Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model

The evolution of the structure factor is studied during the phase-ordering dynamics of the kinetic Ising model with conserved order parameter. A preasymptotic multiscaling regime is found as in the solution of the Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is always approached through a crossover from multiscaling to standard scaling, independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let

Non trivial behavior of the linear response function in phase ordering kinetics

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent $a_{\chi}$ which leads to failure of the connection between static and dynamic properties at the lower dimensionality $d_L$, where $a_{\chi}=0$. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.Comment: 10 pages, 2 figures. Contribution to the International Conference "Perspectives on Quantum Field Theory, Statistical Mechanics and Stochastics" in honour of the 60th birthday of Francesco Guerr

Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi$ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures

Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below TCT_C

In order to check on a recent suggestion that local scale invariance [M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to $T_C$ in $d=4$, where Gaussian behavior is expected to apply, and in the two other cases of the $d=2$ model quenched to $T_C$ and to below $T_C$, where instead deviations from Gaussian behavior are expected to appear. We find that in the $d=4$ case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the $d=2$ cases, both in the quench to $T_C$ and to below $T_C$, sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain $a=0.27 \pm 0.002$ for the scaling exponent of the response function in the $d=2$ Ising model quenched to below $T_C$, in agreement with previous results.Comment: 24 pages, 6 figures. Resubmitted version with improved discussions and figure

Set of Boundary Conditions for Aerodynamic Design

Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be nonreflecting, to avoid spurious perturbations that can provocate unsteadiness or instabilities. The reflectiveness of various boundary conditions is analyzed in the context of the Godunov methods. A nonlinear, isentropic wave propagation model is used to investigate the reflection mechanism on the flowfield borders, and a parameter τ is defined to give a measure of the boundary reflectiveness. A new set of boundary conditions, in which τ =0, that is, totally nonreflecting, is then proposed. The approach has been integrated in an aerodynamic design procedure using a distributed boundary control

Scaling Behavior of Response Functions in the Coarsening Dynamics of Disordered Ferromagnets

We study coarsening dynamics in the ferromagnetic random bond Ising model in d = 1; 2. We focus on the validity of super-universality and the scaling properties of the response functions. In the d = 1 case, we obtain a complete understanding of the evolution, from pre- asymptotic to asymptotic behavior. The corresponding response function shows a clear violation of super-universality. Further, our results for d = 1; 2 settle the controversy regarding the decay exponent which characterizes the response function

Fluctuation-Dissipation relations far from Equilibrium

In this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo-Kurchan \cite{Cugliandolo93} fluctuation dissipation relation for aging systems and the theorem by Franz {\it et. al.} \cite{Franz98} relating static and dynamic properties. We than specialize the subject to phase-ordering systems examining the scaling properties of the linear response function and how these are determined by the behavior of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or as due to stochastic instability.Comment: 18 pages, 10 figure

Slow relaxation in the large N model for phase ordering

The basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large $N$ model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function $\chi_{ag}(t,t_w)$ is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality $(d=4)$ above which $\chi_{ag}(t,t_w)$ is proportional to the defect density $\rho_D(t)$, while for $d<4$ it vanishes more slowly than $\rho_D(t)$ and at $d=2$ does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect.Comment: 27 pages, 4 figures, accepted for publication on Phys.Rev.

Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems

The relationship between statics and dynamics proposed by Franz, Mezard, Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81}, 1758 (1998)] is investigated in the framework of non disordered coarsening systems. Separating the bulk from interface response we find that for statics to be retrievable from dynamics the interface contribution must be asymptotically negligible. How fast this happens depends on dimensionality. There exists a critical dimensionality above which the interface response vanishes like the interface density and below which it vanishes more slowly. At $d=1$ the interface response does not vanish leading to the violation of the FMPP scheme. This behavior is explained in terms of the competition between curvature driven and field driven interface motion.Comment: 11 pages, 3 figures. Significantly improved version of the paper with new results, new numerical simulations and new figure

In vitro and in vivo evaluation of In-111-DTPAGlu-G-CCK8 for cholecystokinin-B receptor imaging

Regulatory peptides and their analogs are being extensively investigated as radiopharmaceuticals for cancer imaging and therapy. Receptors of the cholecystokinin family have been shown to be overexpressed in different types of neuroendocrine tumors. The purposes of this study were to evaluate the cholecystokinin octapeptide amide (CCK8) peptide tagged with a diethylenetriaminepentaacetic acid derivative (DTPAGlu) and to test whether a 111In-labeled conjugate (111In-DTPAGlu-G-CCK8, a derivative containing the chelating agent DTPAGlu bound through a glycine linker at the N-terminal end of the bioactive peptide CCK8) is suitable for cholecystokinin-B receptor (CCKBR) imaging. Methods: CCK8 was synthesized by solidphase techniques and covalently coupled to DTPAGlu through a glycine linker at its amino terminus. The compound was labeled with 111In. The radiochemical purity and stability of the compound were assessed by chromatographic methods. NIH-3T3 and A431 cells overexpressing CCKBR were used to characterize the in vitro properties of the compound. Nude mice bearing control and CCKBR-overexpressing A431 xenografts were used as an in vivo model. Results: DTPAGlu-G-CCK8 showed rapid and efficient labeling with 111In. The radiolabeled conjugate showed specific binding to both cell lines overexpressing CCKBR. Binding was saturable, with a dissociation constant of 20 nmol/L in both cell systems. Both cell lines showed internalization of the ligand after interaction with the receptor. Biodistribution studies showed rapid localization of 111In-DTPAGlu- G-CCK8 on CCKBR-overexpressing A431 xenografts that was severalfold higher than that on control tumors at all time points tested. Unbound activity showed rapid clearance of over 80% through the kidneys by 30 min after injection. The labeled peptide conjugate was very stable in serum but showed a rapid breakdown after injection. Incubation with kidney homogenates suggested that most breakdown occurred in the kidneys, favoring the clearance of unbound activity. Conclusion: Our findings indicate that the in vitro and in vivo characteristics of 111In-DTPAGlu-G-CCK8 are favorable for CCKBR imaging, as thepeptide shows high-affinity binding to the receptor, is internalized in CCKBR-expressing cells, and shows avid uptake in CCKBR-overexpressing xenografts, with rapid clearance of unbound radioactivity through the kidneys. Furthermore, the ease of synthesis, high labeling efficiency, and chemical stability of DTPAGlu make this chelating moiety an ideal candidate for widespread use in peptide radiolabeling for nuclear medicine applications