624 research outputs found

    Convolution of multifractals and the local magnetization in a random field Ising chain

    Full text link
    The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifractals. In this paper we prove relations between the multifractal properties of two measures and the multifractal properties of their convolution. The pointwise dimension at the boundary of the support of the convolution is the sum of the pointwise dimensions at the boundary of the support of the convoluted measures and the generalized box dimensions of the convolution are bounded from above by the sum of the generalized box dimensions of the convoluted measures. The generalized box dimensions of the convolution of Cantor sets with weights can be calculated analytically for certain parameter ranges and illustrate effects we also encounter in the case of the measure of the local magnetization. Returning to the study of this measure we apply the general inequalities and present numerical approximations of the D_q-spectrum. For the first time we are able to obtain results on multifractal properties of a physical quantity in the one-dimensional random-field Ising model which in principle could be measured experimentally. The numerically generated probability densities for the local magnetization show impressively the gradual transition from a monomodal to a bimodal distribution for growing random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the introduction and the conclusions, some typos were corrected, 24 pages, LaTeX2e, 9 figure

    The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory

    Full text link
    We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field theory. A novel type of first order phase transition related to spontaneous symmetry breaking and dynamic freezing is found. The non-equilibrium stationary state has a complex structure, which changes as a function of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one.Comment: 12 pages REVTeX/LaTeX format, 12 eps/ps figures. Submitted to Journal of Physics

    Orbits and phase transitions in the multifractal spectrum

    Full text link
    We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective field exhibits a sharp drop of all D_q with q < 0 at some critical strength of the random field. We introduce the concept of orbits which naturally group the points of the support of the invariant measure. We then show that the pointwise dimension at all points of an orbit has the same value and calculate it for a class of periodic orbits and their so-called offshoots as well as for generic orbits in the non-overlapping case. The sharp drop in the D_q-spectrum is analytically explained by a drastic change of the scaling properties of the measure near the points of a certain periodic orbit at a critical strength of the random field which is explicitly given. A similar drastic change near the points of a special family of periodic orbits explains a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a decisive role in this mechanism is played by a specific offshoot. We furthermore give rigorous upper and/or lower bounds on all D_q in a wide parameter range. In most cases the numerically obtained D_q coincide with either the upper or the lower bound. The results in this paper are relevant for the understanding of random iterated function systems in the case of moderate overlap in which periodic orbits with weak singularity can play a decisive role.Comment: The article has been completely rewritten; the title has changed; a section about the typical pointwise dimension as well as several references and remarks about more general systems have been added; to appear in J. Phys. A; 25 pages, 11 figures, LaTeX2

    Adjustment with aphasia after stroke: study protocol for a pilot feasibility randomised controlled trial for SUpporting wellbeing through PEeR Befriending (SUPERB)

    Get PDF
    Background: Despite the high prevalence of mood problems after stroke, evidence on effective interventions particularly for those with aphasia is limited. There is a pressing need to systematically evaluate interventions aiming to improve wellbeing for people with stroke and aphasia. This study aims to evaluate the feasibility of a peer-befriending intervention. Methods/design: SUPERB is a single blind, parallel group feasibility trial of peer befriending for people with aphasia post-stroke and low levels of psychological distress. The trial includes a nested qualitative study and pilot economic evaluation and it compares usual care (n = 30) with usual care + peer befriending (n = 30). Feasibility outcomes include proportion screened who meet criteria, proportion who consent, rate of consent, number of missing/incomplete data on outcome measures, attrition rate at follow-up, potential value of conducting main trial using value of information analysis (economic evaluation), description of usual care, and treatment fidelity of peer befriending. Assessments and outcome measures (mood, wellbeing, communication, and social participation) for participants and significant others will be administered at baseline, with outcome measures re-administered at 4 and 10 months post-randomisation. Peer befrienders will complete outcome measures before training and after they have completed two cycles of befriending. The qualitative study will use semi-structured interviews of purposively sampled participants (n = 20) and significant others (n = 10) from both arms of the trial, and all peer befrienders to explore the acceptability of procedures and experiences of care. The pilot economic evaluation will utilise the European Quality of life measure (EQ-5D-5 L) and a stroke-adapted version of the Client Service Receipt Inventory (CSRI). Discussion: This study will provide information on feasibility outcomes and an initial indication of whether peer befriending is a suitable intervention to explore further in a definitive phase III randomised controlled trial. Trial registration: ClinicalTrials.gov identifier NCT02947776, registered 28th October 2016

    Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

    Full text link
    We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table
    • …
    corecore