Scaling of interfaces in brittle fracture and perfect plasticity

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical ``overlap cluster'' length between pairs of such interfaces converges to a constant with $L$ increasing.Comment: Accepted for publication in Phys. Rev.

Minimum spanning trees on random networks

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to $P(\epsilon)$. We discuss the relationship to invasion percolation (IP), to the directed polymer in a random media (DPRM) and the implications for the broader issue of universality in disordered systems.Comment: 4 pages, 3 figure

Order to disorder transition in the XY-like quantum magnet Cs2CoCl4 induced by noncommuting applied fields

We explore the effects of noncommuting applied fields on the ground-state ordering of the quasi-one-dimensional spin-1/2 XY-like antiferromagnet Cs2CoCl4 using single-crystal neutron diffraction. In zero field interchain couplings cause long-range order below T_N=217(5) mK with chains ordered antiferromagnetically along their length and moments confined to the (b,c) plane. Magnetic fields applied at an angle to the XY planes are found to initially stabilize the order by promoting a spin-flop phase with an increased perpendicular antiferromagnetic moment. In higher fields the antiferromagnetic order becomes unstable and a transition occurs to a phase with no long-range order in the (b,c) plane, proposed to be a spin liquid phase that arises when the quantum fluctuations induced by the noncommuting field become strong enough to overcome ordering tendencies. Magnetization measurements confirm that saturation occurs at much higher fields and that the proposed spin-liquid state exists in the region 2.10 < H_SL < 2.52 T || a. The observed phase diagram is discussed in terms of known results on XY-like chains in coexisting longitudinal and transverse fields.Comment: revtex, 14 figures, 2 tables, to appear in Phys. Rev.

Stochastic Renormalization Group in Percolation: I. Fluctuations and Crossover

A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical self-similarity through a non-stationary branching process. The SRG provides a theoretical basis for analytical or numerical approximations, both at and away from criticality, whenever the correlation length is much larger than the lattice spacing (regardless of the system size). For example, the SRG predicts order-parameter distributions and finite-size scaling functions for the complete crossover between phases. For percolation, the simplest SRG describes structural quantities conditional on spanning, such as the total cluster mass or the minimum chemical distance between two boundaries. In these cases, the Central Limit Theorem (for independent random variables) holds at the stable, off-critical fixed points, while a ``Fractal Central Limit Theorem'' (describing long-range correlations) holds at the unstable, critical fixed point. This first part of a series of articles explains these basic concepts and a general theory of crossover. Subsequent parts will focus on limit theorems and comparisons of small-cell SRG approximations with simulation results.Comment: 33 pages, 6 figures, to appear in Physica A; v2: some typos corrected and Eqs. (26)-(27) cast in a simpler (but equivalent) for

The Stardust – a successful encounter with the remarkable comet Wild 2

On January 2, 2004 the Stardust spacecraft completed a close flyby of comet Wild2 (P81). Flying at a relative speed of 6.1 km/s within 237km of the 5 km nucleus, the spacecraft took 72 close-in images, measured the flux of impacting particles and did TOF mass spectrometry

Phase diagram of an Ising model with long-range frustrating interactions: a theoretical analysis

We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground-state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of ``flowers'', each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.Comment: 32 pages, 7 figure

Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism

This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in defining the ensemble. Ensembles are obtained by dividing a huge rock sample into many mesoscopic volumes. Because rocks are a disordered collection of grains in cohesive contact, we expect that once shear strain is applied and cracks begin to arrive in the system, the mesoscopic volumes will have a wide distribution of different crack states. These mesoscopic volumes are the members of our ensembles. We determine the probability of observing a mesoscopic volume to be in a given crack state by maximizing Shannon's measure of the emergent crack disorder subject to constraints coming from the energy-balance of brittle fracture. The laws of thermodynamics, the partition function, and the quantification of temperature are obtained for such cracking systems.Comment: 11 pages, 2 figure

Staff experiences and understandings of the REsTRAIN Yourself initiative to minimise the use of physical restraint on mental health wards

International efforts to minimize coercive practices include the US Six Core Strategies© (6CS). This innovative approach has limited evidence of its effectiveness, with few robustly designed studies, and has not been formally implemented or evaluated in the UK. An adapted version of the 6CS, which we called ‘REsTRAIN Yourself’ (RY), was devised to suit the UK context and evaluated using mixed methods. RY aimed to reduce the use of physical restraint in mental health inpatient ward settings through training and practice development with whole teams, directly in the ward settings where change is to be implemented and barriers to change overcome. In this paper we present qualitative findings that report on staff perspectives on the impact and value of RY following its implementation. Thirty-six staff participated in semi-structured interviews with data subject to thematic analysis. Eight themes are reported that highlight perceived improvements in every domain of the 6CS after RY had been introduced. Staff reported more positively on their relationships with service users and felt their attitudes towards the use of coercive practices such as restraint were changed; the service as a whole shifted in terms of restraint awareness and reduction; and new policies, procedures and language were introduced despite certain barriers. These findings need to be appreciated in a context wherein substantial reductions in the use of physical restraint was proven possible, largely due to building upon empathic and relational alternatives. However, yet more could be achieved with greater resourcing of inpatient care

Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased percolations consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady-state of the RRN focusing on the properties of the non-Ohmic regime. In constant voltage conditions, a scaling relation is found between $/_0$ and $V/V_0$, where $$ is the average network resistance, $_0$ the linear regime resistance and $V_0$ the threshold value for the onset of nonlinearity. A similar relation is found in constant current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the pre-breakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.Comment: 15 figures, 23 page