471 research outputs found

    Analysis of segmental residual growth after progressive bone lengthening in congenital lower limb deformity

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    SummaryIntroductionThe issue of prognosis in limb length discrepancy in children affected by congenital abnormality remains a subject of concern. Therapeutic strategy must take length prediction into account, to adapt equalization techniques and the timing of treatment. Initial prognosis, however, may need revising after completion of one or several surgical interventions on the pathologic limb. The aim of this study was to determine the different types of growth response that a bone segment can present after progressive lengthening in case of congenital limb length discrepancy.Materials and methodsA series of 114 bone lengthenings with external fixator, performed in 36 girls and 50 boys with congenital lower limb length discrepancy, was retrospectively analyzed. Bone segment growth rates were measured before lengthening, during the first year after frame removal and finally over long-term follow-up, calculating the ratios of radiological bone length to the number of months between two measurements. Mean follow-up was 4.54±0.2 years.ResultsChanges in short- and long-term growth rate distinguished five patterns of bone behavior after lengthening, ranging from growth acceleration to total inhibition.DiscussionThese five residual growth patterns depended on certain factors causing acceleration or, on the contrary, slowing down of growth: age at the lengthening operation, percentage lengthening, and minimal period between two lengthenings. These criteria help optimize conditions for resumed growth after progressive segmental lengthening, avoiding conditions liable to induce slowing down or inhibition, and providing a planning aid in multi-step lengthening programs.Level of evidenceLevel IV. Retrospective study

    Hierarchy of boundary driven phase transitions in multi-species particle systems

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    Interacting systems with KK driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions which are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary driven phase transition (BDPT) is observed and reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths one generically encounters ZZ discontinuous and 2(KZ)2(K-Z) continuous BDPTs with ZZ taking values 0ZK0\leq Z\leq K depending on the path. As model examples we consider solvable exclusion processes with product measure states and K=1,2,3K=1,2,3 particle species and a non-solvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.Comment: 12 pages, 11 figure

    Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

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    We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure

    Steady-state selection in driven diffusive systems with open boundaries

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    We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic current irrespective of the local dynamics. In particular, we predict a minimal current phase for systems with local minimum in the current--density relation. This phase is explained by a dynamical phenomenon, the branching and coalescence of shocks, Monte-Carlo simulations confirm the theoretical scenario.Comment: 6 pages, 5 figure

    On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics

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    We present a lattice gas model that without fine tuning of parameters is expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ) universality class. To this end, we review briefly how non-linear fluctuating hydrodynamics in one dimension predicts that all dynamical universality classes in its range of applicability belong to an infinite discrete family which we call Fibonacci family since their dynamical exponents are the Kepler ratios zi=Fi+1/Fiz_i = F_{i+1}/F_{i} of neighbouring Fibonacci numbers FiF_i, including diffusion (z2=2z_2=2), KPZ (z3=3/2z_3=3/2), and the limiting ratio which is the golden mean z=(1+5)/2z_\infty=(1+\sqrt{5})/2. Then we revisit the case of two conservation laws to which the modified KPZ model belongs. We also derive criteria on the macroscopic currents to lead to other non-KPZ universality classes.Comment: 17 page

    Symmetry breaking and phase coexistence in a driven diffusive two-channel system

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    We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of coupling to two reservoirs, it is investigated analytically and numerically. In addition to the known one-channel phases, two new regions are found, in particular the one, where the total density is fixed, but the filling of the individual chains changes back and forth, with a preference for strongly different densities. The corresponding probability distribution is determined and shown to have an universal form. The phase diagram and general aspects of the problem are discussed.Comment: 12 pages, 10 figures, to appear in Phys.Rev.

    Scaling of the von Neumann entropy across a finite temperature phase transition

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    The spectrum of the reduced density matrix and the temperature dependence of the von Neumann entropy (VNE) are analytically obtained for a system of hard core bosons on a complete graph which exhibits a phase transition to a Bose-Einstein condensate at T=TcT=T_c. It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T=0 to purely linear in block size nn behaviour for TTcT\geq T_{c}. For intermediate temperatures, VNE is a sum of two contributions which are identified as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.Comment: 4 pages, 2 figure

    Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model

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    A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within mean-field approximation, and compared with Monte-Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to zero, an exact solution is obtained. We present and analyze a physical picture which serves to explain the different phases of the model

    The Fokker-Planck equation, and stationary densities

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    The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated. Finally, stochastic one-dimensional fields with local interactions are studied that have kink-solutions.Comment: 10 page

    Phase diagram of two-lane driven diffusive systems

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    We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail
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