Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

State equation for shape-memory alloys. Aplication to Cu-Zn-Al

We deal with the hysteretic behavior of partial cycles in the two¿phase region associated with the martensitic transformation of shape¿memory alloys. We consider the problem from a thermodynamic point of view and adopt a local equilibrium formalism, based on the idea of thermoelastic balance, from which a formal writing follows a state equation for the material in terms of its temperature T, external applied stress ¿, and transformed volume fraction x. To describe the striking memory properties exhibited by partial transformation cycles, state variables (x,¿,T) corresponding to the current state of the system have to be supplemented with variables (x,¿,T) corresponding to points where the transformation control parameter (¿¿ and/or T) had reached a maximum or a minimum in the previous thermodynamic history of the system. We restrict our study to simple partial cycles resulting from a single maximum or minimum of the control parameter. Several common features displayed by such partial cycles and repeatedly observed in experiments lead to a set of analytic restrictions, listed explicitly in the paper, to be verified by the dissipative term of the state equation, responsible for hysteresis. Finally, using calorimetric data of thermally induced partial cycles through the martensitic transformation in a Cu¿Zn¿Al alloy, we have fitted a given functional form of the dissipative term consistent with the analytic restrictions mentioned above.

Spatial planning to the test of property rights in Switzerland : an innovative land management approach to coordinate spatial planning goals with property rights interests

In Switzerland, the land management regime is characterized by a liberal attitude towards the institution of property rights, which is guaranteed by the Constitution. Under the present Swiss constitutional arrangement, authorities (municipalities) are required to take into account landowners' interests when implementing their spatial planning policy. In other words, the institution of property rights cannot be restricted easily in order to implement zoning plans and planning projects. This situation causes many problems. One of them is the gap between the way land is really used by the landowners and the way land should be used based on zoning plans. In fact, zoning plans only describe how landowners should use their property. There is no sufficient provision for handling cases where the use is not in accordance with zoning plans. In particular, landowners may not be expropriated for a non-conforming use of the land. This situation often leads to the opening of new building areas in greenfields and urban sprawl, which is in contradiction with the goals set into the Federal Law on Spatial Planning. In order to identify legal strategies of intervention to solve the problem, our paper is structured into three main parts. Firstly, we make a short description of the Swiss land management regime. Then, we focus on an innovative land management approach designed to implement zoning plans in accordance with property rights. Finally, we present a case study that shows the usefulness of the presented land management approach in practice. We develop three main results. Firstly, the land management approach brings a mechanism to involve landowners in planning projects. Coordination principle between spatial planning goals and landowners' interests is the cornerstone of all the process. Secondly, the land use is improved both in terms of space and time. Finally, the institution of property rights is not challenged, since there is no expropriation and the market stays free.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Solutions of the telegrapher's equation in the presence of traps

Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Quantum decay of metastable states in small magnetic particles

We present an imaginary-time path-integral study of the problem of quantum decay of a metastable state of a uniaxial magnetic particle placed in the magnetic field at an arbitrary angle. Our findings agree with earlier results of Zaslavskii obtained by mapping the spin Hamiltonian onto a particle Hamiltonian. In the limit of low barrier, weak dependence of the decay rate on the angle is found, except for the field which is almost normal to the anisotropy axis, where the rate is sharply peaked, and for the field approaching the parallel orientation, where the rate rapidly goes to zero. This distinct angular dependence, together with the dependence of the rate on the field strength, provides an independent test for macroscopic spin tunneling.

New microfluidic-based sampling procedure for overcoming the hematocrit problem associated with dried blood spot analysis.

Hematocrit (Hct) is one of the most critical issues associated with the bioanalytical methods used for dried blood spot (DBS) sample analysis. Because Hct determines the viscosity of blood, it may affect the spreading of blood onto the filter paper. Hence, accurate quantitative data can only be obtained if the size of the paper filter extracted contains a fixed blood volume. We describe for the first time a microfluidic-based sampling procedure to enable accurate blood volume collection on commercially available DBS cards. The system allows the collection of a controlled volume of blood (e.g., 5 or 10 μL) within several seconds. Reproducibility of the sampling volume was examined in vivo on capillary blood by quantifying caffeine and paraxanthine on 5 different extracted DBS spots at two different time points and in vitro with a test compound, Mavoglurant, on 10 different spots at two Hct levels. Entire spots were extracted. In addition, the accuracy and precision (n = 3) data for the Mavoglurant quantitation in blood with Hct levels between 26% and 62% were evaluated. The interspot precision data were below 9.0%, which was equivalent to that of a manually spotted volume with a pipet. No Hct effect was observed in the quantitative results obtained for Hct levels from 26% to 62%. These data indicate that our microfluidic-based sampling procedure is accurate and precise and that the analysis of Mavoglurant is not affected by the Hct values. This provides a simple procedure for DBS sampling with a fixed volume of capillary blood, which could eliminate the recurrent Hct issue linked to DBS sample analysis.

Innovative Solutions for Slope Stability Reinforcement and Characterization: Vol. III, TR-489, 2005

Soil slope instability concerning highway infrastructure is an ongoing problem in Iowa, as slope failures endanger public safety and continue to result in costly repair work. Volume I of this current study summarizes research methods and findings, while Volume II provides procedural details for incorporating into practice an infrequently-used testing technique–borehole shear tests. Volume III of this study of field investigation of fifteen slopes in Iowa demonstrates through further experimental testing how lateral forces develop along stabilizing piles to resist slope movements. Results establish the feasibility of an alternative stabilization approach utilizing small-diameter pile elements. Also, a step-by-step procedure that can be used by both state and county transportation agencies to design slope reinforcement using slender piles is documented. Initial evidence of the efficiency and cost-effectiveness of stabilizing nuisance slope failures with grouted micropiles is presented. Employment of the remediation alternative is deemed more appropriate for stabilizing shallow slope failures. Overall, work accomplished in this research study included completing a comprehensive literature review on the state of the knowledge of slope stability and slope stabilization, the preparation and performance of fourteen full-scale pile load tests, the analysis of load test results, and the documentation of a design methodology for implementing the technology into current practices of slope stabilization. Recommendations for further research include monitoring pilot studies of slope reinforcement with grouted micropiles, supplementary experimental studies, and advanced numerical studies.

Innovative Leak Test for Pavement Joint Seals, Progress Report, HR-318, 1993

Premature failure of concrete pavement contraction joint seals is an ongoing and costly problem for the Iowa Department of Transportation. Several joint seal test sections consisting of variations in sawing methods, joint cleaning techniques, sealant installation, and sealant types have been established over the past few years. Laboratory analysis and field inspections were done as a part of the tests, and core samples were taken for laboratory adhesion pull tests. Such methods often cover specifically small areas and may not expose hidden failures. Some tests are also labor-intensive and destructive, especially that of coring. An innovative, nondestructive, broad coverage joint seal tester that yields quick results has been designed and developed for evaluation of pavement joint seal performance. The Iowa vacuum joint seal tester (IA-VAC) applies a low vacuum above a joint seal that has been spray-covered with a foaming water solution. Any unsealed area or leak that exists along the joint will become quickly and clearly visible by the development of bubbles at the leak point. By analyzing the results from the IA-VAC tests, information on the number and types of leaks can be obtained; such information will help identify the source of the problem and direct efforts toward a solution.

Effect of Grooved Concrete on Curing Efficiency, MLR-83-4, 1983

The textured concrete surface on all PCC primary paving projects (and when specified on secondary projects) is required to be grooved in a specified manner. The laboratory test for determining the efficiency index of concrete curing compounds is made on slabs that are not grooved. This short investigation was undertaken to determine any changes in the curing efficiency index when using various rates of application of curing compound on grooved concrete. Currently a 95 percent curing efficiency index is specified at an application rate of 15 square yards per gallon. Can this efficiency be achieved, and if so at what application rate, on grooved concrete? Grooving the concrete greatly increases the surface area and also causes the liquid curing compound to run off the high spots and collect in the grooves.

Assessment of skinfold thickness equations in estimating body composition in children with inflammatory bowel

Introduction: Growth is a central process in paediatrics. Weight and height evaluation are therefore routine exams for every child but in some situation, particularly inflammatory bowel disease (IBD), a wider evaluation of nutritional status needs to be performed. The assessment of body composition is essential in order to maintain acceptable growth using the following techniques: Dual-energy X-ray absorptiometry (DEXA), bio-impedance-analysis (BIA) and anthropometric measurements (skinfold thickness skin), the latter being most easily available and most cost effective. Objectives: To assess the accuracy of skinfold equations in estimating percentage body fat (%BF) in children with inflammatory bowel disease (IBD), compared with assessment of body fat dual energy X-ray absorptiometry (DEXA). Methods: Twenty-one patients (11 females, 10 males; mean age: 14.3 years, range 12 - 16 years) with IBD (Crohn's disease n = 15, ulcerative colitis n = 6)). Estimated%BF was computed using 6 established equations based on the triceps, biceps, subscapular and suprailiac skinfolds (Deurenberg, Weststrate, Slaughter, Durnin & Rahaman, Johnston, Brook) and compared to DEXA. Concordance analysis was performed using Lin's concordance correlation and the Bland-Altman limits of agreement method. Results: Durnin & Rahaman's equation shows a higher Lin's concordance coefficient with a small difference amongst raw values for skinfolds and DEXA compared to the other equations. Correlation coefficient between mean and difference is close to zero with a non-significant Bradley-Blackwood test. Conclusion: Body composition in paediatric IBD patients using the Durnin & Rahaman skinfold-equation adequately reflects values obtained by DEXA.

Comparison of interferon-gamma release assay versus tuberculin skin test for tuberculosis screening in inflammatory bowel disease.

OBJECTIVES: Reactivation of latent tuberculosis (TB) in inflammatory bowel disease (IBD) patients treated with antitumor necrosis factor-alpha medication is a serious problem. Currently, TB screening includes chest x-rays and a tuberculin skin test (TST). The interferon-gamma release assay (IGRA) QuantiFERON-TB Gold In-Tube (QFT-G-IT) shows better specificity for diagnosing TB than the skin test. This study evaluates the two test methods among IBD patients. METHODS: Both TST and IGRA were performed on 212 subjects (114 Crohn's disease, 44 ulcerative colitis, 10 indeterminate colitis, 44 controls). RESULTS: Eighty-one percent of IBD patients were under immunosuppressive therapy; 71% of all subjects were vaccinated with Bacille Calmette Guérin; 18% of IBD patients and 43% of controls tested positive with the skin test (P < 0.0001). Vaccinated controls tested positive more often with the skin test (52%) than did vaccinated IBD patients (23%) (P = 0.011). Significantly fewer immunosuppressed patients tested positive with the skin test than did patients not receiving therapy (P = 0.007); 8% of patients tested positive with the QFT-G-IT test (14/168) compared to 9% (4/44) of controls. Test agreement was significantly higher in the controls (P = 0.044) compared to the IBD group. CONCLUSIONS: Agreement between the two test methods is poor in IBD patients. In contrast to the QFT-G-IT test, the TST is negatively influenced by immunosuppressive medication and vaccination status, and should thus be replaced by the IGRA for TB screening in immunosuppressed patients having IBD.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.