LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Development of new rapid prototyping process

Purpose - The purpose of this paper is to identify the key elements of a new rapid prototyping process, which involves layer-by-layer deposition of liquid-state material and at the same time using an ultraviolet line source to cure the deposited material. This paper reports studies about the behaviour of filaments, deposition accuracy, filaments interaction and functional feasibility of system. Additionally, the author describes the process which has been proposed, the equipment that has been used for these studies and the material which was developed in this application. Design/methodology/approach - The research has been separated into three study areas in accordance with their goals. In the first, both the behaviour of filament and deposition accuracy was studied. The design of the experiment is described with focus on four response factors (bead width, filament quality, deposition accuracy and deposition continuity) along with function of three control factors (deposition height, deposition velocity and extrusion velocity). The author also studied the interaction between filaments as a function of bead centre distance. In addition, two test samples were prepared to serve as a proof of the methodology and to verify the functional feasibility of the process which has been studied. Findings - The results show that the proposed process is functionally feasible, and that it is possible to identify the main effects of control factors over response factors. That analysis is used to predict the condition of process as a function of the parameters which control the process. Also identified were distances of centre beads which result in a specific behaviour. The types of interaction between filaments were analysed and sorted into: union, separation and indeterminate. At the end, the functional feasibility of process was proved whereby two test parts could be built. Originality/value - This paper proposes a new rapid prototyping process and also presents test studies related to this proposition. The author has focused on the filament behaviour, deposition accuracy, interaction between filaments and studied the functional feasibility of process to provide new information about this process, which at the same time is useful to the development of other rapid prototyping processes.

Modeling and simulation of severe slugging in air-water pipeline-riser systems

A mathematical model, numerical simulations and stability and flow regime maps corresponding to severe slugging in pipeline riser systems, are presented. In the simulations air and water were used as flowing fluids. The mathematical model considers continuity equations for liquid and gas phases, with a simplified momentum equation for the mixture, neglecting inertia. A drift-flux model, evaluated for the local conditions in the riser, is used as a closure law. The developed model predicts the location of the liquid accumulation front in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. The numerical procedure is convergent for different nodalizations. A comparison is made with experimental results corresponding to a catenary riser, showing very good results for slugging cycle and stability and flow regime maps. (c) 2010 Elsevier Ltd. All rights reserved.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Influence of Suture on Peripheral Nerve Regeneration and Collagen Production at the Site of Neurorrhaphy: An Experimental Study

BACKGROUND: Restoration of nerve continuity and effective maintenance of coaptation are considered fundamental principles of end-to-end peripheral nerve repair. OBJECTIVE: To evaluate the influence of the number of stitches on axonal regeneration and collagen production after neurorrhaphy. METHODS: Thirty male Wistar rats were equally divided into 3 groups and were all operated on with the right sciatic nerve exposed. In 2 groups, the nerve was sectioned and repaired by means of 3 (group B) or 6 (group C) epineurium sutures with 100 monofilament nylon. One group (group A) was used as a control. Each animal from groups B and C underwent electrophysiological evaluation with motor action potential recordings before nerve section and again at an 8-week interval after neurorrhaphy. Nerve biopsy specimens were used for histomorphometric assessment of axonal regeneration and quantification of collagen at the repair site. RESULTS: Animals from group C had significantly lower motor action potential conduction velocities compared with control animals (P = .02), and no significant difference was seen between groups B and C. Parameters obtained from morphometric evaluation were not significantly different between these 2 groups. Type I collagen and III collagen in the epineurium were significantly higher in group C than in either the control group (P = .001 and P = .003) or group B (P = .01 and P = .02). No differences were identified for collagen I and III in the endoneurium. CONCLUSION: Using 6 sutures for nerve repair is associated with worse electrophysiological outcomes and higher amounts of type I and III collagen in the epineurium compared with control. Neurorraphy with 6 stitches is also related to a significant increase in epineurium collagen I and III compared with 3-stitch neurorraphy.

Ultrasonographic Evaluation of Achilles Tendon Repair After Percutaneous Sectioning for the Correction of Congenital Clubfoot Residual Equinus

Background: Most cases of congenital clubfoot treated with the Ponseti technique require percutaneous Achilles tenotomy to correct the residual equinus. Clinical evidence suggests that complete healing occurs between the cut tendon stumps, but there have not yet been any detailed studies investigating this reparative process. This study was performed to assess Achilles tendon repair after percutaneous section to correct the residual equinus of clubfoot treated with the Ponseti method. Method: A prospective study analyzed 37 tenotomies in 26 patients with congenital clubfoot treated with the Ponseti technique, with a minimum follow-up of 1 year after the section. The tenotomy was performed percutaneously with a large-bore needle bevel with patient sedation and local anesthesia. Ultrasonographic scanning was performed after section to ascertain that the tenotomy had been completed and to measure the stump separation. In the follow-up period, the reparative process was followed ultrasonographically and assessed at 3 weeks, 6 months, and 1 year posttenotomy. Results: The ultrasonography performed immediately after the procedure showed that in some cases, residual strands between the tendon ends persisted, and these were completely sectioned under ultrasound control. A mean retraction of 5.65 mm +/- 2.26 mm (range, 2.3 to 11.0 mm) between tendon stumps after section was observed. Unusual bleeding occurred in one case and was controlled by digital pressure, with no interference with the final treatment. After 3 weeks, ultrasonography showed tendon repair with the tendon gap filled with irregular hypoechoic tissue, and also with transmission of muscle motion to the heel. Six months after tenotomy, there was structural filling with a fibrillar aspect, mild or moderate hypoechogenicity, and tendon scar thickening when compared with a normal tendon. One year after tenotomy, ultrasound showed a fibrillar structure and echogenicity at the repair site that was similar to a normal tendon, but with persistent tendon scarring thickness. Conclusions: There is a fast reparative process after Achilles tendon percutaneous section that reestablishes continuity between stumps. The reparative tissue evolved to tendon tissue with a normal ultrasonographic appearance except for mild thickening, suggesting a predominantly intrinsic repair mechanism.

Push-out strength of methacrylate resin-based sealers to root canal walls

P>Aim To assess the push-out strength of Epiphany SE, Epiphany and Hybrid Root SEAL to the dentine walls of root canals. Methodology Sixty roots of canines were prepared and distributed to six groups (n = 10) according to the filling material: GI - Epiphany SE, GII - Epiphany primer and sealer, GIII - Epiphany primer, sealer and resinous solvent, GIV - Clearfil DC Bond and Epiphany sealer, GV - Clearfil, Epiphany sealer and solvent and GVI - Hybrid Root SEAL. Resilon cones were used in all groups. Roots were sectioned transversally to obtain three slices from each third. One slice was subjected to the push-out test (MPa), and results were analysed by anova and Tukey`s test (P < 0.05). The other two slices were prepared for scanning electron microscopy (SEM). Failure mode was also analysed. Results A statistically significant difference (P < 0.05) occurred between Hybrid Root SEAL (5.27 +/- 2.07) and the other materials, GI (0.40 +/- 0.23), GII (0.78 +/- 0.45), GIII (0.57 +/- 0.28), GIV (0.40 +/- 0.24) and GV (0.50 +/- 0.41), which did not differ significantly from each other (P > 0.05). Adhesive failures predominated in groups I, II, IV and V, whilst mixed and cohesive failures were the most frequent in groups III and VI, respectively. There were gaps in the adhesive interface of GI and GII, continuity areas of the filling material with dentine in GIV and GV and good adaptation of the interface of GVI. Conclusion Hybrid Root SEAL had greater push-out strength to root canal dentine than Epiphany SE and Epiphany. The use of primer, solvent and adhesive system did not influence the adhesion of Epiphany.

Valuing of firm's prior knowledge: A measure of knowledge distance

Knowledge, especially scientific and technological knowledge, grows according to knowledge trajectories and guideposts that make up the prior knowledge of an organization. We argue that these knowledge structures and their specific components lead to successful innovation. A firm's prior knowledge facilitates the absorption of new knowledge, thereby renewing a firm's systematic search, transfer and acquisition of knowledge and capabilities. In particular, the exponential growth in biotechnology is characterized by the convergence of disparate scientific and technological knowledge resources. This paper examines the shift from protein-based to DNA-based diagnostic technologies as an example, to quantify the value of a firm's prior knowledge using relative values of knowledge distance. The distance between core prior knowledge and the rate of transition from one knowledge system to another has been identified as a proxy for the value a firm's prior knowledge. The overall difficulty of transition from one technology paradigm to another is discussed. We argue this transition is possible when the knowledge distance is minimal and the transition process has a correspondingly high value of absorptive capacities. Our findings show knowledge distance is a determinant of the feasibility, continuity and capture of scientific and technological knowledge. Copyright © 2003 John Wiley & Sons, Ltd.

Reported Use of Anabolic Steroids and Ergogenic Substances in Gym/Health Club Settings: Associations with Psychosocial and Exercise Behavior Factors

The industry of ergogenic supplements is increasing rapidly (Cole et al., 2003). Supplements may constitute an important aid for some vigourous exercise routines, but they may also be used as a hypothetical mean to achieve increases in muscular mass. This supposed effect of suplements can lead to its use by individuals who have high levels of drive for muscularity, a condition that is known to be associated with muscular dismorphy (or as it has been called recently vigorexia, Pope et al., 1997). Another psychological factor which can influence supplement consumption is exercise dependence, a borderline problem, as most studies present a prevalence of less than 10% in regular exercisers (Palmeira & Matos, 2006). Symptoms like tolerance or continuity could lead to the use of ergogenic aids to maintain the exercise levels. Also of interest for the understanding of the use of suplements are exercise frequency, volume and intensity, which could explain the ratesof consumption on a more physicological level.

Demsi - a demand response simulator in the context of intensive use of distributed generation

Demand response can play a very relevant role in future power systems in which distributed generation can help to assure service continuity in some fault situations. This paper deals with the demand response concept and discusses its use in the context of competitive electricity markets and intensive use of distributed generation. The paper presents DemSi, a demand response simulator that allows studying demand response actions and schemes using a realistic network simulation based on PSCAD. Demand response opportunities are used in an optimized way considering flexible contracts between consumers and suppliers. A case study evidences the advantages of using flexible contracts and optimizing the available generation when there is a lack of supply.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Coordinated transportation of a large object by a team of three robots

Dynamical systems theory in this work is used as a theoretical language and tool to design a distributed control architecture for a team of three robots that must transport a large object and simultaneously avoid collisions with either static or dynamic obstacles. The robots have no prior knowledge of the environment. The dynamics of behavior is defined over a state space of behavior variables, heading direction and path velocity. Task constraints are modeled as attractors (i.e. asymptotic stable states) of the behavioral dynamics. For each robot, these attractors are combined into a vector field that governs the behavior. By design the parameters are tuned so that the behavioral variables are always very close to the corresponding attractors. Thus the behavior of each robot is controlled by a time series of asymptotical stable states. Computer simulations support the validity of the dynamical model architecture.