Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Termination of major ductile strike-slip shear and differential cooling along the Insubric line (Central Alps): U-Pb, Rb-Sr and 40Ar/39Ar ages of cross-cutting pegmatites

To constrain the age of strike-slip shear, related granitic magmatism, and cooling along the Insubric line, 29 size fractions of monazite and xenotime were dated by the U-Pb method, and a series of 25 Rb-Sr and Ar-40/Ar-39 ages were measured on different size fractions of muscovite and biotite. The three pegmatitic intrusions analyzed truncate high-grade metamorphic mylonite gneisses of the Simplon shear zone, a major Alpine structure produced in association with dextral strike-slip movements along the southern edge of the European plate, after collision with its Adriatic indenter. Pegmatites and aplites were produced between 29 and 25 Ma in direct relation to right-lateral shear along the Insubric line, by melting of continental crust having Sr-87/Sr-86 between 0.7199 and 0.7244 at the time of melting. High-temperature dextral strike-slip shear was active at 29.2 +/- 0.2 (2 sigma) Ma, and it terminated before 26.4 +/- 0.1 Ma. During dike injection, temperatures in the country rocks of the Isorno-Orselina and Monte Rosa structural units did not exceed approximate to 500 degrees C, leading to fast initial cooling, followed by slower cooling to approximate to 350 degrees C within several million years. In one case, initial cooling to approximate to 500 degrees C was significantly delayed by about 4 m.y., with final cooling to approximate to 300 degrees C at 20-19 Ma in all units. For the period between 29 and 19 Ma, cooling of the three sample localities was non-uniform in space and time, with significant variations on the kilometre scale. These differences are most likely due to strongly varying heat flow, and/or heterogeneous distribution of unroofing rates within the continuously deforming Insubric line. If entirely ascribed to differences in unroofing, corresponding rates would vary between 0.5 and 2.5 mm/y, for a thermal gradient of 30 degrees/km.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Early Entry Sawed Portland Cement Concrete Transverse Joint Ends, MLR-97-5, 2003

Experiments with early entry light sawing of Portland cement concrete (PCC) contraction joints began in Iowa in 1989. Since that time, changes in early sawing equipment have occurred as well as changes in specifications for sawing. The option to use early sawing for transverse contraction joints was specified in 1992. A problem happening occasionally with early sawing was the break out of some of the concrete around the end of the joint as the saw blade approached the edge of the slab. To prevent this, it was proposed that the sawing would terminate approximately 1/2" to 3/4" before the edge of the slab, creating a "short joint". This procedure would also leave a concrete "dam" to prevent the run-out and waste of the hot liquid joint sealant onto the shoulder. It would also eliminate the need for the labor and material for applying a duct tape dam at the open ends of each sawed joint to stop hot liquid sealant run-out Agreements were made with the contractor to apply the "short joint" technique for 1 day of paving. The evaluation and results are compared with an adjoining control section. The research found no negative aspects from sawing the "short joint". Three specific findings were noted. They are the following: 1) No joint end "blow-out" spalls of concrete occurred. 2) The need for the duct tape dam to stop liquid sealant overflow was eliminated. 3) Joint end corner spalls appear to be caused mainly by construction shouldering operations equipment. The "short joint" sawing technique can be routinely applied to early entry sawed transverse contraction joints with expectations of only positive results.

Reducing the Problem of Transverse Cracking, HR-232, 1985

The Iowa Department of Transportation (DOT) is continually improving the pavement management program and striving to reduce maintenance needs. Through a 1979 pavement management study, the Iowa DOT became a participant in a five state Federal Highway Administration (FHWA) study of "Transverse Cracking of Asphalt Pavements". There were numerous conclusions and recommendations but no agreement as to the major factors contributing to transverse cracking or methods of preventing or reducing the occurrence of transverse cracking. The project did focus attention on the problem and generated ideas for research. This project is one of two state funded research projects that were a direct result of the FHWA project. Iowa DOT personnel had been monitoring temperature susceptibility of asphalt cements by the Norman McLeod Modified Penetration Index. Even though there are many variables from one asphalt mix to another, the trend seemed to indicate that the frequency of transverse cracking was highly dependent on the temperature susceptibility. Research project HR-217 "Reducing the Adverse Effects of Transverse Cracking" was initiated to verify the concept. A final report has been published after a four-year evaluation. The crack frequency with the high temperature susceptible asphalt cement was substantially greater than for the low temperature susceptible asphalt cement. An increased asphalt cement content in the asphalt treated base also reduced the crack frequency. This research on prevention of transverse cracking with fabric supports the following conclusions: 1. Engineering fabric does not prevent transverse cracking of asphalt cement concrete. 2. Engineering fabric may retard the occurrence of transverse cracking. 3. Engineering fabric does not contribute significantly to the structural capability of an asphalt concrete pavement.

Estimating the apparent transverse relaxation time (R2(*)) from images with different contrasts (ESTATICS) reduces motion artifacts.

Relaxation rates provide important information about tissue microstructure. Multi-parameter mapping (MPM) estimates multiple relaxation parameters from multi-echo FLASH acquisitions with different basic contrasts, i.e., proton density (PD), T1 or magnetization transfer (MT) weighting. Motion can particularly affect maps of the apparent transverse relaxation rate R2(*), which are derived from the signal of PD-weighted images acquired at different echo times. To address the motion artifacts, we introduce ESTATICS, which robustly estimates R2(*) from images even when acquired with different basic contrasts. ESTATICS extends the fitted signal model to account for inherent contrast differences in the PDw, T1w and MTw images. The fit was implemented as a conventional ordinary least squares optimization and as a robust fit with a small or large confidence interval. These three different implementations of ESTATICS were tested on data affected by severe motion artifacts and data with no prominent motion artifacts as determined by visual assessment or fast optical motion tracking. ESTATICS improved the quality of the R2(*) maps and reduced the coefficient of variation for both types of data-with average reductions of 30% when severe motion artifacts were present. ESTATICS can be applied to any protocol comprised of multiple 2D/3D multi-echo FLASH acquisitions as used in the general research and clinical setting.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Reducing the Adverse Effects of Transverse Cracking, HR-217, 1984

This research was initiated to identify methods of reducing the occurrence of transverse cracking. Eight (four repetitive) research sections were established to study three variations in the asphalt concrete pavement. The first variation was the comparison of low- and high-temperature-susceptible asphalt cement (AC) from two different sources. The second variable was to saw and seal transverse joints at spacings varying from 40 to 100 ft. The third variable was to increase the AC content in the asphalt treated base by 1 percent. The research sections were constructed with relatively few problems. Crack and joint surveys have been conducted on all research sections at intervals of less than 1 year since construction. No cracking was identified after the first winter season. The sawed joints also remained sealed through the first winter. At an age of approximately 1 1/2 years there was substantial cracking of the high-temperature-susceptible AC sections and substantial failure of the sealant material in the sawed joints. After almost 4 years, the asphalt pavement constructed with the high-temperature-susceptible AC produced a crack interval of 35 ft, the low-temperature-susceptible AC yielded an interval of 170 ft, and the low-temperature-susceptible AC with an increased AC content yielded an interval of 528 ft. The Pen-Vis number is an effective measure of temperature susceptibility of asphalt cements. The frequency of transverse cracking is affected by the temperature susceptibility of the AC. An increased AC content also reduces the frequency of transverse cracking.

Longitudinal Grinding and Transverse Grooving to Improve Frictional and Profile Properties, HR-1035, 1983

There are many miles of portland cement concrete pavement in Iowa that due to normal wear, and in some cases accelerated wear from studded tires, the surface has become polished resulting in less than desirable friction values. Retexturing the surface may be an economical way to re-establish desirable friction values. Retexturing by grinding with diamond blades and transverse grooving with diamond blades are two methods of rehabilitating p.c.c. surfaces. MU Inc. of Lebanan, Tennessee proposed to provide without charge to the Iowa Department of Transportation, one 1500 ft x 12 ft section each of three methods of texturing. They are longitudinal grinding, transverse grooving and longitudinal grinding followed by transverse grooving. A section of 1500 feet is needed to properly evaluate a texturing method. It was decided by Iowa DOT personnel that due to possible differential friction it would be undesirable to texture only one lane. The decision was made to do test sections of 1500 ft x 24 ft with the cost of the additional texturing paid by the Iowa DOT. Iowa also has areas where the p.c.c. pavement has faulted at the joints and cracks which results in poor riding quality. Methods of correcting the faulting are to underseal the pavement where needed and/or grinding the surface to eliminate the faulted areas. It was decided to include in this research project a section for profiling by grinding.