phenomenological description of tracer motion in active media in terms of a simple linear stochastic equation even with a memory-mobility kernel is not appropriate, in the general case.
To understand the nature of the evolutionary process, it is of paramount importance that temporal patterns of change in biological traits are accurately documented. The paleontological record is, ...however, inherently incomplete, leaving researchers with only a limited set of observed taxonomic units (OTUs) to estimate broader patterns of biological change. In this context, phylogenetic comparative methods have been developed aiming to estimate patterns of phenotypic change through time based on a phylogenetic tree and a limited set of OTUs. Such methods typically employ mathematical models proposing how change is likely to have unfolded over time. The most commonly used model, Brownian motion (BM), assumes that average trait change is proportional to the square root of time and that the rate of evolution is stochastically constant across all branches. This, however, lies in contrast to the commonly agreed notion that many biological traits change at different rates along different branches of the tree of life. We present a method for inferring ancestral states that allows for different evolutionary rates along different branches of the phylogenetic tree. The goal is to include the effects of variation in rates of phenotypic change across phylogenetic space. Based on the available phenotypic and phylogenetic information, we estimate measures of the rate of evolution on each individual branch and, subsequently, these estimates are used to parameterize a multiple variance BM model inferring the phenotypic values at all internal nodes. We demonstrate the validity of our approach with a series of simulations and an empirical example. We show that values for internal nodes inferred using our approach are equivalent to those inferred with a constant variance BM model if phenotypic evolution occurs according to standard BM. When evolution occurs at different rates along different branches of the phylogeny, our approach greatly outperforms constant variance BM. We further demonstrate that our approach accurately detects bursts of change in phylogenetic space. An empirical analysis of the evolution of primate brain and body mass reveals that our approach yields an improved statistical fit relative to both traditional and recent methods, and provides estimates of nodal values that lie within a range expected based on the fossil record.
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