Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains

The free energy and correlation lengths of the spin-1/2 $XYZ$ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the critical $XXZ$ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-critical $XXZ$ chain and the related spin-1 biquadratic chain at arbitrary temperature.Comment: 31 pages, LATEX, 5 PostScript figures appended, preprint cologne-93-471

Exact solution of new integrable nineteen-vertex models and quantum spin-1 chains

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical Hamiltonians is a realization of an integrable Haldane system. The finite-size spectra of the critical Hamiltonians deviate in their structure from standard predictions by conformal invariance.Comment: 16 pages, to appear in Z. Phys. B, preprint Cologne-94-474

Molecular basis for bacterial peptidoglycan recognition by LysM domains.

Carbohydrate recognition is essential for growth, cell adhesion and signalling in all living organisms. A highly conserved carbohydrate binding module, LysM, is found in proteins from viruses, bacteria, fungi, plants and mammals. LysM modules recognize polysaccharides containing N-acetylglucosamine (GlcNAc) residues including peptidoglycan, an essential component of the bacterial cell wall. However, the molecular mechanism underpinning LysM-peptidoglycan interactions remains unclear. Here we describe the molecular basis for peptidoglycan recognition by a multimodular LysM domain from AtlA, an autolysin involved in cell division in the opportunistic bacterial pathogen Enterococcus faecalis. We explore the contribution of individual modules to the binding, identify the peptidoglycan motif recognized, determine the structures of free and bound modules and reveal the residues involved in binding. Our results suggest that peptide stems modulate LysM binding to peptidoglycan. Using these results, we reveal how the LysM module recognizes the GlcNAc-X-GlcNAc motif present in polysaccharides across kingdoms

Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where $\xi$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of size $300 \times 300$, $120 \times 120$, and $80 \times 80$, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length $\xi_d(\beta_t)$ in the disordered phase at the first-order transition point $\beta_t$ with an accuracy of about $1$ for all considered values of $q$. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Dynamics of Phase Transitions by Hysteresis Methods I

In studies of the QCD deconfining phase transition or crossover by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. Motivated by this, we look at hysteresis methods to study the dynamics of phase transitions. Our systems are temperature driven through the phase transition using updating procedures in the Glauber universality class. Hysteresis calculations are presented for a number of observables, including the (internal) energy, properties of Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d Potts models, which provide a rich collection of phase transitions with a number of rigorously known properties. Comparing with equilibrium configurations we find a scenario where the dynamics of the transition leads to a spinodal decomposition which dominates the statistical properties of the configurations. One may expect an enhancement of low energy gluon production due to spinodal decomposition of the Polyakov loops, if such a scenario is realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Glassiness and constrained dynamics of a short-range non-disordered spin model

We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual description in terms of free defects subject to dynamical constraints, and is an explicit realization of the ``hierarchically constrained dynamics'' scenario for glassy systems. We give a number of exact results for the statics of the model, and study in detail the dynamical behaviour of one-time and two-time quantities. We also consider the role played by the configurational entropy, which can be computed exactly, in the relation between fluctuations and response.Comment: 10 pages, 9 figures; minor changes, references adde

Targeting Potential Drivers of COVID-19: Neutrophil Extracellular Traps

Coronavirus disease 2019 (COVID-19) is a novel, viral-induced respiratory disease that in ∼10-15% of patients progresses to acute respiratory distress syndrome (ARDS) triggered by a cytokine storm. In this Perspective, autopsy results and literature are presented supporting the hypothesis that a little known yet powerful function of neutrophils-the ability to form neutrophil extracellular traps (NETs)-may contribute to organ damage and mortality in COVID-19. We show lung infiltration of neutrophils in an autopsy specimen from a patient who succumbed to COVID-19. We discuss prior reports linking aberrant NET formation to pulmonary diseases, thrombosis, mucous secretions in the airways, and cytokine production. If our hypothesis is correct, targeting NETs directly and/or indirectly with existing drugs may reduce the clinical severity of COVID-19

Road avoidance and its energetic consequences for reptiles

Roads are one of the most widespread human-caused habitat modifications that can increase wildlife mortality rates and alter behavior. Roads can act as barriers with variable permeability to movement and can increase distances wildlife travel to access habitats. Movement is energetically costly, and avoidance of roads could therefore impact an animal's energy budget. We tested whether reptiles avoid roads or road crossings and explored whether the energetic consequences of road avoidance decreased individual fitness. Using telemetry data from Blanding's turtles (Emydoidea blandingii; 11,658 locations of 286 turtles from 15 sites) and eastern massasaugas (Sistrurus catenatus; 1,868 locations of 49 snakes from 3 sites), we compared frequency of observed road crossings and use of road-adjacent habitat by reptiles to expected frequencies based on simulated correlated random walks. Turtles and snakes did not avoid habitats near roads, but both species avoided road crossings. Compared with simulations, turtles made fewer crossings of paved roads with low speed limits and more crossings of paved roads with high speed limits. Snakes made fewer crossings of all road types than expected based on simulated paths. Turtles traveled longer daily distances when their home range contained roads, but the predicted energetic cost was negligible: substantially less than the cost of producing one egg. Snakes with roads in their home range did not travel further per day than snakes without roads in their home range. We found that turtles and snakes avoided crossing roads, but road avoidance is unlikely to impact fitness through energetic expenditures. Therefore, mortality from vehicle strikes remains the most significant impact of roads on reptile populations