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This is a digest of how various researchers in biology and astrobiology have explored questions of what defines living organisms-definitions based on functions or structures observed in organisms, or on systems terms, or on mathematical conceptions like closure, chirality, quantum mechanics and thermodynamics, or on biosemiotics, or on Darwinian evolution-to clarify the field and make it easier for endeavors in artificial intelligence to make progress. Current ideas are described to promote work between astrobiologists and computer scientists, each concerned with living organisms. A four-parameter framework is presented as a scaffold that is later developed into what machines lack to be considered alive: systems, evolution, energy and consciousness, and includes Jagers operators and the idea of dual closure. A novel definition of consciousness is developed which describes mental objects both with and without communicable properties, and this helps to clarify how consciousness in machines may be studied as an emergent process related to choice functions in systems. A perspective on how quantization, acting on nucleic acids, sets up natural limits to system behavior is offered as a partial address to the problem of biogenesis.

Background The prevalence of inflammatory bowel diseases (IBD) is high in women of childbearing age. Maintaining remission from conception to delivery is associated with improved pregnancy outcomes, and continued drug therapy throughout pregnancy is often needed. Data regarding pregnancy outcomes in patients with IBD treated with ustekinumab (UST) are limited. We aimed to assess maternal, pregnancy, and neonatal outcomes in patients with IBD treated with ustekinumab (UST). Methods In a multicenter, prospective, cohort study, women with IBD treated with UST during conception and pregnancy were recruited between 2019–2021. Outcomes were compared between patients treated with: UST, anti-tumor necrosis factor (TNF)-a, and non-UST,non anti-TNF therapy (thiopurines or mesalazine) or no therapy. UST treated patients were matched to controls in a 1:2 ratio according to age, BMI, and number of previous pregnancies. Newborns were followed up-to 12 months. Results Pregnant patients recruited: 129, 27-UST; 52- anti-TNF; 30-non-UST, non anti-TNF 20- no therapy (the latter 50=conventional control group). The vast majority (96.9%) had Crohn’s disease (CD). Patients treated with UST compared to those treated with anti-TNF or conventional therapy, showed a trend towards longer disease duration (11 vs 7 vs 6 years, respectively, p=0.06), higher proportion of smokers (30.8% vs 5.9% vs 0%, respectively, p Among UST-treated patients, pregnancy outcomes included: two spontaneous abortions, 4% of of preterm labor and low birth weight, one congenital anomaly (tetralogy of Fallot) (4%), and 42% cesarean section. Maternal outcomes, specifically obstetric complications and hospitalizations, pregnancy, and neonatal outcomes were comparable between treatment groups. Rates of newborn 1st-year infections, hospitalizations, and developmental delay were also comparable. Conclusion Pregnant patients with IBD treated with UST comprise a highly refractory group, with high rates of disease activity at conception. Their pregnancy and neonatal outcomes were favorable, and comparable to those in patients treated with anti-TNF or conventional therapy.

This discussion assumes that there are ionospheric anomalies in total electron count (TEC) as precursors to major earthquakes. Very careful work by Thomas et al. (2017) and others remove TEC anomalies when correlated with natural events such as geomagnetic or solar activity. Without these data, correlation between ionospheric disturbances and large earthquakes (M ≥ 7.0) occurs infrequently (~20% of events) and is within the standard error resulting from the small sample size. There are two possibilities: (1) either the mechanism of volatile (including radon) release that occurs in some regions precursory to major seismic events is unrelated to ionospheric disturbances; or (2) the occurrence of these volatiles is related first to geomagnetic and solar activity. The first hypothesis is easily falsified. In addition to careful statistical analysis by Thomas et al. and others, the mechanism for travel through the lower atmosphere of matter arising on the ground as a stable electric signal is not physically plausible. The second hypothesis awaits falsification, as the correlation fits the data. If natural events such as geomagnetic and solar activity are a trigger for large earthquakes, a plausible mechanism ought to be explored. In considering the effects of ionospheric disturbances on ground-based phenomena, geomagnetically induced currents (GIC) are a reasonable model. GIC occur generally at high latitudes and are responsible for the electrocorrosion of bridges and other metal infrastructure. Fluids laden with dissolved ions occur in faults and are a potential conduit for GIC. Electromagnetic fields induced by ionospheric anomalies may be present at depth. Can these types of fields weaken earth materials? One reason dilatancy diffusion models fell out of favor is scale. The microcracks observed are too small to hold the volume of volatiles required to account for observed changes to groundwater. If instead the presence of electric and magnetic fields aid in the liberation of volatiles and dissolution of certain minerals in rock, seismic events may occur. Andrén et al. (2016), for example, note decreasing groundwater (Si and Na) ion concentrations (ratio 2:1) as well as a small decrease in Ca and an increase in K ion concentrations during a period leading up to two consecutive M > 5 earthquakes in Hafralækur, Iceland. They took well cuttings for petrographic analysis: The observed groundwater changes are consistent with contemporary replacement of labradorite with analcime and the precipitation of zeolite minerals before and during the seismic activity, respectively, when the cuttings were taken. These observations fit the data well. In some cases, solar and geomagnetic activity cause ionospheric anomalies. These then induce electromagnetic currents in faults. The resulting fields aid in the dissolution of certain minerals and release volatiles, which are then precursory to seismic events. Groundwater changes before and after such events are related to the dissolution and subsequent precipitation of minerals in the rock. This rock weakening hypothesis fits the data, and is a simple explanation for how correlations between ionospheric disturbances caused by solar or geomagnetic events and large seismic events may arise.

The average atmospheric charge density of Earth is neutral. Charge built up from thunderstorms and lightning phenomena is offset by oceanic surface charging, and offers a source of energy that has not been harnessed broadly. Unfortunately, the total terrestrial energy of the Earth’s atmospheric electrical system is modest (250–500 MW) compared to industrial requirements: Innovations are likely to offer improvements to societal efficiency rather than broad transformations. Direct capture systems located in places with very high occurrence of lightning discharge can generate ≈1 kWh per year on average. Material processing via triggered lightning is limited to techniques that utilize rapid discharges, e.g., metal and glass preprocessing of materials, waste volume reduction, biomass energy conversion, where current prices make plasma‐arc processes prohibitive. Triggered lightning may be used to assist blasting of mountain rock; or as a high‐voltage input for processes such as nuclear fusion. Passive collection of atmospheric electricity is modest but may be used in urban agriculture to increase biomass production. Thunderstorm charge‐separation processes suggest a new class of electricity generators based on kinetic energy and material collision. Ball lightning suggests additional research in dusty plasmas. These methods are all at proof‐of‐concept or early translation stages., The article highlights several current techniques including passive energy harvesting systems and the use of supercapacitors, plus material processing, and applications for agriculture. The electrical potential from lightning phenomena does not offer sufficient energy for direct use even in locations with the highest lightning frequency, but passive capture may be of benefit, and lightning may be suitable for material processing.

Introduction: Caries experience among preschool-age children has remained relatively unchanged for the past 2 decades, despite recently documented decreases in untreated decay. Objectives: In a community-based cluster-randomized controlled trial, a motivational interviewing (MI) intervention administered to primary caregivers was hypothesized to reduce caries increment over 2 y as compared with controls, among children aged 0 to 5 y at baseline living in public housing. Methods: Public housing residents, who served as interventionists, were trained in MI with a focus on early childhood caries prevention. All 26 eligible public housing developments were randomized to either control (quarterly clinical examinations, fluoride varnish applications, toothbrush/toothpaste, and educational brochures) or intervention (same procedures as control plus MI counseling). Quarterly MI sessions were delivered in English or Spanish over 2 y, audio recorded, and assessed for treatment fidelity. The primary outcome was the increment in dmfs (decayed, missing, and filled tooth surfaces) as assessed by clinical examination at baseline, 12 mo, and 24 mo. Secondary outcomes included caregiver oral health knowledge and child oral health behaviors (child toothbrushing and sugar-sweetened beverage intake). Baseline characteristics were compared between groups and adjusted for housing-site clusters. Longitudinal outcomes were analyzed with mixed models. Results: A total of 1,065 children (49% female, 55% non-White, 61% Hispanic, 89% below poverty level, n = 686 control) and their caregivers were enrolled. During 2 y of follow-up, the mean dmfs increment increased in both groups; however, there were no statistically significant group differences at 24 mo or group × time interactions. The mean increase in intervention caregivers’ knowledge was significantly greater than that of control, F(2, 1,593) = 3.48, P = 0.0310, but there were no significant intervention effects on caregiver-reported child sugar-sweetened beverage intake or child toothbrushing. Conclusion: MI counseling plus intensive caries prevention activities resulted in knowledge increases but did not improve oral health behaviors or caries increment (ClinicalTrials.gov NCT01205971). Knowledge Transfer Statement: When viewed in light of the findings from the companion Pine Ridge study and other recent MI studies, the results of this study suggest that when the complex disease of early childhood caries is addressed in high-risk populations, MI is not effective, and alternative approaches are warranted.

Schizophrenia is a major mental illness with a disease course that is influenced by lifestyle. The risk-benefit ratio for alternative interventions is more favorable than for antipsychotics in long-term treatment. Dietary interventions may target autoimmune features, vitamin or mineral deficiencies, abnormal lipid metabolism, gluten sensitivity, or others. Examples of interventions involving diet, physical activity, or physical processes or social interventions including talk therapy exist in the literature. Notwithstanding, the general utility of these types of interventions remains inconclusive, awaiting long-term randomized trials. A perspective that separates the cause of the disease from its symptoms may be helpful in treatment planning and is warranted to distinguish between short-term and long-term recovery goals.

Medication- and symptom-free recovery has been the author’s experience since March 2006. Details of 127 potentially therapeutic lifestyle activities were explored using a structured reflective analysis. These activities were divided into twelve communities: family, arts, romance, etc. Perceived therapeutic effects are noted. Also included is the author’s method for weaning from psychiatric medication very slowly, plus personal details of success.

Review

Electromagnetic phenomena are sometimes associated with seismic events, but earthquake prediction using seismic electric signals (SES) has not been seriously considered since the early 1990s. There are several causes: (1) false alarms that have created panics in Greece, and (2) a strong critique of the Varotsos-Alexopoulos-Nomicos (VAN) method used there. An updated VAN method that includes time series analysis has made successful medium-range predictions, and short-range predictions when coupled with seismic time series analysis. Four types of potential mechanisms to create precursory SES relying on deformation effects, temperature effects, ore-mineral movement or groundwater variation are reviewed. Data relevant to each are insufficient to favor a single mechanism. Records of the number of false positive and missed events for an updated VAN method have not been well maintained. False positives appear to be abundant and render the method unusable. Co-seismic groundwater fluctuations are addressed, and two novel hypotheses of earthquake trigger mechanism are also presented: ionospherically induced electric (and resultant magnetic) fields to weaken rock thereby causing failure; and volatiles liberated from minerals additionally promoting rock failure. Recommendations for further study are included.

OBJECTIVE Traditionally, amniocentesis is performed between 17 and 23 weeks of gestation. This enables decisions regarding the course of pregnancy to be made before viability. Less frequently, amniocentesis is performed in the third trimester. Advanced genomic technologies such as chromosomal microarray analysis (CMA) provide more detailed information about the fetus compared with traditional G-banded chromosomal analysis. The aim of this study was to assess the indications for and safety of late amniocentesis, genetic-test results (especially in the context of CMA technology) and outcome of pregnancies that underwent the procedure after 24 weeks. METHODS Medical records were analyzed retrospectively of all women in whom amniocentesis was performed at a gestational age of 24 + 0 to 38 + 6 weeks, at Hadassah Medical Center, between June 2013 and March 2017. Parameters investigated included indications for late amniocentesis, complications, CMA results and pregnancy outcome. RESULTS During the study period, 291 women (303 fetuses, 277 singleton and 14 twin pregnancies; in two twin pairs, one fetus was terminated before amniocentesis) underwent late amniocentesis. CMA was performed in all instances of amniocentesis. The most frequent indication was abnormal sonographic finding(s) (204/303 fetuses, 67%). Preterm delivery occurred in 1.7% and 5.1% of pregnancies within the first week and within 1 month following the procedure, respectively. Aneuploidy was detected in nine (3%) fetuses and nine (3%) others had a pathogenic/likely pathogenic copy number variant, suggesting that CMA doubled the diagnostic yield of traditional karyotyping. Maximal diagnostic yield (17.5%) was achieved for the subgroup of fetuses referred with abnormal sonographic findings in two or more fetal anatomical systems. Variants of uncertain significance or susceptibility loci were found in another nine (3%) fetuses. CONCLUSIONS In pregnancies undergoing late amniocentesis, CMA increased detection rates of fetal abnormalities and had a shorter turnaround time compared with traditional chromosomal analysis; therefore, late amniocentesis may serve as a helpful tool for detecting fetal abnormalities or reassuring parents following late-appearing abnormal sonographic findings. However, CMA may expose findings of uncertain significance, about which the couple should be precounseled. The procedure appears to be safe. Copyright © 2018 ISUOG. Published by John Wiley & Sons Ltd.

Supplemental material, DS_10.1177_2380084418794377 for Randomized Trial of Motivational Interviewing to Prevent Early Childhood Caries in Public Housing by M.M. Henshaw, B. Borrelli, S.E. Gregorich, B. Heaton, E.M. Tooley, W. Santo, N.F. Cheng, M. Rasmussen, S. Helman, S. Shain and R.I. Garcia in JDR Clinical & Translational Research

Conceptualizing planetary habitability depends on understanding how living organisms originated and what features of environments are essential to foster abiogenesis. Estimates of the abundance of life's building blocks are confounded by incomplete knowledge of the role of chirality and racemization in organic compounds in the origination of living organisms. Chirality is an essential feature of enzymes as well as many lock-and-key type structures. There are four known processes that can act on complex organic molecules to promote racemization for abiogenesis: quantum-tunneling effects; selection via interaction with circularly polarized light (CPL); templating processes; and interactions with electrical and magnetic (EM) fields. These occur in different places, respectively: cold interstellar space; regions of space with energetic photons, dust and/or magnetic fields; and mineral surfaces (for both templating and EM fields). Chirality as a feature of terrestrial life suggests neither a special place for local development of homochirality nor for extra-terrestrial enrichment and delivery. The presence of these molecules in three competing scenarios for life's origin - chemical gardens, geothermal fields, and ice substrates - relies on a framework of hypothesis and estimation. An easily-modified worksheet is included in the supplemental material that allows a user to generate different scenarios and data related to the distribution of chiral organic molecules as building blocks for living organisms within the galaxy. A simple hypothetical mechanism for planetary magnetic field reversals, based on a high-density plasma inner core, is also presented as a means to aid in estimating field polarity and hence the orientation of racemization processes based on planetary magnetic fields., Originally written in consultation with Richard Gordon and Alexei Sharov who were putting together the Elsevier volume "Habitability of the Universe Before Earth."

The article reviews the current literature related to lightning and makes a case for using lightning as an alternative source of energy. Objections to using lightning as an alternative source of energy are listed. Current literature is reviewed and articles are suggested as useful for building a tower, or using rockets or lasers to target a strike, or for quantifying a lightning strike.

Stevenson, Susan K., Armleder, Harold M., Arsenauly, Andre, Coxson, Darwyn, Delong, S. Craig and Jull, Michael. British Columbia's Inland Rainforest: Ecology, Conservation, and Management. Vancouver, Canada: University of British Columbia Press, 2011. 456 pp. ISBN: 9780774818506, paperback. US$ 41.95, illustrated. Also available in hardcover format ISBN 9780774818490.A fact-filled and extremely useful offering from silvicultural and ecosystem professionals, biologists, ecologists, systems scientists and others, British Columbia's Inland Rainforest provides a snapshot, a look at the present conditions of this unique ecosystem in light of past and future management choices. Included are 128 figures, color plates and illustrations, 20 tables, three appendices, a species index, glossary and various exposes that highlight features of the text, which itself includes more than 50 sections detailing everything from carbon stocks to soil horizons to forest edge effects on plant and animal life to native medicine and many others. The book grew from a project with scientific goals-to supplement a government forestry report with data so that managers and other stakeholders could make well-informed choices. The authors made a wonderful choice to expand their scope and offer the work to the public.British Columbia's inland rainforest is unique. There is no other place on the planet where a temperate rainforest exists so far from the coast, with much of its biome determined by continental rather than coastal geography. For example, many of the species in the inland rainforest migrated from elsewhere in continental North America during the end of the last glaciation, or from the coast via specific vectors. They continue to survive in a setting that includes thousand-year-old red cedar trees and lichen species (e.g. cyanolichen) that are not found elsewhere or nowhere else in such great diversity and abundance. Snowmelt during the summer promotes groundwater abundance and a humidity level unrivaled in a continental forest setting.Here, ancient red cedar and western hemlock make unique rotted-out settings for fungus, bryophyte, lichen, vascular plants, invertebrates and vertebrate animals, dens in hollowed out trees for martens and black bears. Yet in human terms, the same trees providing the substrate for such a rich ecology have also driven management choices that have led to their destruction.Historically, such immense trees with internal voids are called "decadent" and forest management has opted to harvest these old landscapes to allow planting of young plantation stands that replace them, often with changes to species for a standardized harvest regime. Ironically, the work is done in winter when the marshy rainforest soil has frozen and ice roads or other means of transport can be constructed. …

Book Review

Most of us have special powers. When a child we care about is hurt and we are nearby, we can generally find something to say or do that will bring a smile (or sense of safety) to them. This can go so far as to take physical pain (eg, from a scraped elbow) and transform it so that it no longer hurts. We are all analgesics for those we love, to some extent. This is one of the fruits of adulthood. There are others, such as the ability not to notice when our bodies are falling apart. Perhaps this is not a special power! Maybe it is just that we are less sensitive to some things. And perhaps it is the case that the things we cannot change, we do not spend time on. Life does become more dear with age. Gratitude is not a gift of adulthood. It is something that children enjoy as well. Schizophrenia typically manifests during adolescence, in the period between childhood and adulthood, when hormonal and other changes are also transforming the person from who they were to who they dreamed of being. Those dreams are hard to realize for all of us, not just for the person with schizophrenia. Life and growth are a challenge! I am 44 years old at the time of this writing, autumn of 2013. My first psychotic episode was at age 20, in January of 1989. The last time I took any psychiatric medication was in March, 2006. Over the course of the illness, I was hospitalized 10 times, for a combined period of about 6 months. The period from January 2001 until my last dose of psychiatric medication I undertook a self-initiated protocol of weaning from the drugs, as slowly as one may imagine. I do not have symptoms which would classify me as having schizophrenia any more. I do not fear relapse, nor do I spend any time thinking about it. I have beat the diagnosis, and recovered. In truth, I did have special powers. I still do, as do we all. But I also had a few effects which were difficult to manage. Imagine that a person wishes to move their shoulder. They can think about moving their shoulder, and they can consciously move it—and that might be termed agency. We all have agency with our bodies. I can move my shoulder as much as I like. This is not distressing. Much more distressing is the sense that one has some agency for things outside one’s body. Not that there is not something to this. I have been known to try hard to make someone smile, or otherwise affect the world by my actions. But this is much more distressing when the sense of agency and ability to transform the world hinges on one’s thoughts. This was a major symptom of schizophrenia that I had. There is nothing wrong with odd conditions so long as they do not interfere with one’s life. For the shaman or social worker who can successfully transform the world, God bless them. What makes the thing an illness is when it interferes. Other symptoms I had were

Book Review

A magnetic plane, exchange coupled to an electron gas, generates a spin polarization and in the nonlinear theory also a charge distribution. The corresponding electrostatic energy per unit surface is evaluated. For an electron gas at metallic densities this turns out to be negligible, while it must be taken into account in dilute degenerate semiconductors.

Thomas A. Lyson, G.W. Stevenson, and Rick Welsh (Eds.) Food and the Mid-Level Farm: Renewing an Agriculture of the Middle. Cambridge, MA: The MIT Press, 2008. 296 pp. ISBN 9780262622158. US $27.00, paperback.

Using planar Dirac \ensuremath{\delta} functions to describe the coupling of magnetic layers to an electron gas, the interaction between the layers is calculated. Both the bound and free states give contributions which are shaped by the range of the bound states. Due to a remarkable cancellation of terms the combined result does not show this shape. In fact, it differs appreciably from the weak-coupling limit only when the binding energy of the bound states is comparable or larger than the Fermi energy. \textcopyright{} 1996 The American Physical Society.

The paper promotes urban parks as suitable locations for geology field trips. A sample field guide of Griffith Park in Los Angeles is presented. The area described includes fault splays in the Santa Monica Fault Zone, and shows an inferred linkage between the Hollywood Fault and the Eagle Rock Fault. A conjunction of three faults is described, along with prominent jointing.

Exact expressions for the spin polarization due to a point field have been obtained for various inhomogeneous situations. The presence of boundaries or potentials modifies the nodes and amplitudes of the polarization, which determines the coupling between ion spins or nuclear magnetic moments in metals. For the half-space both in three and one dimensions, the analytic solution contains the usual Ruderman-Kittel-Kasuya-Yosida polarization around the source plus a polarization wave originating from the mirror point, although with the same phase at the border; there both are canceled by a third term. The case of a slab in three and one dimensions has been treated. A one-dimensional model with a reflectionsless localized potential with one bound state proved to be tractable. It is shown that the integrated polarization is given by the probability densities of the electron states at the position of the field summed over the Fermi surface.

The basis of dry friction is discussed using an independent oscillator model with longitudinal motion. This sample system is treated both numerically and with analytical methods. At vanishing velocity a sliding dry friction force is calculated which is smaller than the pinning force. At finite but not too large velocities the system displays bifurcation, chaotic motion, resonances at fractional and multiple frequencies of the oscillator, and hysteresis. Dry friction results from these complicated features. This force varies rapidly with velocity within this range, however, with a roughly constant mean value.

It is shown that the spin polarization of the electron cloud in thermal equilibrium with a ferromagnetic surface decays within a few Angstroms from the surface. This explains the vanishing spin polarization found in thermoemission from Ni and Fe by Vaterlaus et al. [Phys. Rev. Letters 65, 3041 (1990)].

The fluorescence lifetime of ${\mathrm{Cr}}^{3+}$ in ${\mathrm{GdAlO}}_{3}$ was measured in the range 1.8\char21{}4.2 K in magnetic fields up to 6 T. The results show a remarkable dependence of the transition probabilities on magnetic order. A model based on the exchange interaction between ${\mathrm{Cr}}^{3+}$ in highly excited states and the ${\mathrm{Gd}}^{3+}$ ions is proposed.

The exact static solutions of the Landau-Lifshitz equations for the magnetization, which have been identified as describing nucleation centers for the magnetization reversal in ferromagnets, are compared with those of phenomenological models of spherical and cylindrical symmetry. It is found that the latter have higher critical fields.

On etablit une solution plane generale de ces equations. De la, on evalue l'evolution dans le temps de petites deviations planes de forme arbitraire. On developpe en detail l'exemple d'une paroi se deplacant dans un champ magnetique brusquement eteint. Analyse des effets d'un champ magnetique dependant de l'espace et du temps et des modifications de l'anisotropie

When metals are structured on nanometre length scales, their electrons are subject to confinement effects: the response of a confined electron gas is governed by Friedel oscillations1 of the electron density and Rudermann–Kittel–Kasuya–Yosida oscillations2 of the spin density. Spatial oscillations of electron density have been observed directly at surfaces (in the vicinity of defects and steps) by scanning tunnelling spectroscopy3,4. But it has proved more difficult to probe such oscillations in bulk materials and over large distances5. Here we report the detection of quantum oscillations in a three-dimensional electron gas confined to a half space by a surface. To facilitate this detection, we have inserted an atomically thin ferromagnetic cobalt film at a variable distance τ from the surface of a copper single crystal. The cobalt film induces5 a total spin polarization P in the conduction electrons of the copper and, by virtue of the confining effects of the copper–vacuum interface, P varies as a function of τ. Our measurements of P reveal both quantum oscillations (the wavelengths of which are governed by the extremal diameters of the copper Fermi surface) and a decay with τ that are consistent with theoretical expectations2. These observations show that a consequence of improving the quality of nanostructured materials is that long-range quantum interactions can emerge more effectively, so that even distant boundaries and defects can become pivotal in determining physical properties.

An analytical treatment of the Ruderman–Kittel–Kasuya–Yosida polarization in inhomogeneous media is possible for some simple models. This is exemplified with the half‐spaces and slabs in one and three dimensions, and with an especially chosen potential barrier in one dimension.

Since dissipation requires motion, the velocity‐independent friction of macroscopic systems must result from quick motions of some of its components. A model of coupled spins, some of which have irregular anisotropy directions, presents velocity independent loss. During a collective motion of the spin ensemble, an irregular spin can fall into its potential minimum, from which it is subsequently dragged out again. The effect is pronounced for a range of the ratio between the anisotropy and interatomic exchange coupling constants which is typical for rare‐earth ions.

Dry friction is introduced into the Landau-Lifshitz equations. Numerical simulations show sustained motions or transitions to rest in a critical state. Hysteresis and Barkhausen noise can be modeled with simple structures. Dry friction in the Landau-Lifshitz equation can be a useful element in the modeling of ferromagnets. >

The relation between the potential r −β and the asymptotic behavior of the eigenvalues of the ordinary wave equation for space dimension N → ∞ is found. An analogous relation is discussed when the wave equation involves an iterated Laplacian. A criterion is given to determine when a potential should be considered singular, depending on the space dimension and the degree of iteration of the Laplacian. Finally, a modification is suggested for the approximation proposed by Witten which sensibly improves the results for the ground state energy of the hydrogen and helium atoms.

The Ruderman-Kittel interaction in one dimension is presented for an arbitrary coupling constant, as a by-product of previous considerations for a problem with planar symmetry in three dimensions. For coupling constants which are smaller than or even comparable to the Fermi energy, the interaction oscillates as a function of distance like the perturbation result, however, with a reduced amplitude. The interaction between two parallel magnetic lines in two dimensions is also discussed. \textcopyright{} 1996 The American Physical Society.

For a ferromagnet with exchange, uniaxial anisotropy, demagnetizing field, and an external magnetic field directed oppositely to the magnetization, the Landau-Lifshitz equations have time-independent, planar, local solutions of the Bloch and N\'eel type. These solutions are unstable. Analogous to a water droplet in supersaturated vapor for which a radius of unstable equilibrium exists, the solution for a given magnetic field is the configuration of smallest energy through which a magnetization reversal can nucleate.