Instantaneous Reflection Research Articles

Dynamic minimisation of the commute time for a one-dimensional diffusion

AbstractMotivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel to 1 and then return to the origin (the so-called commute time from 0 to 1). Substantially extending results in a previous paper, we consider a dynamic version of this problem where the control mechanism is related to the diffusion’s drift via the corresponding scale function. We are only able to choose the drift at each point at the time of first visiting that point and the drift is constrained on a set of the form $$[0,\ell )\cup (i,1]$$ [ 0 , ℓ ) ∪ ( i , 1 ] . This leads to a type of stochastic control problem with infinite dimensional state.

Using sulfur stable isotope ratios (δ34 S) for animal geolocation: Estimating the delay mechanisms between diet ingestion and isotope incorporation in tail hair.

Metabolism and diet quality play an important role in determining delay mechanisms between an animal ingesting an element and depositing the associated isotope signal in tissue. While many isotope mixing models assume instantaneous reflection of diet in an animal- tissue, this is rarely the case. Here we use data from wildebeest to measure the lag time between ingestion of 34 S and its detection in tail hair. We use time-lagged regression analysis of δ34 S data from GPS-collared blue wildebeest from the Serengeti ecosystem in combination with δ34 S isoscape data to estimate the lag time between an animal ingesting and depositing 34 S in tail hair. The best fitting regression model of δ34 S in tail hair and an individual- position on the δ34 S isoscape is generated assuming an average time delay of 78 days between ingestion and detection in tail hair. This suggests that sulfur may undergo multiple metabolic transitions before being deposited in tissue. Our findings help to unravel the underlying complexities associated with sulfur metabolism and are broadly consistent with results from other species. These findings will help to inform research aiming to apply the variation of δ34 S in inert biological material for geolocation or understanding dietary changes, especially for fast moving migratory ungulates such as wildebeest.

Experimental investigation on thermal performance of an actively cooled light shelf

Although the energy efficiency of light shelves has been studied, the thermal effects due to reflected solar radiation from light shelves have yet to be adequately investigated in previous research. The key research questions are whether this radiation results in additional heat load in buildings in tropical climates and how this can be reduced. In this work, the performance of an exterior aluminium light shelf is studied experimentally using a scaled prototype. The total amount of heat transmitted by the light shelf is about 40 W/ m2, which is close to the average thermal transmission of the envelope of a low-energy building. Experimental data analysis has revealed two components of the radiant heat transmitted by a light shelf: a) a direct instantaneous reflection of infrared radiations and b) secondary long-wave radiation resulting from the heating up of the light shelf material. The secondary radiation is a significant part of the overall heat transmitted by the light shelf. The light shelf was actively cooled by circulating water through hydronic radiant capillary mat tubes to reduce this component, and the radiant heat transmitted was measured. These experiments showed that an actively cooled light shelf could considerably reduce the secondary radiant heat transmitted through a clerestory window. A significant decrease in secondary heat transmission within a range of 3.8–5.9 W/m2 was observed when compared to an identical light shelf that was not cooled. This reduction is about 10% of the total heat transmitted by the light shelf.

Sticky Feller diffusions

We consider a Feller branching diffusion process X with drift c having 0 as a slowly reflecting (sticky) boundary point with a stickiness parameter 1∕μ∈(0,∞). We show that (i) the process X can be characterised as a unique weak solution to the SDE system dXt=(bXt+c)I(Xt>0)dt+ 2aXtdBt I(Xt=0)dt= 1μdℓt0(X) where b∈R and 0<c<a are given and fixed, B is a standard Brownian motion, and ℓ0(X) is a diffusion local time process of X at 0, and (ii) the transition density function of X can be expressed in the closed form by means of a convolution integral involving a new special function and a modified Bessel function of the second kind. The new special function embodies the stickiness of X entirely and reduces to the Mittag-Leffler function when b=0. We determine a (sticky) boundary condition at zero that characterises the transition density function of X as a unique solution to the Kolmogorov forward/backward equation of X. Letting μ↓0 (absorption) and μ↑∞ (instantaneous reflection) the closed-form expression for the transition density function of X reduces to the ones found by Feller [6] and Molchanov [14] respectively. The results derived for sticky Feller diffusions translate over to yield closed-form expressions for the transition density functions of (a) sticky Cox-Ingersoll-Ross processes and (b) sticky reflecting Vasicek processes that can be used to model slowly reflecting interest rates.

Improving the Specular Point Positioning Accuracy of Ship-Borne GNSS-R Observations in China Seas Based on Comprehensive Geophysical Correction

The accurate modeled GNSS-R reflection delay, which is indispensable for the quantification, modeling, and correction of the GNSS-R altimetry sea-state bias, can be obtained based on the accurate modeled position of the specular point. At present, the reflection surface model of the specular point positioning still has the mean dynamic topography (MDT) error and the deviation of the vertical (DOV) error relative to the instantaneous sea surface. In this study, the following studies have been carried out. Based on the ship-borne GNSS-R observations in China seas, we introduced various elevation parameters including the MDT to correct the elevation error of the reflection surface. We introduced the DOV based on the elevation correction, and the DOV correction positioning method was proposed to correct the slope error of the reflection surface. The specular point was positioned on the instantaneous sea reflection surface. We verified the instantaneous sea reflection surface model and the specular point positioning results, analyzed the relationship between the position correction distance and the reflection incident angle, and discussed the spatial distribution characteristics of the MDT correction distance. The results showed that the reflection surface modeling and the specular point positioning were accurate. The positioning error increased to varying degrees with the increase of the reflection incident angle. The MDT correction improved the positioning by 0.91 m, and the DOV correction further improved the positioning by 0.12 m. Based on the combined application of the two kinds of correction positioning, the positioning was comprehensively improved by 0.99 m. The MDT correction of China seas gradually increased from the north to south. While in the regional sea areas, it gradually decreased from the north to south and showed randomness. The relative position between the antennas and their random changes introduced uncertainty, which can be reduced by integration. The new instantaneous sea reflection surface model and the corresponding specular point positioning method can provide accurate modeled reflection delay for the sea-state bias correction of ship-borne GNSS-R observations, and they can be extended to satellite-borne global observations.

Sticky Bessel diffusions

We consider a Bessel process X of dimension δ∈(0,2) having 0 as a slowly reflecting (sticky) boundary point with a stickiness parameter 1/μ∈(0,∞). We show that (i) the process X can be characterised through its square Y=X2 as a unique weak solution to the SDE system dYt=δI(Yt>0)dt+2YtdBtI(Yt=0)dt=12μdℓt0(Y) where B is a standard Brownian motion and ℓ0(Y) is a diffusion local time process of Y at 0, and (ii) the transition density function of X can be expressed in the closed form as a convolution integral involving a Mittag-Leffler function and a modified Bessel function of the second kind. Appearance of the Mittag-Leffler function is novel in this context. We determine a (sticky) boundary condition at zero that characterises the transition density function of X as a unique solution to the Kolmogorov backward/forward equation of X. We also show that the convolution integral can be characterised as a unique solution to the generalised Abel equation of the second kind. Letting μ↓0 (absorption) and μ↑∞ (instantaneous reflection) the closed-form expression for the transition density function of X reduces to the ones found by Feller (1951) and Molchanov (1967) respectively.

Single-shot, shadowless total internal reflection fluorescence microscopy via annular fiber bundle.

We demonstrate a method of generating instantaneous and uniform total internal reflection fluorescence (TIRF) excitation by using an annular fiber bundle and spatially incoherent light sources. We show the flexibility of our method in that it can generate TIRF excitation with either a laser light source or an LED of different wavelengths, and facilitate switching between TIRF and epi illumination. In this report we detail the design of the fiber bundle, then demonstrate the performance via single-molecule imaging in the presence of high background and high throughput, and uniform TIRF imaging of cells over a large field of view. Our versatile method will enable quantitative shadowless TIRF imaging.

Invisible Electromagnetic Huygens’ Metasurface Operational in Wide Frequency Band and Its Experimental Validation

Wideband operation ability becomes an obstacle for many metamaterial applications since they are generally based on effective material (medium) hypothesis, which is intrinsically functional on single frequency or narrowband. Effective biological camouflage strategies involve concealment under sunlight with multiple frequency (color) components, for example, a shark could fuse itself into sea water environment for better invisibility and hunting effectiveness. A wideband 3-D metasurface ground cloak in gigahertz frequency order is proposed and realized in the experiment with a hemispherical profile. A complex unit structure to broaden the operational frequency range for a phase-preserved electromagnetic metasurface based on the difference of elevation is also proposed. Comparison between the wideband and its contrast narrowband metasurface clearly indicates the scattering improvement effect that demonstrates the proposed metasurface’s significance. Both instantaneous electric field scanning and reflection cross section shrinking quantitatively give strong evidence of the wideband operational functions. Comparison between simulation and experiment validated each other. These results indicate that the proposed metasurface conceals itself into a background inside a wide frequency spectrum of 7.0–9.5 GHz. This structure has a great application value for object security under wave package illumination and in landscape fusion. This mechanism also demonstrates the possibility to change other effective material properties in a wide frequency band.

Possibility of intrusive igneous body beneath the Cretaceous sequence in Abu Gharadig Basin, Egypt: integration of geophysical data interpretations

Based on the explanation of seismic data covering the middle part of Abu Gharadig Basin in northern Western Desert, a diapiric structure has been detected eastward of the study area. The resolution of this diapiric feature has been enhanced using different five seismic volume attributes including instantaneous bandwidth, reflection strength, instantaneous frequency and reflection intensity. The interpreted diapiric feature exhibits discordant, nearly vertical, almost symmetric and mounded structure with uplifted overburden and upturned host rocks. The magnetic map for the study area represents high anomaly directly above the interpreted diapiric feature in the eastern part of the area of study confirming the high density of the intrusive body. The area of study also delineated on a temperature gradient map for the northern Western Desert showing high temperature gradient over the interpreted diapiric feature towards the eastern portion of the study area. This suggests that the examined body is a subsurface source for high temperature. Accordingly, the detected diapiric feature has been interpreted to be large body of igneous intrusion forming domal masses beneath the Cretaceous succession in the study area. This igneous intrusion is expected to have positive or negative effect on the hydrocarbon potential in Abu Gharadig Basin.

Minimising the expected commute time

Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion’s drift via the corresponding scale function. In the static version the diffusion’s drift can be chosen at each point in [0,1], whereas in the dynamic version we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem.

A constrained Langevin approximation for chemical reaction networks

Continuous-time Markov chain models are often used to describe the stochastic dynamics of networks of reacting chemical species, especially in the growing field of systems biology. These Markov chain models are often studied by simulating sample paths in order to generate Monte-Carlo estimates. However, discrete-event stochastic simulation of these models rapidly becomes computationally intensive. Consequently, more tractable diffusion approximations are commonly used in numerical computation, even for modest-sized networks. However, existing approximations either do not respect the constraint that chemical concentrations are never negative (linear noise approximation) or are typically only valid until the concentration of some chemical species first becomes zero (Langevin approximation). In this paper, we propose an approximation for such Markov chains via reflected diffusion processes that respect the fact that concentrations of chemical species are never negative. We call this a constrained Langevin approximation because it behaves like the Langevin approximation in the interior of the positive orthant, to which it is constrained by instantaneous reflection at the boundary of the orthant. An additional advantage of our approximation is that it can be written down immediately from the chemical reactions. This contrasts with the linear noise approximation, which involves a two-stage procedure—first solve a deterministic reaction rate ordinary differential equation, followed by a stochastic differential equation for fluctuations around those solutions. Our approximation also captures the interaction of nonlinearities in the reaction rate function with the driving noise. In simulations, we have found the computation time for our approximation to be at least comparable to, and often better than, that for the linear noise approximation. Under mild assumptions, we first prove that our proposed approximation is well defined for all time. Then we prove that it can be obtained as the weak limit of a sequence of jump-diffusion processes that behave like the Langevin approximation in the interior of the positive orthant and like a rescaled version of the Markov chain on the boundary of the orthant. For this limit theorem, we adapt an invariance principle for reflected diffusions, due to Kang and Williams [Ann. Appl. Probab. 17 (2007) 741–779], and modify a result on pathwise uniqueness for reflected diffusions due to Dupuis and Ishii [Ann. Probab. 21 (1993) 554–580]. Some numerical examples illustrate the advantages of our approximation over direct simulation of the Markov chain or use of the linear noise approximation.

Preservation of the Markov Property Under Delayed Reflection

A one-dimensional locally Markov diffusion process with positive range of values is considered. It is assumed that this process is reflected from the point 0. All the variants of reflection with preservation of the semi-Markov property are described. The reflected process is still locally Markov in open intervals, but it can lose the global Markov property. The reflection is characterized by the time α(r) which is the first exit time from the semi-interval [0, r) after the first hitting time at level 0 (for r > 0). A distribution of this time is used to derive a time change transforming a process with instantaneous reflection into a process with delayed reflection. It is proved that a process that preserves its Markov property after the delayed reflection has a special distribution of the set of times at which the process has zero values during the interval [0, α(r)). For such a process, this set has exponentially distributed Lebesgue measure. Bibliography: 7 titles.

3-D seismic attributes analysis in Balad Oil Field—center of Iraq

Seismic attributes techniques were applied after conventional interpretation (structural interpretation) on 3-D seismic volume of 250 km2 of the Balad Oil Field, located in the central part of Iraq within Salah Al-din province (Balad area), were made. Seismic attribute sections are very important for the distribution of reflector surfaces’ continuity and termination. Top Hartha, intra Hartha, top Sadi, and top Khasib reflectors represent the upper Cretaceous Formation defined from synthetic seismogram of the well in the study area and picked over 3-D seismic volume. New seismic attribute volumes are processed and time slice sets are constructed, and then converted from seismic signal in time domain to one of the attribute views. Instantaneous frequency, reflection strength, and amplitude extraction attribute were applied for intra Hartha, top Sadi, and top Khasib reflectors to get attribute sections view and mapped for these reflectors; they represent the main reservoirs in the field. These types of attributes are important to detect the hydrocarbon accumulation on seismic sections and confirm the structural interpretation.

On the Neumann problem for PDE’s with a small parameter and the corresponding diffusion processes

The diffusion process in a region \({G \subset \mathbb R^2}\) governed by the operator \({\tilde L^\varepsilon = \frac{\,1}{\,2}\, u_{xx} + \frac1 {2\varepsilon}\, u_{zz}}\) inside the region and undergoing instantaneous co-normal reflection at the boundary is considered. We show that the slow component of this process converges to a diffusion process on a certain graph corresponding to the problem. This allows to find the main term of the asymptotics for the solution of the corresponding Neumann problem in G. The operator \({\tilde L^\varepsilon}\) is, up to the factor e− 1, the result of small perturbation of the operator \({\frac{\,1}{\,2}\, u_{zz}}\). Our approach works for other operators (diffusion processes) in any dimension if the process corresponding to the non-perturbed operator has a first integral, and the e-process is non-degenerate on non-singular level sets of this first integral.

On Markov diffusion processes with delayed reflection from boundaries of a segment

A continuous semi-Markov process with values in a closed interval is considered. This process coincides with a Markov diffusion process inside the interval. Thus, violation of the Markov property is only possible at the boundary of the interval. We prove a sufficient condition under which a semi-Markov process is Markov. We show that, in addition to Markov processes with instantaneous reflection from the boundary of the interval. there exists a class of Markov processes with delayed reflection from the boundary. Such a process has a positive average measure of time at which its trajectory belongs to the boundaries. This gives a different proof of a similar result by Gikhman and Skorokhod of 1968. Bibliography: 5 titles.

Wiener Process with Reflection in Non-Smooth Narrow Tubes

Wiener process with instantaneous reflection in narrow tubes of width $\epsilon\ll 1$ around axis $x$ is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let $V^{\epsilon}(x)$ be the volume of the cross-section of the tube. We assume that $\frac{1}{\epsilon}V^{\epsilon}(x)$ converges in an appropriate sense to a non-smooth function as $\epsilon\downarrow 0$. This limiting function can be composed by smooth functions, step functions and also the Dirac delta distribution. Under this assumption we prove that the $x$-component of the Wiener process converges weakly to a Markov process that behaves like a standard diffusion process away from the points of discontinuity and has to satisfy certain gluing conditions at the points of discontinuity.

Fast response of lake plankton and nutrients to river inundations on floodplain lakes

AbstractKey variables in ecosystems tend to operate on widely different time‐scales. These time‐scales become relevant when a disturbance rocks the ecosystem. Here we try to explain the fast dynamics of plankton and nutrients in the water column of floodplain lakes after disturbances (inundations). We take advantage of natural experiments, that is occasional massive overflow of floodplain lakes with river water. We sampled 10 lakes in two floodplains along the Dutch river Waal monthly for 3 years, capturing the impact of three inundation events. The inundations reset the plankton as well as chemical composition of most lakes to largely the same state. While biologically inert macro‐ion data reflected a large and long lasting impact of the river water, dynamics of nutrients, phytoplankton and zooplankton communities between lakes diverged in a few weeks to regimes characteristic for the different lakes. While one spring inundation synchronized plankton dynamics to let the subsequent clear water phase occur at the same moment in different lakes, winter inundations did not have the same effect and apparently dynamics quickly diverged. Our results showed that effects of inundations and other processes that affect the state of the ecosystem should be studied considering the level of the slow components such as the sediment nutrient pool, fish stock and macrophyte communities. Plankton communities and lake water nutrient status give a practically instantaneous reflection of the condition of these slow components. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Semi-Analytical Solution of Dirac Equation in Schwarzschild-de Sitter Spacetime

In the present paper, we solve the radial parts of Dirac equation between the inner and the outer horizon in the Schwarzschild-de Sitter (SdS for short) geometry. Complete physical parameter space is divided into two regions depending on the height of the potential barrier and the energy of the incoming particle. In each region, we concentrate on two limiting cases. The first case is when the two horizons are close to each other and the second case is when the horizons are far apart. In each case, we give the semi-analytical solution by using WKB (Wentzel-Krames-Brillouin) approximation and show the instantaneous reflection and transmission coefficients as well as the radial wave functions graphically.

Instantaneous Reflection of Inter-IA Interaction Development Using the Script Language Approach

Information appliances (IAs) are able to interact and share information with each other using their communication abilities. However, current inter-IA interaction development using the general purpose programming language, e.g., C/C++ and Java approach, involves lots of time for system development process, i.e., (1) program writing, (2) source code compilation, (3) executable code loading, and (4) executable code distribution. In this paper, we introduce the concept of instantaneous reflection of inter-IA interaction development to help fast inter-IA interaction development without going through the above 4 processes. In this paper, we have designed an Inter-IA Interaction Development Platform (I^2DP) that enables instantaneous reflection of inter-IA interaction development using the high level script language approach. Main components of the I^2DP platform architecture include (ⅰ) IAs and (ⅱ) Administration Gateway that is responsible for the inter-entity communication and execution of inter-IA interactions. The core of I^2DP consists of (ⅰ) Service Invocation Protocol (SIP), which is a control protocol for IAs, and (ⅱ) Service Interaction Script language (SIS), which is a script language that can specify inter-IA interactions. As a result, instantaneous reflection of inter-IA interaction development using high level script language can be achieved in I^2DP.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth—death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.