Classical evolution of fractal measures generated by a scalar field on the lattice

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution.Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys.

Kink-Antikink Interaction Forces and Bound States in a nonlinear Schr{\"o}dinger Model with Quadratic and Quartic dispersion

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{\"o}dinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a ``lower branch'' adhering to the energy landscape of the 2-kink states. We also, however, study in detail the ``upper branches'' bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics

Kink-Antikink Interaction Forces and Bound States in a φ\u3csup\u3e4\u3c/sup\u3e Model with Quadratic and Quartic dispersion

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schrödinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a “lower branch” adhering to the energy landscape of the 2-kink states. We also, however, study in detail the “upper branches” bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics

Classical evolution of fractal measures on the lattice

We consider the classical evolution of a lattice of non-linear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular we show that traces of the critical fractal measure can sustain for large times and we extract the properties of the chain which determine the associated time-scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges in time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry broken phase.Comment: 15 pages, 15 figures, version publiced at Physical Review

Mixed dispersion nonlinear Schrödinger equation in higher dimensions: Theoretical analysis and numerical computations

In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schrödinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension d = 2, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent p, there exists a progressively narrowing range of stable frequencies. Finally, above the critical p all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor b and nonlinearity power p

Long-term clinical outcome of HBeAg-negative chronic hepatitis B patients who discontinued nucleos(t)ide analogues

Background & Aims: Discontinuation of nucleos(t)ide analogues (NA) remains a debatable issue in HBeAg-negative chronic hepatitis B (CHB). This study aimed to address the outcome of HBeAg-negative CHB patients who discontinued NA therapy. Methods: This prospective study included 57 non-cirrhotic HBeAg-negative Caucasian CHB patients who discontinued NA therapy after median virological remission of 6 years. All patients had regular blood tests. Virological relapse was defined as HBV DNA > 2000 IU/mL or >20 000 IU/mL and biochemical relapse as ALT > ULN (40 IU/mL) or >2xULN. All patients with retreatment predefined criteria restarted entecavir or tenofovir. Results: Of the 57 patients, 29 remained without retreatment after median follow-up of 65 months (range: 36-87) following treatment discontinuation. At 3, 6, 12, 24, 36 and 48 months, cumulative rates of retreatment were 16%, 20%, 32%, 35%, 46% and 50%, while the proportion of patients with HBV DNA < 2000 IU/mL and ALT < ULN were 73%, 60%, 52%, 52%, 47% and 37% respectively. All patients had virological and biochemical response after retreatment. No patient developed liver failure, hepatocellular carcinoma or death. Cumulative rates of HBsAg loss were 2%, 4%, 7%, 10% and 20% at 3, 6, 12, 24 and 36 months. HBsAg levels < 100 IU/mL at the end of NA treatment could predict HBsAg loss (P =.001). Conclusions: Our study supports that NA therapy can be safely stopped in non-cirrhotic patients with HBeAg-negative CHB. Over a median follow-up of more than 5 years, half of the patients remained without retreatment with a substantial proportion of them achieving functional cure. © 2020 John Wiley & Sons A/S. Published by John Wiley & Sons Lt

Natural history of grade 1 ascites in patients with liver cirrhosis

Background No evidence is available on the natural history of grade 1 ascites and its progression to grade 2/3 in patients with liver cirrhosis. The aim of the current study was to address this issue, to assess the development of main comorbid disorders closely related to ascites progression, and to identify the predictive factors for survival in this setting. Methods Consecutive Caucasian cirrhotic patients with grade 1 ascites were retrospectively analyzed. None of patients was under treatment with diuretics at diagnosis. Control groups consisted of 145 cirrhotics with grade 2/3 ascites and 175 cirrhotics without ascites. Results Diuretics were initiated in 58 patients with grade 1 ascites at baseline by the attending physician. At the last follow up, 29 patients had no ascites, 33 patients had grade 1 and 38 patients had grade 2/3 ascites. No variable was found to be an independent predictor of grade 2/3 ascites. Seven patients developed spontaneous bacterial peritonitis while under treatment with diuretics; at that time only 1 patient had grade 1 ascites. The mortality rate was similar among all examined groups. Conclusions This study suggests that the presence of grade 1 ascites does not constitute a precursor of grade 2/3 ascites in patients with cirrhosis. Thus, patients with grade 1 ascites do not require specific treatment with diuretics. © 2021 Hellenic Society of Gastroenterology