Chappell Churchill (sinkfir8)

We calculate exactly cumulant generating functions (full counting statistics) for the transverse, staggered magnetization, and the domain walls at zero temperature for a finite interval of the XY spin chain. In ARV-771 ic50 , we also derive a universal interpolation formula in the scaling limit for the full counting statistics of the transverse magnetization and the domain walls which is based on the solution of a Painlevé V equation. By further determining subleading corrections in a large interval asymptotics, we are able to test the applicability of conformal field theory predictions at criticality. As a by-product, we also obtain exact results for the probability of formation of ferromagnetic and antiferromagnetic domains in both the σ^z and σ^x basis in the ground state. The analysis hinges upon asymptotic expansions of block Toeplitz determinants, for which we formulate and check numerically a different conjecture.Despite the recognition of the layered structure and evident criticality in the cortex, how the specification of input, output, and computational layers affects the self-organized criticality has not been much explored. By constructing heterogeneous structures with a well-accepted model of leaky neurons, we find that the specification can lead to robust criticality rather insensitive to the strength of external stimuli. This naturally unifies the adaptation to strong inputs without extra synaptic plasticity mechanisms. Low degree of recurrence constitutes an alternative explanation to subcriticality other than the high-frequency inputs. Unlike fully recurrent networks where external stimuli always render subcriticality, the dynamics of networks with sufficient feedforward connections can be driven to criticality and supercriticality. These findings indicate that functional and structural specification and their interplay with external stimuli are of crucial importance for the network dynamics. The robust criticality puts forward networks of the leaky neurons as promising platforms for realizing artificial neural networks that work in the vicinity of critical points.In aggregation-fragmentation processes, a steady state is usually reached. This indicates the existence of an attractive fixed point in the underlying infinite system of coupled ordinary differential equations. The next simplest possibility is an asymptotically periodic motion. Never-ending oscillations have not been rigorously established so far, although oscillations have been recently numerically detected in a few systems. For a class of addition-shattering processes, we provide convincing numerical evidence for never-ending oscillations in a certain region U of the parameter space. The processes which we investigate admit a fixed point that becomes unstable when parameters belong to U and never-ending oscillations effectively emerge through a Hopf bifurcation.The adsorption of colloidal particles at liquid interfaces is of great importance scientifically and industrially, but the dynamics of the adsorption process is still poorly understood. In this paper we use a Langevin model to study the adsorption dynamics of ellipsoidal colloids at a liquid interface. Interfacial deformations are included by coupling our Langevin dynamics to a finite element model while transient contact line pinning due to nanoscale defects on the particle surface is encoded into our model by renormalizing particle friction coefficients and using dynamic contact angles relevant to the adsorption timescale. Our simple model reproduces the monotonic variation of particle orientation with time that is observed experimentally and is also able to quantitatively model the adsorption dynamics for some experimental ellipsoidal systems but not others. #link# However, even for the latter case, our model accurately captures the adsorption trajectory (i.e., particle orientation versus height) of the particles. Our study clarifies the subtle interplay between capillary, viscous, an