Non-affine displacements in crystalline solids in the harmonic limit

A systematic coarse graining of microscopic atomic displacements generates a local elastic deformation tensor ${\mathsf D}$ as well as a positive definite scalar $\chi$ measuring non-affinity, i.e. the extent to which the displacements are not representable as affine deformations of a reference crystal. We perform an exact calculation of the statistics of $\chi$ and ${\mathsf D}$ and their spatial correlations for solids at low temperatures, within a harmonic approximation and in one and two dimensions. We obtain the joint distribution $P(\chi, {\mathsf D})$ and the two point spatial correlation functions for $\chi$ and ${\mathsf D}$. We show that non-affine and affine deformations are coupled even in a harmonic solid, with a strength that depends on the size of the coarse graining volume $\Omega$ and dimensionality. As a corollary to our work, we identify the field, $h_{\chi}$, conjugate to $\chi$ and show that this field may be tuned to produce a transition to a state where the ensemble average, $$, and the correlation length of $\chi$ diverge. Our work should be useful as a template for understanding non-affine displacements in realistic systems with or without disorder and as a means for developing computational tools for studying the effects of non-affine displacements in melting, plastic flow and the glass transition.Comment: 15 pages, 13 figures, RevTex4-

Non-affine fluctuations and the Statistics of Defect Precursors in the Planar Honeycomb Lattice

Certain localised displacement fluctuations in the planar honeycomb lattice may be identified as precursors to topological defects. We show that these fluctuations are among the most pronounced {\em non-affine} distortions of an elemental coarse graining volume of the honeycomb structure at non zero temperatures. We obtain the statistics of these precursor modes in the canonical ensemble, evaluating exactly their single point and two-point spatio-temporal distributions, for a lattice with harmonic nearest neighbour and next near neighbour bonds. As the solid is destabilised by tuning interactions, the precursor fluctuations diverge and correlations become long-lived and long-ranged.Comment: 14 pages, 7 figures, IOP forma

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal(BCT) to a body-centred-orthorhombic(BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids. Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic(affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample

Do thermodynamically stable rigid solids exist?

Customarily, crystalline solids are defined to be {\em rigid} since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the {\em metastable} state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then employed to obtain the equilibrium free energy as a function of this variable. Our results lead to a new view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable by switching on an external field, which penalises particle rearrangements. This produces a line of first-order phase transitions in the field - strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.Comment: 11 pages, 7 figure

Sterol 14,15 reductase (erg-3) mutations switch the phenotype of Neurospora crassa from sensitivity to the tomato saponin alpha-tomatine to sensitivity to the pea phytoalexin pisatin

The erg-3 gene of Neurospora crassa encodes the sterol biosynthetic enzyme sterol 14,15 reductase. This was first suggested by the finding that the erg-3 mutant strain accumulated precursors of ergosterol that retain the double bond between carbons 14 and 15 in the sterol C ring (Ellis et al. 1991, J. Gen. Microbiol. 137:2627-2630). Consistent with this result, cloning and sequencing of erg-3 revealed that the encoded protein is highly homologous to the sterol 14, 15 reductase of yeast (Papavinasasundaram and Kasbekar, 1994, J. Genet. 73:33-41). The cloning of erg-3 (and of erg-1, the structural gene encoding sterol 8,7 isomerase) was made possible by the discovery that their mutants are sensitive to the pea phytoalexin pisatin (Papavinasasundaram and Kasbekar, 1993, J. Gen. Microbiol. 139:3035-3041)

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed