Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

Time-dependent increases in ouabain-sensitive Na(+), K(+)-ATPase activity in aortas from diabetic rats: The role of prostanoids and protein kinase C

Aims: Na(+), K(+)-ATPase activity contributes to the regulation of vascular contractility and it has been suggested that vascular Na(+), K(+)-ATPase activity may be altered during the progression of diabetes; however the mechanisms involved in the altered Na(+), K(+)-ATPase activity changes remain unclear. Thus, the aim of the present study was to evaluate ouabain-sensitive Na(+), K(+)-ATPase activity and the mechanism(s) responsible for any alterations on this activity in aortas from 1- and 4-week streptozotocin-pretreated (50 mg kg(-1), i.v.) rats. Main methods: Aortic rings were used to evaluate the relaxation induced by KCl (1-10 mM) in the presence and absence of ouabain (0.1 mmol/L) as an index of ouabain-sensitive Na(+), K(+)-ATPase activity. Protein expression of COX-2 and p-PKC-beta II in aortas were also investigated. Key findings: Ouabain-sensitive Na(+), K(+)-ATPase activity was unaltered following 1-week of streptozotocin administration, but was increased in the 4-week diabetic aorta (27%). Endothelium removal or nitric oxide synthase inhibition with L-NAME decreased ouabain-sensitive Na(+), K(+)-ATPase activity only in control aortas. In denuded aortic rings, indomethacin. NS-398, ridogrel or Go-6976 normalized ouabain-sensitive Na(+), K(+)-ATPase activity in 4-week diabetic rats. In addition, COX-2 (51%) and p-PKC-beta II (59%) protein expression were increased in 4-week diabetic aortas compared to controls. Significance: In conclusion, diabetes led to a time-dependent increase in ouabain-sensitive Na(+), K(+)-ATPase activity. The main mechanism involved in this activation is the release of TxA(2)/PGH(2) by COX-2 in smooth muscle cells, linked to activation of the PKC pathway. (C) 2010 Elsevier Inc. All rights reserved.

On ""Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field""

Recently the paper ""Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field"" by G. C. Nayak was published [Eur. Phys. J. C 59: 715, 2009; arXiv:0708.2430]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the socalled ""shift theorem""[arXiv:hep-th/0609192] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.

Labile Plasma Iron Generation After Intravenous Iron is Time-dependent and Transitory in Patients Undergoing Chronic Hemodialysis

Iron supplementation in hemodialysis patients is fundamental to erythropoiesis, but may cause harmful effects. We measured oxidative stress using labile plasma iron (LPI) after parenteral iron replacement in chronic hemodialysis patients. Intravenous iron saccharate (100 mg) was administered in patients undergoing chronic hemodialysis (N = 20). LPI was measured by an oxidant-sensitive fluorescent probe at the beginning of dialysis session (T0), at 10 min (T1), 20 min (T2), and 30 min (T3) after the infusion of iron and at the subsequent session; P < 0.05 was significant. The LPI values were significantly raised according to the time of administration and were transitory: -0.02 +/- 0.20 mu mol/L at the beginning of the first session, 0.01 +/- 0.26 mu mol/L at T0, 0.03 +/- 0.23 mu mol/L at T1, 0.09 +/- 0.28 mmol/L at T2, 0.18 +/- 0.52 mmol/L at T3, and -0.02 +/- 0.16 mmol/L (P = 0.001 to 0.041) at the beginning of the second session. The LPI level in patients without iron supplementation was -0.06 +/- 0.16 mmol/L. Correlations of LPI according to time were T1, T2, and T3 vs. serum iron (P = 0.01, P = 0.007, and P = 0.0025, respectively), and T2 and T3 vs. transferrin saturation (P = 0.001 and P = 0.0003, respectively). LPI generation after intravenous saccharate administration is time-dependent and transitorily detected during hemodialysis. The LPI increment had a positive correlation to iron and transferrin saturation.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Melatonin and the time window for the expression of the alpha 8 nicotinic acetylcholine receptor in the membrane of chick retinal cells in culture

We have previously shown that melatonin influences the development of alpha 8 nicotinic acetylcholine receptor (nAChR) by measurement of the acetylcholine-induced increase in the extracellular acidification rate (ECAR) in chick retinal cell cultures. Cellular differentiation that takes place between DIV (days in vitro) 4 and DIV 5 yields cells expressing alpha 8 nAChR and results in a significant increase in the ECAR acetylcholine-induced. Blocking melatonin receptors with luzindole for 48 h suppresses the development of functional alpha 8 nAChR. Here we investigated the time window for the effect of melatonin on retinal cell development in culture, and whether this effect was dependent on an increase in the expression of alpha 8 nAChR. First, we confirmed that luzindole was inhibiting the effects of endogenous melatonin, since it increases 2-[(125)I] iodomelatonin (23 pM) binding sites density in a time-dependent manner. Then we observed that acute (15, 60 min, or 12 h) luzindole treatment did not impair acetylcholine-induced increase in the ECAR mediated by activation of alpha 8 nAChR at DIV 5, while chronic treatment (from DIV 3 or DIV 4 till DIV 5, or DIV 3.5 till DIV 4.5) led to a time-dependent reduction of the increase in the acetylcholine-induced ECAR. The binding parameters for [(125)I]-alpha-bungarotoxin (10 nM) sites in membrane were unaffected by melatonin suppression that started at DIV 3. Thus, melatonin surges in the time window that occurs at the final stages of chick retinal cell differentiation in culture is essential for development of the cells expressing alpha 8 nAChR subtype in full functional form. (C) 2010 ISDN. Published by Elsevier Ltd. All rights reserved.

Hydrogen peroxide is a novel mediator of inflammatory hyperalgesia, acting via transient receptor potential vanilloid 1-dependent and independent mechanisms

Inflammatory diseases associated with pain are often difficult to treat in the clinic due to insufficient understanding of the nociceptive pathways involved. Recently, there has been considerable interest in the role of reactive oxygen species (ROS) in inflammatory disease, but little is known of the role of hydrogen peroxide (H(2)O(2)) in hyperalgesia. In the present study, intraplantar injection of H(2)O(2)-induced a significant dose- and time-dependent mechanical and thermal hyperalgesia in the mouse hind paw, with increased c-fos activity observed in the dorsal horn of the spinal cord. H(2)O(2) also induced significant nociceptive behavior Such as increased paw licking and decreased body liftings. H(2)O(2) levels were significantly raised in the carrageenan-induced hind paw inflammation model, showing that this ROS is produced endogenously in a model of inflammation. Moreover, superoxide dismutase and catalase significantly reduced carrageenan-induced mechanical and thermal hyperalgesia, providing evidence of a functionally significant endogenous role. Thermal, but not mechanical, hyperalgesia in response to H(2)O(2) (i.pl.) Was longer lasting in TRPV1 wild type mice compared to TRPV1 knockouts. It is unlikely that downstream lipid peroxidation was increased by H(2)O(2). In conclusion, we demonstrate a notable effect of H(2)O(2) in mediating inflammatory hyperalgesia, thus highlighting H(2)O(2) removal as a novel therapeutic target for anti-hyperalgesic drugs in the clinic. (C) 2008 International Association for the Study of Pain. Published by Elsevier B.V. All rights reserved.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Velocity-dependent KAM islands

We revisit the non-dissipative time-dependent annular billiard and we consider the chaotic dynamics in two planes of conjugate variables in order to describe the behavior of the growth, or saturation, of the mean velocity of an ensemble of particles. We observed that the changes in the 4-d phase space occur without changing any parameter. They occur depending on where the initial conditions start. The emerging KAM islands interfere in the behavior of the particle dynamics especially in the Fermi acceleration mechanism. We show that Fermi acceleration can be suppressed, without dissipation, even considering the non-dissipative energy context. (C) 2011 Published by Elsevier Ltd.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.