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

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

Orbits and phase transitions in the multifractal spectrum

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

Einfluss der Aufschlusstemperatur auf die morphologischen Eigenschaften von TMP aus Kiefernholz

Chips from pine wood were subjected to thermomechanical pulping (TMP) at 140 and 180 degrees C for 5 minutes, whereas the cooked chips were defibrated using a single disk pressurized refiner at the same temperatures (140 and 180 degrees C). The fibres were tested for some of their morphological properties including fibre length, fibre width, cell-wall thickness. Moreover, the fine fibre fraction (zero fibres) and the content of splinters were also estimated. The results reveal, that increasing the temperature during thermomechanical pulping decreases the fibre length, the cell width and the fibre wall thickness. It also increases the amount of fine fibres and increases the curl factor

Post-entrapment modification of volatiles and oxygen fugacity in olivine-hosted melt inclusions

The solubilities of volatiles (H_2O, CO_2, S, F, and Cl) in basaltic melts are dependent on variables such as temperature, pressure, melt composition, and redox state. Accordingly, volatile concentrations can change dramatically during the various stages of a magma's existence: from generation, to ascent through the mantle and crust, to final eruption at the Earth's surface. Olivine-hosted melt inclusions have the potential to preserve volatile concentrations at the time of entrapment due to the protection afforded by the host olivine against decompression and changes to the oxidation state of the external magma. Recent studies, however, have demonstrated that rapid diffusive re-equilibration of H_2O and oxygen fugacity (f_(O_2)) can occur within olivine-hosted melt inclusions. Here we present volatile, hydrogen isotope, and major element data from dehydration experiments and a quantitative model that assesses proposed mechanisms for diffusive re-equilibration of H_2O and f_(O_2) in olivine-hosted melt inclusions. Our comprehensive set of data for the behavior of common magmatic volatiles (H_2O, CO_2, F, Cl, and S) demonstrates that post-entrapment modification of CO_2, and to a lesser extent S, can also occur. We show that the CO_2 and S concentrations within an included melt decrease with progressive diffusive H_2O loss, and propose that this occurs due to dehydration-induced changes to the internal pressure of the inclusion. Therefore, deriving accurate estimates for pre-eruptive CO_2 and S concentrations from olivine-hosted melt inclusions requires accounting for the amount of CO_2 and S hosted in vapor bubbles. We find, however, that Cl and F concentrations in olivine-hosted melt inclusions are not affected by diffusive re-equilibration through the host olivine nor by dehydration-induced pressure changes within the melt inclusion. Our results indicate that measured H_2O, CO_2 and S concentrations and Fe^(3+)/ΣFe ratios of included melts are not necessarily representative of the melt at the time of entrapment and thus are not reliable proxies for upper mantle conditions

Melt segregation and depletion during ascent of buoyant diapirs in subduction zones

Author Posting. © American Geophysical Union, 2020. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Solid Earth 125(2), (2020): e2019JB018203, doi:10.1029/2019JB018203.Cold, low‐density diapirs arising from hydrated mantle and/or subducted sediments on the top of subducting slabs have been invoked to transport key chemical signatures to the source region of arc magmas. However, to date there have been few quantitative models to constrain melting in such diapirs. Here we use a two‐phase Darcy‐Stokes‐energy model to investigate thermal evolution, melting, and depletion in a buoyant sediment diapir ascending through the mantle wedge. Using a simplified 2‐D circular geometry, we investigate diapir evolution in three scenarios with increasing complexity. In the first two scenarios we consider instantaneous heating of a diapir by thermal diffusion with and without the effect of the latent heat of melting. Then, these simplified calculations are compared to numerical simulations that include melting, melt segregation, and the influence of depletion on the sediment solidus along pressure‐temperature‐time (P ‐T ‐t ) paths appropriate for ascent through the mantle wedge. The high boundary temperature induces a rim of high porosity, into which new melts are focused and then migrate upward. The rim thus acts like an annulus melt channel, while the effect of depletion buffers additional melt production. Solid matrix flow combined with recrystallization of melt pooled near the top of the diapir can result in large gradients in depletion across the diapir. These large depletion gradients can either be preserved if the diapir leaks melt during ascent, or rehomogenized in a sealed diapir. Overall our numerical simulations predict less melt production than the simplified thermal diffusion calculations. Specifically, we show that diapirs whose ascent paths favor melting beneath the volcanic arc will undergo no more than ~40–50% total melting.We thank careful reviews by Juliane Dannberg, Harro Schmeling, and Bernhard steinberger. This work is supported by NSF‐1316333 (MB & NZ), NSF‐1551023 (MB), NSF‐1316310 (CK), and by China's Thousand Talents Plan (2015) and NSFC‐41674098 funding to NZ. The public data repository of Deal.ii (www.dealii.org) is thanked for distributing the software and examples that are used in this study. Computational work was conducted in High‐performance Computing Platform of Peking University, Kenny cluster of WHOI, and Pawsey Supercomputing Centre of Western Australia. We thank Timo Heister and Juliane Dannberg for deal.II technical assistance. The data of mantle wedge thermal structure and diapir trajectories, and the source code to compute the model results are available in the Mendeley data (http://dx.doi.org/10.17632/73n8zkc68s.1).2020-07-3

Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

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

Experimental investigation of insolation-driven dust ejection from Mars’ CO2 ice caps

Mars’ polar caps are – depending on hemisphere and season - partially or totally covered with CO2 ice. Icy surfaces such as the polar caps of Mars behave differently from surfaces covered with rock and soil when they are irradiated by solar light. The latter absorb and reflect incoming solar radiation within a thin layer beneath the surface. In contrast, ices are partially transparent in the visible spectral range and opaque in the infrared. Due to this fact, the solar radiation can penetrate to a certain depth and raise the temperature of the ice or dust below the surface. This may play an important role in the energy balance of icy surfaces in the solar system, as already noted in previous investigations. We investigated the temperature profiles inside CO2 ice samples including a dust layer under Martian conditions. We have been able to trigger dust eruptions, but also demonstrated that these require a very narrow range of temperature and ambient pressure. We discuss possible implications for the understanding of phenomena such as arachneiform patterns or fan shaped deposits as observed in Mars’ southern polar region

Randomly Evolving Idiotypic Networks: Modular Mean Field Theory

We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular architectures, the building principles of which are known. The nodes of the network can be classified into groups of nodes, the modules, which share statistical properties. Each node experiences only the mean influence of the groups to which it is linked. Given the size of the groups and linking between them the statistical properties such as mean occupation, mean life time, and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations. For a pattern which consists of pairs of occupied nodes correlations are taken into account.Comment: 14 pages, 8 figures, 4 table