Time-dependent Drift Research Articles

Precise Hydrodynamic Leveling by Using Pressure Gauges

This study investigates the applicability of hydrodynamic leveling by means of contemporary pressure gauges for achieving geodetic accuracy in height determination. The main problems associated with pressure gauges are rigorous connection to a national leveling network and data processing, for example, determination of time-dependent drift and data filtering principles. The equipment and methodology were tested in a test area in the Baltic Sea. It can be concluded that the year-long sea level series may provide ±2.0 cm accuracy for hydrodynamic leveling within the water stretches up to 65 km. This is confirmed by alternative height determination methods and additional field experiments.

Accurate Pricing of Continuous Barrier Options With Local Volatility

In this paper we develop accurate technics to price continuous barrier options using a one-dimensional finite difference scheme, allowing for time-dependent drift as well as time- and state-dependent volatilities. We provide numerical examples which demonstrate the smoothness and accuracy of such methods in the Black-Scholes context as well as in the Dupire Local Volatility model.

Nanometric locking of the tight focus for optical microscopy and tip-enhanced microscopy

We have successfully stabilized the tight focus onto the sample surface of an optical microscope within ±1.0 nm for a virtually unlimited time duration. The time-dependent thermal drift of the tight focus and the mechanical tilt of the sample surface were simultaneously sensed by a non-optical means based on a capacitive sensor and were compensated for in real-time. This non-optical scheme is promising for the suppression of background light sources for optical microscopy. The focus stabilization is crucial for microscopic measurement at an interface, particularly when scanning a large surface area, because there is always a certain amount of mechanical tilt of the sample substrate, which degrades the contrast of the image. When imaging nanoscopic materials such as carbon nanotubes or silicon nanowires, more stringent nanometric stabilization of the focus position relative to such samples is required, otherwise it is often difficult to interpret the results from the observations. Moreover, the smaller the sample volume is, the smaller the signal becomes, resulting in a long exposure time at each position. In this sense, long-term stability of the tight focus is essential for both microscopic large area scanning and nanosized sample scanning (high-resolution/large-area imaging). In addition, the recently developed tip-enhanced microscopy requires long-term stability of the relative position of the tip, sample and focus position. We were able to successfully demonstrate a stability improvement for tip-enhanced microscopy in the same manner. The stabilization of the tight focus enables us to perform long-term and robust measurements without any degradation of optical signal, resulting in the capability of true nanometric optical imaging with good reproducibility and high precision. The technique presented is a simple add-on for any kind of optical microscope.

Evaluation of continuous water vapor δD and δ<sup>18</sup>O measurements by off-axis integrated cavity output spectroscopy

Abstract. Recent commercially available laser spectroscopy systems enabled us to continuously and reliably measure the δD and δ18O of atmospheric water vapor. The use of this new technology is becoming popular because of its advantages over the conventional approach based on cold trap collection. These advantages include much higher temporal resolution/continuous monitoring and the ability to make direct measurements of both isotopes in the field. Here, we evaluate the accuracy and precision of the laser based water vapor isotope instrument through a comparison of measurements with those found using the conventional cold trap method. A commercially available water vapor isotope analyzer (WVIA) with the vaporization system of a liquid water standard (Water Vapor Isotope Standard Source, WVISS) from Los Gatos Research (LGR) Inc. was used for this study. We found that the WVIA instrument can provide accurate results if (1) correction is applied for time-dependent isotope drift, (2) normalization to the VSMOW/SLAP scale is implemented, and (3) the water vapor concentration dependence of the isotopic ratio is also corrected. In addition, since the isotopic value of water vapor generated by the WVISS is also dependent on the concentration of water vapor, this effect must be considered to determine the true water vapor concentration effect on the resulting isotope measurement. To test our calibration procedure, continuous water vapor isotope measurements using both a laser instrument and a cold trap system were carried out at the IAEA Isotope Hydrology Laboratory in Vienna from August to December 2011. The calibrated isotopic values measured using the WVIA agree well with those obtained via the cold trap method. The standard deviation of the isotopic difference between both methods is about 1.4‰ for δD and 0.28‰ for δ18O. This precision allowed us to obtain reliable values for d-excess. The day-to-day variation of d-excess measured by WVIA also agrees well with that found using the cold trap method. These results demonstrate that a coupled system, using commercially available WVIA and WVISS instruments can provide continuous and accurate isotope data, with results achieved similar to those obtained using the conventional method, but with drastically improved temporal resolution.

Subnanometric stabilization of plasmon-enhanced optical microscopy

We have demonstrated subnanometric stabilization of tip-enhanced optical microscopy under ambient condition. Time-dependent thermal drift of a plasmonic metallic tip was optically sensed at subnanometer scale, and was compensated in real-time. In addition, mechanically induced displacement of the tip, which usually occurs when the amount of tip-applied force varies, was also compensated in situ. The stabilization of tip-enhanced optical microscopy enables us to perform long-time and robust measurement without any degradation of optical signal, resulting in true nanometric optical imaging with high reproducibility and high precision. The technique presented is applicable for AFM-based nanoindentation with subnanometric precision.

Series solution to the first-passage-time problem of a Brownian motion with an exponential time-dependent drift

We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an adaptation-like current and reaching the threshold for the first time represents the condition for declaring a spike. Based on the backward Fokker–Planck formulation, we consider the survival probability of this process in a domain restricted by an absorbent boundary. The solution is given as an expansion in terms of the intensity of the time-dependent drift, which results in an infinite set of recurrence equations. We explicitly obtain the complete solution by solving each term in the expansion in a recursive scheme. From the survival probability, we evaluate the first-passage-time statistics, which itself preserves the series structure. We then compare theoretical results with data extracted from numerical simulations of the associated dynamical system, and show that the analytical description is appropriate whenever the series is truncated in an adequate order.

Nonlinear dynamics in wurtzite InN diodes under terahertz radiation

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n+nn+ wurtzite InN diodes by using time-dependent drift diffusion equations. A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect, which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the Γ1 valley. The appearance of different nonlinear oscillatory modes, including periodic and chaotic states, is attributed to the competition between the self-sustained oscillation and the external driving oscillation. The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods, such as the bifurcation diagram, the Fourier spectrum and the first return map. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.

DRIFT COEFFICIENTS OF CHARGED PARTICLES IN TURBULENT MAGNETIC FIELDS

Using test-particle simulations, the off-diagonal elements of the diffusion tensor are evaluated numerically. The comparison of the so-obtained time-dependent drift coefficients with analytical approximations shows that, for weak turbulence strengths or for slab turbulence geometry, the weak scattering result provides an excellent agreement with the numerical results. For two- or three-dimensional turbulence geometry, however, neither the classical scattering result nor alternative analytical approaches provide an accurate description of the numerically obtained values. Furthermore, the influence is discussed of a non-constant energy range in the turbulence spectrum and of non-static turbulence, for which the time dependence is modeled using magnetohydrodynamic plasma waves.

Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed.

Exactly solvable Fokker-Planck equation with time-dependent nonlinear drift and diffusion coefficients – the Lie-algebraic approach

In this paper we have analytically solved the Fokker-Planck equation (FPE) associated with a fairly large class of multiplicative stochastic processes with time-varying nonliner drift and diffusion coefficients, which has wide applicability in various areas of physics, e.g. nonlinear optics and chemical reaction dynamics. By exploiting the dynamical symmetry of the FPE, we apply the Lie-algebraic approach to derive the time-dependent analytical closed-form solutions. The derived solutions fall into two different categories, namely (i) one with a moving absorbing boundary, and (ii) one with a fixed absorbing boundary at the origin, depending upon the model parameters. The corresponding escape (or survival) probabilities are also evaluated analytically. We believe that not only our analytically exact results can serve as standard models upon which the discussion of more complicated problems can be based, but they can also be useful as a benchmark to test approximate numerical or analytical procedures.

Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.

Similarity solutions of a class of perturbative Fokker-Planck equation

In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the Fokker-Planck equations and the Schrodinger equations. In this work, we further explore the possibility of similarity solutions of such a class of Fokker-Planck equations. These solutions possess definite scaling behaviors, and are obtained by means of the so-called similarity method.

Accurate Pricing of Continuous Barrier Options with Local Volatility

In this paper we develop accurate technics to price continuous barrier options using a one dimensional finite difference scheme, allowing for time dependent drift as well as time and state dependent volatilities. We provide numerical examples which demonstrate the smoothness and accuracy of such methods in the Black-Scholes context as well as in the Dupire Local Volatility model.

First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of images, whose applicability to time dependent problems is shown to be limited to state-independent drift and diffusion coefficients that only depend on time and are proportional to each other. First passage time statistics, such as the survival probabilities and first passage time densities are obtained analytically. The analysis includes the study of different functional forms of the time dependent drift and diffusion, including power-law time dependence and different periodic drivers. As a case study of these theoretical results, a stochastic model of water resources availability in snowmelt dominated regions is presented, where both temperature effects and snow-precipitation input are incorporated.

Characterization of K+ and Na+-Sensitive Membrane Fabricated by CF4 Plasma Treatment on Hafnium Oxide Thin Films on ISFET

In this paper, we report the effects of fluorine incorporation on the alkali ion sensing properties of a HfO2 dielectric material. The fluorinated-HfO2 film prepared by the postdeposition CF4 plasma treatment was used as a sensing layer of ion sensitive field-effect transistors (ISFET) for K+ and Na+ ion detection. The fluorinated-HfO2 gate ISFET is sensitive to K+ (25.86 mV/M) and Na+ (33.77 mV/M) ions for both in the concentration range between 3 and 135 mM. In comparison with the same structure without plasma treatment, the sensitivity was improved fivefold, and lower selectivity coefficients of K+ and Na+ ions against H+ ion were obtained. In the stability test, the result of time-dependent drift measurements showed that this low power plasma process could not degrade the sensing performance, and lifetime evaluated based on analysis sensitivity change in time was over 15 months. The chemical states of the HfO2 film after CF4 plasma treatment were examined by x-ray photoelectron spectroscopy. Analysis of the spectra of F 1s, O 1s, and Hf 4f showed that the fluorine atoms are incorporated into the HfO2 film. This fluorinated-HfO2 film fabricated by inorganic CF4 plasma is compatible with advanced complementary metal oxide semiconductor technology and possible biosensor applications.

Survival probability and first-passage-time statistics of a Wiener process driven by an exponential time-dependent drift

The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic process with continuous variables, and important results can be explicitly found from it. The presence of a constant drift does not modify its simplicity; however, when the process has a time-dependent component the analysis becomes difficult. In this work we analyze the statistical properties of the Wiener process with an absorbing boundary, under the effect of an exponential time-dependent drift. Based on the backward Fokker-Planck formalism we set the time-inhomogeneous equation and conditions that rule the diffusion of the corresponding survival probability. We propose as the solution an expansion series in terms of the intensity of the exponential drift, resulting in a set of recurrence equations. We explicitly solve the expansion up to second order and comment on higher-order solutions. The first-passage-time density function arises naturally from the survival probability and preserves the proposed expansion. Explicit results, related properties, and limit behaviors are analyzed and extensively compared to numerical simulations.

The role of hole mobility in scintillator proportionality

Abstract Time-dependent radial diffusion and drift are modeled in the high carrier concentration gradient characteristic of electron tracks in scintillators and other radiation detector materials. As expected, the lower mobility carrier (typically the hole) controls the ambipolar diffusion. Carrier separation when electron and hole mobilities are unequal produces a built-in radial electric field near the track analogous to an n-intrinsic semiconductor junction. The diffusion is shown to have significant effects on both the low dE / dx and high dE / dx ends of electron light-yield curves and their respective contributions to nonproportionality. In CsI:Tl, it is shown that electron confinement toward the end of the track accentuates high-order quenching such as Auger recombination or dipole–dipole transfer, while in HPGe extremely rapid ( dE / dx .

Transient 3D flow of polymer solutions: A Lagrangian computational method

We describe a computational method for the numerical simulation of three-dimensional transient flows of polymer solutions that extends the work of Harlen et al. [O.G. Harlen, J.M. Rallison, P. Szabó, A split Lagrangian–Eulerian method for simulating transient viscoelastic flows, J. Non-Newtonian Fluid Mech. 60 (1995) 81–104]. The method uses a Lagrangian computation of the stress together with an Eulerian computation of the velocity field. Adaptive mesh reconnection based on Delaunay tetrahedra is used to ensure well-shaped elements. Additional shape-quality improvement procedures are developed to improve the algorithm. We validate the method for the benchmark problem of a rigid sphere falling in a cylindrical pipe. Inertia is neglected. We compare results for the axisymmetric case with previous work (using a FENE model), and then consider the off-axis non-axisymmetric case. In the latter case, we find that as the sphere falls, it drifts across the pipe, a phenomenon previously observed in experiments but not fully explained. The physical mechanisms that cause the time-dependent drift are identified, and a simple model based on the normal stresses in the fluid is shown to predict the magnitude of the drift velocity. We also consider a second benchmark problem involving a constriction in an axisymmetric pipe. Numerical difficulties associated with ill-shaped elements near the concave boundary arise for higher Weissenberg numbers. The merits and drawbacks of the new numerical method, and its applicability to various flow geometries are discussed.

Modeling the Cash Flow Dynamics of Private Equity Funds: Theory and Empirical Evidence

This article presents a novel continuous-time approach to modeling the typical cash flow dynamics of private equity funds. The model consists of two independent components. First is a mean-reverting square-root process applied to model the rate at which capital is drawn over time. Second is the stream of capital distributions, which is assumed to follow an arithmetic Brownian motion with a time-dependent drift component that incorporates the typical time-pattern of the repayments of private equity funds. The empirical analysis shows that the model can easily be calibrated to real-world fund data by the method of conditional least squares and nicely fits historical data. The authors use a data set of mature European private equity funds provided by Thomson Venture Economics. Their model explains up to 99.6% of the variation in average cumulated net fund cash flows and provides a good approximation of the empirical distribution of private equity fund cash flows over a typical fund’s lifetime. Overall, the empirical results indicate that the model is of economic relevance in an effort to accurately model the cash flow dynamics of private equity funds.

Extremely low drift of resistance and threshold voltage in amorphous phase change nanowire devices

Time-dependent drift of resistance and threshold voltage in phase change memory (PCM) devices is of concern as it leads to data loss. Electrical drift in amorphous chalcogenides has been argued to be either due to electronic or stress relaxation mechanisms. Here we show that drift in amorphized Ge2Sb2Te5 nanowires with exposed surfaces is extremely low in comparison to thin-film devices. However, drift in stressed nanowires embedded under dielectric films is comparable to thin-films. Our results shows that drift in PCM is due to stress relaxation and will help in understanding and controlling drift in PCM devices.