Elastic to plastic transition in amorphous solids.

The response of amorphous solids to mechanical loads is accompanied by plasticity that is generically associated with "non-affine" quadrupolar events seen in the resulting displacement field. To develop a continuum theory, one needs to assess when these quadrupolar events have a finite density, allowing the development of a field theory. Is there a transition, as a function of the material parameters and the nature of the loads, from isolated plastic events whose density is zero to a regime governed by a finite density? And if so, what is the nature of this transition? The aim of the paper is to explore this issue. The motivation for the present study stems from recent research in which it was shown that gradients of the quadrupolar fields act as dipole charges that can screen elasticity. Analytically soluble examples of mechanical loading that lead to screening and emergent length scales (that are absent in classical elasticity) have been analyzed and tested. However, "gradients of quadrupolar fields" make sense only when the density of quadrupoles is finite, and hence, the issue is central to this article. The article introduces a notion of polarizability under the strain of Eshelby quadrupoles and concludes that the onset of a density of such quadrupoles with random orientations can only appear when the polarizability is finite.

Dynamic screening by plasticity in amorphous solids.

In recent work it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform static loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field associated with plastic responses. Here we study the dynamical responses induced by oscillatory loads. The required modification to classical elasticity is described. Exact solutions for the displacement field in circular geometry are presented, demonstrating that dipole screening results in essential departures from the expected predictions of classical elasticity theory. Numerical simulations are conducted to validate the theoretical predictions and to delineate their range of validity.

Creep failure of amorphous solids under tensile stress.

Applying constant tensile stress to a piece of amorphous solid results in a slow extension, followed by an eventual rapid mechanical collapse. This "creep" process is of paramount engineering concern, and as such was the subject of study in a variety of materials, for more than a century. Predictive theories for τ_{w}, the expected time of collapse, are incomplete, mainly due to its dependence on a bewildering variety of parameters, including temperature, system size, tensile force, but also the detailed microscopic interactions between constituents. The complex dependence of the collapse time on all the parameters is discussed below, using simulations of strip of amorphous material. Different scenarios are observed for ductile and brittle materials, resulting in serious difficulties in creating an all-encompassing theory that could offer safety measures for given conditions. A central aim of this paper is to employ scaling concepts, to achieve data collapse for the probability distribution function (pdf) of lnτ_{w}. The scaling ideas result in a universal function which provides a prediction of the pdf of lnτ_{w} for out-of-sample systems, from measurements at other values of these parameters. The predictive power of the scaling theory is demonstrated for both ductile and brittle systems. Finally, we present a derivation of universal scaling function for brittle materials. The ductile case appears to be due to a plastic necking instability and is left for future research.

Scaling theory for Wöhler plots in amorphous solids under cyclic forcing.

In mechanical engineering Wöhler plots serve to measure the average number of load cycles before materials break, as a function of the maximal stress in each cycle. Although such plots have been prevalent in engineering for more than 150 years, their theoretical understanding is lacking. Recently a scaling theory of Wöhler plots in the context of cyclic bending was offered [Bhowmik, arXiv:2103.03040 (2021)]. Here we elaborate further on cyclic bending and extend the considerations to cyclic tensile loads on an amorphous strip of material; the scaling theory applies to both types of cyclic loading equally well. On the basis of atomistic simulations we conclude that the crucial quantities to focus on are the accumulated damage and the average damage per cycle. The dependence of these quantities on the loading determines the statistics of the number of cycles to failure. Finally, we consider the probability distribution functions of the number of cycles to failure and demonstrate that the scaling theory allows prediction of these distributions at one value of the forcing amplitude from measurements and another value.

Aging and Failure of a Polymer Chain under Tension.

The rupture of a polymer chain maintained at temperature T under fixed tension is prototypical to a wide array of systems failing under constant external stress and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a universal exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.

Precise spatial memory in local random networks.

Self-sustained, elevated neuronal activity persisting on timescales of 10 s or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of the most well-known modeling frameworks for persistent activity, have been able to model crucial aspects of such spatial memory. These models tend to require highly structured or regular synaptic architectures. In contrast, we study numerical simulations of a geometrically embedded model with a local, but otherwise random, connectivity profile; imposing a global regulation of our system's mean firing rate produces localized, finely spaced discrete attractors that effectively span a two-dimensional manifold. We demonstrate how the set of attracting states can reliably encode a representation of the spatial locations at which the system receives external input, thereby accomplishing spatial memory via attractor dynamics without synaptic fine-tuning or regular structure. We then measure the network's storage capacity numerically and find that the statistics of retrievable positions are also equivalent to a full tiling of the plane, something hitherto achievable only with (approximately) translationally invariant synapses, and which may be of interest in modeling such biological phenomena as visuospatial working memory in two dimensions.

Plastic instabilities in charged granular systems: Competition between elasticity and electrostatics.

Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby-like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to an external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined, and a theoretical analysis is presented. Plastic instabilities are discussed as saddle-node bifurcations that can be fully understood in terms of eigenvalues and eigenfunctions of the relevant Hessian matrix. This system exhibits moduli that describe how electric polarization and stress are influenced by strain and the electric field. Theoretical expression for these moduli are offered and compared to the measurements in numerical simulations.

Diffusion in agitated frictional granular matter near the jamming transition.

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction ϕ and mean-square velocity fluctuations 〈v^{2}〉 the mean-square displacement of the disks 〈d^{2}〉 spans four to five orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behavior at long times. The statistics of 〈d^{n}〉 at all times are multiscaling, since the probability distribution function (PDF) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of ϕ and 〈v^{2}〉. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean-square displacement and the PDF of displacements into collapsed scaling functions for all ϕ and 〈v^{2}〉. These scaling functions provide a predictive tool, allowing one to infer from one set of measurements (at a given ϕ and 〈v^{2}〉) what are the expected results at any value of ϕ and 〈v^{2}〉 within the scaling range.

Scaling theory of shear-induced inhomogeneous dilation in granular matter.

Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity, various material parameters, and the preparation protocol. In spite of numerous studies of granular flows a predictive theory of the amount of dilation is still lacking. Here, we offer a scaling theory that is focused on such a prediction as a function of shear rate and the dissipative parameters of the granular assembly. The resulting scaling laws are universal with respect to changing the interparticle force laws.

Force distributions in frictional granular media.

We report a joint experimental and theoretical investigation of the probability distribution functions (PDFs) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint PDF of normal and tangential forces together, and the marginal PDFs of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulation data are reported. The proposed joint PDF predicts giant slip events at low pressures, again in agreement with observations.

The sandpile revisited: computer assisted determination of constitutive relations and the breaking of scaling.

We revisit the problem of the stress distribution in a frictional sandpile with both normal and tangential (frictional) inter-granular forces, under gravity, equipped with a new numerical method of generating such assemblies. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field, principle stress axis, angle of repose, as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. We compare these results with the predictions of a theory based on continuum equilibrium mechanics. Basic to the theory of sandpiles are assumptions about the form of scaling solutions and constitutive relations for cohesive-less hard grains for which no typical scale is available. We find that these constitutive relations must be modified; moreover for smaller friction coefficients and smaller piles these scaling assumptions break down in the bulk of the sandpile due to the presence of length scales that must be carefully identified. Fortunately, for larger friction coefficient and for larger piles the breaking of scaling is weak in the bulk, allowing an approximate analytic theory which agrees well with the observations. After identifying the crucial scale, triggering the breaking of scaling, we provide a predictive theory to when scaling solutions are expected to break down. At the bottom of the pile the scaling assumption breaks always, due to the different interactions with the bottom surface. The consequences for measurable quantities like the pressure distribution and shear stress at the bottom of the pile are discussed. For example one can have a transition from no dip in the base-pressure to a dip at the center of the pile as friction increases.

[Development and Periodicity of Human Exposures in Suicidal Intention Reported to the Centre Erfurt from 2004-2013]. / Entwicklung und Periodizität humaner Expositionen in suizidaler Absicht im Einzugsbereich des Giftnotrufs Erfurt von 2004­2013.

Aim of the Study: Exposures in suicide attempts are demanding for hospitals and poisons information centres (PICs). Therefore, the time characteristics of their frequency were studied. Methods: A retrospective analysis was undertaken of all human exposures reported to Centre Erfurt from the beginning of 2004 to the end of 2013 according to their frequency in the respective year, season, month, weekday, time of the weekday, circumstances of exposure, age and gender. Results: 59.7% of all exposures (n=137 104) were accidental, 23.4% occurred in suicide attempts and 3.3% in substance abuse. 0.3% of the suicide attempts resulted in death. Their number continuously increased from n=2 422 in 2004 to n=3 458 in 2013, but their relative frequency remained almost constant at 23.4%. Their highest numbers were reached in the spring and summer with maxima in July and August and minima in February and September. During the week, the most suicide attempts were observed between Sunday and Tuesday and the least on Friday. Highest rate of suicide attempts was seen at 10 pm and lowest at 6 am. The median of age was 39 years (first quartile 24 years, third quartile 50 years). The female proportion was almost twice as high as the male. Conclusions: Hospitals the Centre Erfurt is serving should be particularly prepared for exposures in suicide attempts in the spring and summer (especially in July and August), at the beginning of the week and shortly before midnight.

Anatomy of plastic events in magnetic amorphous solids.

Plastic events in amorphous solids can be much more than just "shear transformation zones" when the positional degrees of freedom are coupled nontrivially to other degrees of freedom. Here we consider magnetic amorphous solids where mechanical and magnetic degrees of freedom interact, leading to rather complex plastic events whose nature must be disentangled. In this paper we uncover the anatomy of the various contributions to some typical plastic events. These plastic events are seen as Barkhausen noise or other "serrated noises." Using theoretical considerations we explain the observed statistics of the various contributions to the considered plastic events. The richness of contributions and their different characteristics imply that in general the statistics of these serrated noises cannot be universal, but rather highly dependent on the state of the system and on its microscopic interactions.

[Human Single Drug Exposures to Non-opioid Analgesics Reported to the Poisons Information Centre Erfurt from 2003 to 2012]. / Humane nichtopioide Analgetika-Monoexpositionen im Einzugsbereich des Giftnotrufes Erfurt von 2003-2012.

AIM OF THE STUDY: Because of their frequency, non-opioid analgesics (NOA) single drug exposures registered by Poisons Information Centre (PIC) Erfurt have been studied over a decade. METHODS: A retrospective analysis of frequencies, circumstances of exposure, symptom severity, and age groups in NOA single drug exposures received by the PIC Erfurt from the beginning of 2003 to the end of 2012 was undertaken. RESULTS: Of all 4749 NOA single drug exposures, the 10 most frequent were caused by paracetamol (n=1 686), ibuprofen (n=1 439), acetylsalicylic acid (n=456), dipyrone (n=274), diclofenac (n=267), flupirtine (n=138), naproxen (n=41), etoricoxib (n=36), indomethacin (n=24), and dexketoprofen (n=19). Paracetamol single drug exposures increased from 158 in 2003 to 216 in 2007 and fell afterwards to 133 in 2012. Ibuprofen single drug exposures continously rose from 57 in 2003 to 258 in 2012. Adults were more often involved in NOA (53.8%) and all single drug exposures (54.1%) than children (45.9% and 45.6%, respectively). Suicidal attempts were more frequent in NOA (43.1%) than in all single drug exposures (34.2%), whereas accidental exposures or exposures in abuse were less often (33.4 and 0.2%, 46.0 and 0.9% respectively). NOA single drug exposures resulted mostly in none to minor symptoms (77.0%) and rarely in moderate (2.1%) or severe symptoms (1.0%). One adult was found dead after probable ingestion of 32 g of acetylsalicylic acid in suicidal intention. CONCLUSIONS: Because many NOA are over-the-counter drugs, it is difficult to obtain data on their use. PIC data could provide information on the NOA use in the population.

Stochastic approach to plasticity and yield in amorphous solids.

We focus on the probability distribution function (PDF) P(Δγ;γ) where Δγ are the measured strain intervals between plastic events in a athermal strained amorphous solids, and γ measures the accumulated strain. The tail of this distribution as Δγ→0 (in the thermodynamic limit) scales like Δγ(η). The exponent η is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix P(λ) which scales like λ(θ), η=(θ-1)/2. The numerical values of η or θ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as γ increases. Determining the γ dependence of the PDF P(Δγ;γ) can shed important light on plasticity and yield. We conclude that the PDF's of both Δγ and λ are not continuous functions of γ. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at γ=0(+) and then at the yield point γ=γ(Y) to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of 〈Δγ〉 are discussed.

Elasticity and plasticity in stiff and flexible oligomeric glasses.

In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via plastic instabilities, and the geometric responses of the oligomers themselves to a mechanical load. We present a microscopic theory that explains the numerically observed phenomena, including an exact theory of the shear modulus and of the plastic instabilities, both local and system spanning. In addition we present a model to explain the geometric changes in the oligomeric chains under increasing strains.

[Acute poisoning in adults]. / Akute Vergiftungen im Erwachsenenalter.

Acute poisoning is one of the more frequent presentations in acute and emergency medicine. Poisoning with pharmaceuticals is predominantly observed in adults. A detailed medical history and an accurate clinical examination establish the basis for the diagnostics. Typical poisoning syndromes can be classified based on the clinical presentation. Drug screening in urine and examination of blood alcohol levels are useful additional tools because of the rapid and widespread availability. Securing vital organ functions is the mainstay of treatment and early contact with a poisons centre is useful for the assessment of the hazard and the further procedures. Primary and secondary poison elimination methods should be carefully considered because of insufficient evidence. Specific antidotes are only available for a few poisoning cases.

[Human exposures to veterinary medicines reported to the Poisons Information Centre Erfurt from 2003 to 2012]. / Humane Tierarzneimittelexpositionen im Einzugsbereich des Giftnotrufes Erfurt 2003-2012.

AIM OF THE STUDY: The purpose of this study was to get information on all human exposures to veterinary medicines (HEVM) reported to the Poisons Information Centre (PIC) over a 10-year period. METHODS: A retrospective analysis of all HEVM was undertaken and a comparison was made to all human exposures (HE) registered by the PIC from the beginning of 2003 to the end of 2012 according to frequencies, circumstances of exposure, symptom severity, age groups, and substances involved in HEVM. RESULTS: In total, 389 cases of HEVM with 409 veterinary medicines were registered (0.30% of all HE, 360 monoexposures). The relative frequency of children and adults in HEVM (children: 52.4%, adults: 46.0%) and all HE (children: 48.7%, adults 48.7%) was the same with significant (p<0.05) differences in some age subgroups. The portion of accidental exposures was significantly (p<0.05) higher in HEVM (83.3%) than in all exposures (59.3%), whereas the portion of suicidal exposures was significantly (p<0.05) lower (HEVM: 6.4%, all exposures: 23.6%). Most frequent veterinary medicines (ATCvet) in HEVM were antiparasitic substances, insecticides and repellents (n=185), substances for the nervous system (n=48), substances for the cardiovascular system (n=35), and immunologicals (n=35). HEVM mostly resulted in no or mild symptoms (83.8%) and rarely in moderate (10/389, 2.6%) or even severe symptoms (5/389, 1.3%). In 4 of 5 cases of HEVM with severe symptoms, veterinary surgeons used products for animal euthanasia (n=3) or methadone (n=1). Once, self-medication with anthelmintics for several days by a goatherd resulted in transient blindness. CONCLUSIONS: In comparison to other HE, HEVM are rare. Most accidental HEVM in laymen result only in none to mild symptoms. If veterinary surgeons, however, swallow or inject products for animal euthanasia or opioids in suicidal intention, severe symptoms can be expected.

[Poisonings due to Substance Abuse Reported to the Poisons Information Centre Erfurt from 2002 to 2011]. / Substanzmissbrauch - Entwicklung des Vergiftungsgeschehens im Einzugsbereich des Giftnotrufes Erfurt 2002-2011.

AIM OF THE STUDY: Because of their importance for clinical toxicology, developments of sub-stance abuse reported to the Poisons Information Centre (PIC) Erfurt were investigated and compared to other reasons of human exposures. METHODS: A retrospective analysis of all human exposures (exposures of humans to substances in abuse, accidental and unknown circumstances, and suicide attempts) (n=125,130) from the beginning of 2002 to the end of 2011 was undertaken according to substance classes, reasons of exposures, symptom severity, age groups, and gender. RESULTS: Cases of substance abuse (3,760, 3.0% of all exposures) continuously increased from 252 (92 with one and 160 with multiple substances) in 2002 to 507 in 2011 (239 with one and 268 with multiple substances). In relation to all exposures, only the abuse of multiple substances rose significantly (p<0.001). In comparison to all substances of exposure, ethanol, amphetamine-type stimulants, benzodiazepines/analogues, and liquid ecstasy abuse significantly (p<0.005) increased while cannabis and Brugmansia/Datura species abuse significantly (p<0.05) decreased. Substance abuse significantly (p<0.001) more often caused moderate (23.7%) and severe symptoms (6.1%) than in suicide attempts (9.6%; 4.4%). First legal highs exposures were registered in 2010 and led significantly (p<0.001) more often to moderate symptoms (50%) than cannabis exposures (19.4%). CONCLUSIONS: The clinical significance of substance abuse is shown by the fact that it resulted more often in moderate and severe symptoms than suicide attempts. Data on substance abuse from PICs could supplement official annual drug reports in aspects of clinical toxicology.

Local elastic response measured near the colloidal glass transition.

We examine the response of a dense colloidal suspension to a local force applied by a small magnetic bead. For small forces, we find a linear relationship between the force and the displacement, suggesting the medium is elastic, even though our colloidal samples macroscopically behave as fluids. We interpret this as a measure of the strength of colloidal caging, reflecting the proximity of the samples' volume fractions to the colloidal glass transition. The strain field of the colloidal particles surrounding the magnetic probe appears similar to that of an isotropic homogeneous elastic medium. When the applied force is removed, the strain relaxes as a stretched exponential in time. We introduce a model that suggests this behavior is due to the diffusive relaxation of strain in the colloidal sample.