Burst distribution in noisy fiber bundles and fuse models

We study the burst distribution in the fiber bundle model and the fuse model when noise is added to the thresholds, i.e., when the threshold values vary around a fixed value as the breakdown proceeds. The burst distribution follows a power law in the noisy system, but with the exponent τ changed compared to the standard models without noise. The value of τ changes near failure in the noisy models as in the models without noise, hence signaling imminent breakdown.     

Experimental and Theoretical Study of the Generation and Non-Linear Conversion of Picosecond Bursts from an Amplified Ytterbium-Doped Fiber Laser System

Abstract

This article presents an experimental and theoretical study of the generation of picosecond bursts by a non-polarization-maintaining ytterbium-doped fiber master oscillator fiber amplifier system. The peak power and pulse energy of the burst are higher than 45 kW and 350 nJ at 700 kHz, respectively. The master oscillator fiber amplifier was used to generate 3 W of green and 200 mW of UV light with conversion efficiencies of 16% and 8%, respectively. The enhancement of conversion efficiency by the pulse burst compared with regular pulses was analyzed and attributed to dynamically saturated gain of the pump-power-limited fiber amplifier.     

Are citations of scientific papers a case of nonextensivity?

The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner (Eur. Phys. J. B 4, 131 (1998)). To fit the data, a stretched exponential () has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a power law (roughly for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, [0pt] for the available values of x. This is consistent with the connection recently established by Denisov (Phys. Lett. A 235, 447 (1997)) between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number x. Received 13 April 1999     

Failure time and critical behaviour of fracture precursors in heterogeneous materials

The acoustic emission of fracture precursors, and the failure time of samples of heterogeneous materials (wood, fiberglass) are studied as a function of the load features and geometry. It is shown that in these materials the failure time is predicted with a good accuracy by a model of microcrack nucleation proposed by Pomeau. We find that the time interval δt between events (precursors) and the energy ɛ are power law distributed and that the exponents of these power laws depend on the load history and on the material. In contrast, the cumulated acoustic energy E presents a critical divergency near the breaking time τ which is E∼ . The positive exponent γ is independent, within error bars, on all the experimental parameters. Received 31 July 2001 and Received in final form 17 December 2001     

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

Fragmentation and reliable size distributions of large ammonia and water clusters

The interaction of large ammonia and water clusters in the size range from <n> = 10 to 3 400 with electrons is investigated in a reflectron time-of-flight mass spectrometer. The clusters are generated in adiabatic expansions through conical nozzles and are nearly fragmentation free detected by single photon ionization after they have been doped by one sodium atom. For ammonia also the (1+1) resonance enhanced two photon ionization through the state with v = 6 operates similarly. In this way reliable size distributions of the neutral clusters are obtained which are analyzed in terms of a modified scaling law of the Hagena type [Surf. Sci. 106, 101 (1981)]. In contrast, using electron impact ionization, the clusters are strongly fragmented when varying the electron energy between 150 and 1 500 eV. The number of evaporated molecules depends on the cluster size and the energy dependence follows that of the stopping power of the solid material. Therefore we attribute the operating mechanism to that which is also responsible for the electronic sputtering of solid matter. The yields, however, are orders of magnitude larger for clusters than for the solid. This result is a consequence of the finite dimensions of the clusters which cannot accommodate the released energy. Received 21 November 2001     

Peeling model for cell detachment

In many experimental situations, the adhesion of cells to solid substrates is due to non-covalent chemical bonds. It is the thesis of this paper that many phenomena occurring in cell detachment experiments, such as in I (E. Decavé, G. Garriver, Y. Brechet, B. Fourcade, F. Bruckert, Biophys. J. 82, 2383 (2002)), result from the static and dynamic properties of the adhesive bridges at the extreme margin of the cell. This region defines the adhesive belt where the distribution of connected bonds crosses over to zero where the membrane leaves the substrate. The theoretical model we introduce in this paper discusses the threshold force together with the peeling velocity in the same theoretical framework. In this one-dimensional model, the threshold force results from a non-homogeneous distribution of anchor proteins along the membrane so that the adhesive belt increases its capacity to resist motion with increasing the external force. Analyzing the kinetics of the the contact line motion, we derive the characteristic relationship speed versus external force and we describe the non-equilibrium state of the adhesive belt as a function of the speed. We discuss our model in view of the experimental results obtained with D. discoideum for hydrodynamic shear experiments. Our results could be also confronted to single-cell observations. Received 14 January 2002     

The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

We have investigated the proof of the H theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a κ power law generalization of the exponential Juttner distribution, e.g., , with θ=α(x)+β_μp^μ, where α(x) is a scalar, β_μ is a four-vector, and p^μ is the four-momentum. As a simple example, we calculate the relativistic κ power law for a dilute charged gas under the action of an electromagnetic field F^μν. All standard results are readly recovered in the particular limit κ→0.     

Flory radius of polymers in a periodic field: An exact analytic theory

We found an exact expression for the Flory radius R _F of Gaussian polymers placed in an external periodic field. This solution is expressed in terms of the two parameters η and a that describe the reduced strength of an external field and the period of the field to the polymer gyration radius ratio, respectively. R _F is found to be a decaying function of η for any values of a . Provided that the gyration radius is of the order of the period of an external field or less, the ground-state (GS) approximation of the exact result for R _F is shown to give qualitatively incorrect results. In addition to the “ground-state” contribution, the exact solution for R _F contains an additional term that is overlooked by the GS approximation. This term gives rise to the fact that R _F as a function of η exhibits power law behavior (rather than exponential decay obtained from the GS result) once η exceeds the threshold value η_con .     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated elastic energy, the equally important elastic forces are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold F_c are effectively balanced by a homogeneous background medium, forces larger than F_c are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force chains known from granular media.     

Impact of gel balls beyond the Hertzian regime

We study experimentally the impact of spherical gel balls on a rigid substrate, where the balls largely deform like a pancake at high impact velocities. In our previous study (Y. Tanaka, Y. Yamazaki, K. Okumura, Europhys. Lett. 63, 149 (2003)), we measured the contact time τ_f and maximally deformed size versus impact velocity and explained the behaviors at the scaling level. In this study, we further measure τ_m, the time required to reach the maximum deformation (from the initial contact), and the restitution coefficient e. We also make a static experiment where we obtain the force-deformation curve of the gel balls up to fairly large deformations to explain the data on the impact. We propose two phenomenological treatments going beyond the scaling argument, one for intermediate impact velocities and the other for large velocities; the former is based on the static experiment while the latter on a Lagrangian constructed from appropriate constraints. Results from these treatments reproduce the experimental behavior of τ_m.     

69,71Ga NMR studies of a superconducting Ga 84 cluster compound

We present ^69,71Ga-NMR experiments on microcrystalline samples of the recently discovered supramolecular compound Ga ₈₄ [ N ( SiMe ₃ ) ₂ ] ₂₀ Li ₆ Br ₂ ( thf ) ₂₀ ^. 2 toluene, which is composed of ligand-coordinated Ga₈₄ metal clusters, packed together in a fully ordered crystalline matrix. The compound is highly conducting and even shows superconductivity below T _c ~ 7.2 K. Our preliminary results between 10-300 K show a metallic-like behavior: the nuclear spin-lattice relaxation rate T ₁ ^-1 follows the Korringa law ⁶⁹ ( T ₁ T ) ^-1 = 0.36 s ^-1 K ^-1 , but with a relaxation rate approximately three times smaller than in bulk -Ga metal. No quantum-size effects are observed, the Korringa law being followed down to 10 K, whereas the quantum-gaps for individual clusters should amount to ~ 10 ³ K. These results therefore suggest a transport process based on intermolecular charge transfer, similar as in alkali-doped fullerenes and silicon-clathrates.     

Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets

In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers found in certain seashells . We then analyzed a crack running perpendicular to the layers and suggested one possible reason for the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the deformation field is governed by a parabolic differential equation while the field away from the tip follows the usual elliptic equation. Analytical results show that the fracture tip is lenticular, as suggested in a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett. 13, 709 (1990)). On the contrary, away from the tip, the stress and deformation distribution recover the usual singular behaviors ( and 1/, respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture. Received 16 November 2001     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998     

Appearance of anisotropic non s-wave superconductivity above the critical pressure of antiferromagnetic CeRhIn5

We have carried out ¹¹⁵In nuclear quadrupole resonance (NQR) measurements in CeRhIn₅. At ambient pressure, CeRhIn₅ undergoes an antiferromagnetic AF phase transition at K. The ¹¹⁵In NQR spectrum has shown the appearance of a small internal field in the direction perpendicular to the tetragonal c-axis. With application of a hydrostatic pressure, the AF state is suppressed and the superconductivity appears just above the critical pressure (P = 17 kbar). The nuclear spin lattice relaxation rate 1/T₁ of ¹¹⁵In measured at P = 27 kbar indicates the occurrence of the superconductivity in the nearly AF region. In the superconducting state, 1/T₁ has no Hebel-Slichter coherence peak just below of 2 K and has a power law T-dependence (T³) down to 300 mK. This is consistent with anisotropic superconductivity, with line nodes in the superconducting energy gap: non-s-wave superconductivity occurs in CeRhIn₅. Received 5 July 2000     

Mössbauer study of the vibrational anisotropy and of the light-induced population of metastable states in single-crystalline guanidinium nitroprusside

M?ssbauer studies were performed on single crystals of guanidinium nitroprusside with different orientations of their principal crystallographic axes (a, b, c) with respect to the incident radiation. The markedly anisotropic Lamb-M?ssbauer factor f _LM , i.e. f _LM ^(a) = 0.118(8), f _LM ^(b) = 0.174(8), f _LM ^(c) = 0.202(8) is in contrast to that of nitroprussides with inorganic anions. The observed anisotropy is ascribed to the anisotropic vibrational mean-square displacement of the nitroprusside anions as a whole which is due to the specific packing of both, anions and cations, as well as the very weak chemical bonding between the ions, typical only for guanidinium nitroprusside. The vibrational anisotropy of iron atoms in barium nitroprusside that has been observed by X-ray structural investigations has a different origin and therefore does not result in an anisotropic Lamb-M?ssbauer factor. We have also investigated metastable states in guanidinium nitroprusside that have been populated by means of incoherent irradiation from light-emitting diodes. With a specific orientation of the guanidinium nitroprusside single crystal a population of the metastable states up to 26% could be achieved. Populations of comparable size on lithium, sodium and potassium nitroprussides have only been reached using coherent laser irradiation. Received 15 December 1998 and Received in final form 3 March 1999     

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998