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

Thermal-mechanical behavior of oceanic transform faults : implications for the spatial distribution of seismicity

Author Posting. © American Geophysical Union, 2010. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 11 (2010): Q07001, doi:10.1029/2010GC003034.To investigate the spatial distribution of earthquakes along oceanic transform faults, we utilize a 3-D finite element model to calculate the mantle flow field and temperature structure associated with a ridge-transform-ridge system. The model incorporates a viscoplastic rheology to simulate brittle failure in the lithosphere and a non-Newtonian temperature-dependent viscous flow law in the underlying mantle. We consider the effects of three key thermal and rheological feedbacks: (1) frictional weakening due to mantle alteration, (2) shear heating, and (3) hydrothermal circulation in the shallow lithosphere. Of these effects, the thermal structure is most strongly influenced by hydrothermal cooling. We quantify the thermally controlled seismogenic area for a range of fault parameters, including slip rate and fault length, and find that the area between the 350°C and 600°C isotherms (analogous to the zone of seismic slip) is nearly identical to that predicted from a half-space cooling model. However, in contrast to the half-space cooling model, we find that the depth to the 600°C isotherm and the width of the seismogenic zone are nearly constant along the fault, consistent with seismic observations. The calculated temperature structure and zone of permeable fluid flow are also used to approximate the stability field of hydrous phases in the upper mantle. We find that for slow slipping faults, the potential zone of hydrous alteration extends greater than 10 km in depth, suggesting that transform faults serve as a significant pathway for water to enter the oceanic upper mantle.The material presented here is based on work supported by the National Science Foundation Division of Ocean Sciences (OCE) grants 0623188 (M.B. and G.H.) and 0649103 (M.B.) and Division of Earth Sciences (EAR) grant 0814513 (G.H.)

Modes of extensional faulting controlled by surface processes

We investigate the feedbacks between surface processes and tectonics in an extensional setting by coupling a 2-D geodynamical model with a landscape evolution law. Focusing on the evolution of a single normal fault, we show that surface processes significantly enhance the amount of horizontal extension a fault can accommodate before being abandoned in favor of a new fault. In simulations with very slow erosion rates, a 15 km thick brittle layer extends via a succession of crosscutting short-lived faults (heave 10 km). Using simple scaling arguments, we quantify the effect of surface mass removal on the force balance acting on a growing normal fault. This leads us to propose that the major range-bounding normal faults observed in many continental rifts owe their large offsets to erosional and depositional processes

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

Discontinued SEC Required Disclosures: the Value of Repairs and Maintenance Expenditures using a Variance Decomposition Approach

On December 13, 1994, the Securities and Exchange Commission (SEC) eliminated certain schedules that included repairs and maintenance (R&M) disclosures previously required in annual reports and registration statements filed with the SEC. The purpose of this research is to determine if market participants utilized R&M information when making investment decisions. Resulting from a variance decomposition approach, the findings indicate that market participants did use R&M disclosures in their investment decisions. Thus, as a possible policy implication of this research, the SEC may want to reconsider the decision to eliminate the required R&M expenditure disclosures