Kapitza resistance at a domain boundary in linear and nonlinear chains.

We explore Kapitza thermal resistance on the boundary between two homogeneous chain fragments with different characteristics. For a linear model, an exact expression for the resistance is derived. In the generic case of frequency mismatch between the domains, the Kapitza resistance is well defined in the thermodynamic limit. At the same time, in the linear chain, the resistance depends on the thermostat properties and therefore is not a local property of the considered domain boundary. Moreover, if the temperature difference at the ends of the chain is fixed, then neither the temperature drop at the domain boundary nor the heat flux depend on the system size; for the normal transport, one expects the scaling N^{-1} for both. For specific assessment, we consider the case of an isotopic boundary-only the masses in different domains are different. If the domains are nonlinear, but integrable (Toda lattice, elastically colliding particles), the anomalies are similar to the case of linear chain, with the addition of well-articulated thermal dependence of the resistance. For the case of elastically colliding particles, this dependence follows a simple scaling law R_{k}∼T^{-1/2}. For Fermi-Pasta-Ulam domains, both the temperature drop and the heat flux decrease with the chain length, but with different exponents, so the resistance vanishes in the thermodynamic limit. For the domains comprised of rotators, the thermal resistance exhibits the expected normal behavior.

Kapitza thermal resistance in linear and nonlinear chain models: Isotopic defect.

Kapitza resistance in the chain models with internal defects is considered. For the case of the linear chain, the exact analytic solution for the boundary resistance is derived for arbitrary linear time-independent conservative inclusion or defect. A simple case of isolated isotopic defects is explored in more detail. Contrary to the bulk conductivity in the linear chain, the Kapitza resistance is finite. However, the universal thermodynamic limit does not exist in this case. In other terms, the exact value of the resistance is not uniquely defined, and depends on the way of approaching the infinite lengths of the chain fragments. By this reason, and also due to the explicit dependence on the parameters of the thermostats, the resistance cannot be considered as a local property of the defect. Asymptotic scaling behavior of the heat flux in the case of very heavy defect is explored and compared to the nonlinear counterparts; similarities in the scaling behavior are revealed. For the lightweight isotopic defect in the linear chain, one encounters a typical dip of the temperature profile, related to weak excitation of the localized mode in the attenuation zone. If the nonlinear interactions are included, this dip can still appear at a relatively short timescale, with subsequent elimination due to the nonlinear interactions. This observation implies that even in the nonlinear chains, the linear dynamics can predict the main features of the short-time evolution of the thermal profile if the temperature is low enough.

Kinks in chains with on-site bistable nondegenerate potential: Beyond traveling waves.

This paper revisits the well-known transition fronts (kinks) in chains of coupled oscillators with nondegenerate on-site potentials. Usually, such transition fronts are considered in terms of traveling-wave solutions. We explore the loss of stability of such traveling waves. Generically, it corresponds to one of the common scenarios for fixed points of discrete maps. For example, one can encounter the quasiperiodic kink propagation (due to Hopf bifurcation), or the Feigenbaum cascade of period doublings, leading to a chaoticlike propagation pattern. The aforementioned scenarios show up, for instance, for triparabolic and φ^{4} on-site potentials. Numeric evidence suggests that the loss of stability occurs due to resonances between the frequency associated with the kink propagation, and the linear band gaps of the chain. Particular resonance mechanisms are model dependent. For the classical Atkinson-Cabrera model with a biparabolic on-site potential, the stability threshold is estimated by the simple means of linear algebra. The loss of stability in this model occurs through Hopf bifurcation. The results are in good agreement with numerical simulations.

Introduction to a topical issue 'nonlinear energy transfer in dynamical and acoustical Systems'.

This topical issue is devoted to recent developments in the broader field of energy transfer across scales in nonlinear dynamical and acoustical systems. Nonlinear energy transfers are common in Nature, with perhaps the most famous example being energy cascading from large to small length scales in turbulent flows. Yet nonlinearity has been traditionally perceived either as an unavoidable nuisance or as an unwelcome design restriction in engineering systems. Nowadays, however, this trend is reversing, with nonlinear phenomena being intensely studied in diverse disciplines. Furthermore, strong nonlinearity is now intentionally used and explored in a variety of mechanical and physical settings, such as granular media, acoustic metamaterials, nonlinear energy sinks, essentially nonlinear and nonlocal lattices, vibro-impact oscillators, vibration and shock isolation systems, nanotechnology, biomimetic systems, microelectronics, energy harvesters and in other applications. This topical issue is an attempt to document in a single volume some of these recent research developments, in order to establish a common basis and provide motivation and incentive for further development. The aim is to discuss and compare theoretical and experimental approaches pursued by research groups in different areas, and describe the state of the art of nonlinear energy transfer phenomena in an as broad as possible range of applications of current interest.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold.

We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow flow using the action-angle (AA) formalism. Exact inversion of the action-energy dependence for the linear oscillator with impact constraints is not possible. This difficulty, typical for many models of nonlinear oscillators, is circumvented by matching the asymptotic expansions for the linear and impact limits. The obtained energy-action relation enables the complete analysis of the slow flow and the accurate description of the critical delocalization transition. The transition from the localization regime to the energy-exchange regime is captured by prediction of the critical coupling value. Accurate prediction of the delocalization transition requires a detailed account of the coupling energy with appropriate redefinition and optimization of the limiting phase trajectory on the resonant manifold.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials.

We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.

The association between systemic lupus erythematosus and bipolar disorder - a big data analysis.

BACKGROUND: Systemic lupus erythematosus (SLE) is a chronic, autoimmune disease that has a wide variety of physical manifestations, including neuropsychiatric features. Bipolar disorder (BD) is a chronic, episodic illness, that may present as depression or as mania. The objective of this study was to investigate the association between SLE and BD using big data analysis methods. METHODS: Patients with SLE were compared with age- and sex-matched controls regarding the prevalence of BD in a cross-sectional study. Chi-square and t-tests were used for univariate analysis and a logistic regression model was used for multivariate analysis, adjusting for confounders. The study was performed utilizing the chronic disease registry of Clalit Health Services medical database. RESULTS: The study included 5018 SLE patients and 25,090 matched controls. BD was found in a higher prevalence among SLE patients compared to controls (0.62% vs. 0.26%, respectively, P<0.001). BD patients had a greater prevalence of smokers compared to non-BD patients (62.5% vs 23.5%, respectively, P<0.001). In a multivariate analysis, smoking and SLE were both found to be significantly associated with BD. CONCLUSIONS: SLE was found to be independently associated with BD. These findings may imply that an autoimmune process affecting the central nervous system among SLE patients facilitates the expression of concomitant BD.

Flat bands and compactons in mechanical lattices.

Local configurational symmetry in lattice structures may give rise to stationary, compact solutions, even in the absence of disorder and nonlinearity. These compact solutions are related to the existence of flat dispersion curves (bands). Nonlinearity can destabilize such compactons. One common flat-band-generating system is the one-dimensional cross-stitch model, in which compactons were shown to exist for the photonic lattice with Kerr nonlinearity. The compactons exist there already in the linear regime and are not generally destructed by that nonlinearity. Smooth nonlinearity of this kind does not permit performing complete stability analysis for this chain. We consider a discrete mechanical system with flat dispersion bands, in which the nonlinearity exists due to impact constraints. In this case, one can use the concept of the saltation matrix for the analytic construction of the monodromy matrix. Besides, we consider a smooth nonlinear lattice with linearly connected massless boxes, each containing two symmetric anharmonic oscillators. In this model, the flat bands and discrete compactons also readily emerge. This system also permits performing comprehensive stability analysis, at least in the anticontinuum limit, due to the reduced number of degrees of freedom. In both systems, there exist two types of localization. The first one is the complete localization, and the second one is the more common exponential localization. The latter type is associated with discrete breathers (DBs). Two principal mechanisms for the loss of stability are revealed. The first one is the possible internal instability of the symmetric and/or antisymmetric solution in the individual unit cell of the chain. One can interpret this instability pattern as internal resonance between the compacton and the DB. The other mechanism is global instability related to resonance of the stationary solution with the propagation frequencies. Different instability mechanisms lead to different bifurcations at the stability threshold.

Discrete breathers in an array of self-excited oscillators: Exact solutions and stability.

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions-discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.

Accelerating oscillatory fronts in a nonlinear sonic vacuum with strong nonlocal effects.

We describe and explore accelerating oscillatory fronts in sonic vacua with nonlocal interactions. As an example, a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends, is considered. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. Position of the front obeys the scaling law l(t) ∼ t(4/3). The frequency of the oscillatory tail remains constant, and the wavelength scales as λ ∼ t(1/3). These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initiate the front propagation. The initiation threshold is evaluated on the basis of a simplified discrete model, further reduced to a completely integrable nonlinear system. Given their simplicity, nonlinear sonic vacua of the type considered herein should be common in periodic lattices.

Anti-citrullinated-protein-antibody-specific intravenous immunoglobulin attenuates collagen-induced arthritis in mice.

Administration of intravenous immunoglobulin (IVIg) is a recognized safe and efficient immunomodulation therapy for many autoimmune diseases. Anti-idiotypic antibody binding to pathogenic autoantibodies was proposed as one of the mechanisms attributed to the protective activity of IVIg in autoimmunity. The aim of this study was to fractionate the anti-anti-citrullinated protein anti-idiotypic-antibodies (anti-ACPA) from an IVIg preparation and to test it as a treatment for collagen-induced arthritis in mice. IVIg was loaded onto an ACPA column. The eluted fraction was defined as ACPA-specific-IVIg (ACPA-sIVIg). Collagen-induced-arthritis (CIA) was induced in mice. Mice were treated weekly with ACPA-sIVIg, low-dose-IVIg, high-dose-IVIg and phosphate-buffered saline (PBS). Sera-ACPA titres, anti-collagen anitbodies and cytokine levels were analysed by enzyme-linked immunosorbent assay (ELISA); antibody-forming-cell activity by enzyme-linked imunospot (ELISPOT) assay; and expansion of regulatory T cell (Treg ) population by fluorescence activated cell sorter (FACS). ACPA-sIVIg inhibited ACPA binding to citrullinated-peptides (CCP) in vitro 100 times more efficiently than the IVIg compound. ACPA-sIVIg was significantly more effective than the IVIg-preparation in attenuating the development of collagen-induced arthritis. Splenocytes from CIA mice treated with ACPA-sIVIg reduced the ACPA and anti-collagen-antibody titres, including the number of anti-collagen and ACPA antibody-forming cells. In parallel, splenocytes from ACPA-sIVIg treated mice secreted higher levels of anti-inflammatory cytokines and lower proinflammatory cytokines. The ACPA-sIVIg inhibitory potential was accompanied with expansion of the Treg population. Low-dose IVIg did not affect the humoral and cellular response in the CIA mice in comparison to the PBS-treated mice. Based on our results, IVIg may be considered as a safe compound for treating patients with rheumatoid arthritis by neutralizing pathogenic autoantibodies, reducing proinflammatory cytokines and expanding the Treg population.

Heat conduction in a chain of dissociating particles: Effect of dimensionality.

The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials--hard repulsive core, quasilinear behavior in a ground state, and possibility of dissociation. It has become clear recently that this latter feature has crucial effect on convergence of the heat conduction coefficient in thermodynamic limit. We demonstrate that in one-dimensional chain of elastic particles with hard core the heat conduction coefficient also converges, as one could expect. Then we explore effect of dimensionality on the heat transport in this model. For this sake, longitudinal and transversal motions of the particles are allowed in a long narrow channel. With varying width of the channel, we observe sharp transition from "one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction coefficient drops by about order of magnitude for relatively small widening of the channel. This transition is not unique for the considered system. Similar phenomenon of transition to quasi-1D behavior with growth of aspect ratio of the channel is observed also in a gas of densely packed hard (billiard) particles, both for two- and three-dimensional cases. It is the case despite the fact that the character of transition in these two systems is not similar, due to different convergence properties of the heat conductivity. In the billiard model, the divergence pattern of the heat conduction coefficient smoothly changes from logarithmic to power-like law with increase of the length.

A randomized double-blind placebo-controlled study adding high dose vitamin D to analgesic regimens in patients with musculoskeletal pain.

BACKGROUND: The current mode of therapy for many patients with musculoskeletal pain is unsatisfactory. PURPOSE: We aimed to assess the impact of adding 4000 IU of vitamin D on pain and serological parameters in patients with musculoskeletal pain. MATERIALS AND METHODS: This was a randomized, double-blinded and placebo-controlled study assessing the effect of 4000 IU of orally given vitamin D3 (cholecalciferol) (four gel capsules of 1000 IU, (SupHerb, Israel) vs. placebo on different parameters of pain. Eighty patients were enrolled and therapy was given for 3 months. Parameters were scored at three time points: prior to intervention, at week 6 and week 12. Visual analogue scale (VAS) scores of pain perception were recorded following 6 and 12 weeks. We also measured serum levels of leukotriene B4 (LTB4), interleukin 6 (IL-6), tumor necrosis factor alpha (TNFα) and prostaglandin E2 (PGE2) by ELISA. RESULTS: The group receiving vitamin D achieved a statistically significant larger decline of their VAS measurement throughout the study compared with the placebo group. The need for analgesic 'rescue therapy' was significantly lower among the vitamin D-treated group. TNFα levels decreased by 54.3% in the group treated with vitamin D and increased by 16.1% in the placebo group. PGE2 decreased by39.2% in the group treated with vitamin D and increased by 16% in the placebo group. LTB4 levels decreased in both groups by 24% (p < 0.05). CONCLUSION: Adding 4000 IU of vitamin D for patients with musculoskeletal pain may lead to a faster decline of consecutive VAS scores and to a decrease in the levels of inflammatory and pain-related cytokines.

Front propagation in a bistable system: how the energy is released.

In this Rapid Communication we consider a front of transition between metastable and stable states in a conservative system. Due to the difference of energies between initial and finite states, such transition front can propagate only while radiating energy. A simulation of such a process in a one-dimensional nonlinear lattice shows an essential imbalance between the energy released in each act of transition, and the density of energy of oscillations behind the front. It means that the stationary front propagation must be accompanied by an essentially nonstationary radiative process. We reveal the origin of this phenomenon and show that the characteristics of the front propagation critically depend on boundary conditions. In the framework of a simple model of a bistable system we propose analytic evaluation of all important features of the transition process, such as front velocity, radiation frequency, and oscillation amplitude. All calculated values are in good agreement with numerical simulation data.

Mechanical control of heat conductivity in molecular chains.

We discuss a possibility to control heat conductivity in molecular chains by means of external mechanical loads. To illustrate such possibilities we consider first well-studied one-dimensional chain with degenerate double-well potential of the nearest-neighbor interaction. We consider varying lengths of the chain with fixed number of particles. Number of possible energetically degenerate ground states strongly depends on the overall length of the chain, or, in other terms, on average length of the link between neighboring particles. These degenerate states correspond to mechanical equilibria; therefore, one can say that formation of such structures mimics a process of plastic deformation. We demonstrate that such modification of the chain length can lead to quite profound (almost fivefold) reduction of the heat conduction coefficient. Even more profound effect is revealed for a model with a single-well nonconvex potential. It is demonstrated that in a certain range of constant external forcing, this model becomes effectively double-well and has a multitude of possible states of equilibrium for fixed value of the external load. Due to this degeneracy, the heat-conduction coefficient can be reduced by two orders of magnitude. We suggest a mechanical model of a chain with periodic double-well potential, which allows control of the heat transport. The models considered may be useful for description of heat transfer in biological macromolecules and for control of the heat transport in microsystems. The possibility of the heat transport control in more realistic three-dimensional systems is illustrated by simulation of a three-dimensional model of polymer α-helix. In this model, the mechanical stretching also brings about the structural inhomogeneity and, in turn, to essential reduction of the heat conductivity.

Exact solutions for discrete breathers in a forced-damped chain.

Exact solutions for symmetric on-site discrete breathers (DBs) are obtained in a forced-damped linear chain with on-site vibro-impact constraints. The damping in the system is caused by inelastic impacts; the forcing functions should satisfy conditions of periodicity and antisymmetry. Global conditions for existence and stability of the DBs are established by a combination of analytic and numeric methods. The DB can lose its stability through either pitchfork, or Neimark-Sacker bifurcations. The pitchfork bifurcation is related to the internal dynamics of each individual oscillator. It is revealed that the coupling can suppress this type of instability. To the contrary, the Neimark-Sacker bifurcation occurs for relatively large values of the coupling, presumably due to closeness of the excitation frequency to a boundary of the propagation zone of the chain. Both bifurcation mechanisms seem to be generic for the considered type of forced-damped lattices. Some unusual phenomena, like nonmonotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the initial system and illustrated numerically for small periodic lattices.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Nonstationary heat conduction in one-dimensional models with substrate potential.

The paper investigates nonstationary heat conduction in one-dimensional models with substrate potential. To establish universal characteristic properties of the process, we explore three different models: Frenkel-Kontorova (FK), phi4+ (φ(4)+), and phi4- (φ(4)-). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with the parabolic Fourier equation of heat conduction and clearly demonstrates the necessity for hyperbolic corrections in the phenomenological description of the heat conduction process. The crossover wavelength decreases with an increase in the average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for the temperature field is justified. In all models investigated, the relaxation of thermal perturbations is exponential, contrary to a linear chain, where it follows a power law. The most popular lowest-order hyperbolic generalization of the Fourier law, known as the Cattaneo-Vernotte or telegraph equation, is also not valid for the description of the observed behavior of the models with the substrate potential, since the characteristic relaxation time in an oscillatory regime strongly depends on the excitation wavelength. For some of the models, this dependence seems to obey a simple scaling law.

Discrete breathers in vibroimpact chains: analytic solutions.

We present exact analytic solutions for discrete breathers in essentially nonlinear oscillatory chains, belonging to both of the most common universality classes (Klein-Gordon and Fermi-Pasta-Ulam). The exact solutions can be obtained due to use of vibroimpact potentials, combining extreme nonlinearity with the possibility of description in terms of a forced linear model under conditions of self-consistency. A crossover between the cases of high and low energies can be studied directly. The solutions obtained may be used as a high-energy limit for models with other realistic potentials, as well as benchmarks for the testing of approximate approaches in the theory of discrete breathers.

Heat conduction in a one-dimensional chain of hard disks with substrate potential.

Heat conduction in a one-dimensional chain of equivalent rigid particles in the field of the external on-site potential is considered. The zero diameters of the particles correspond to the integrable case with the divergent heat conduction coefficient. By means of a simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters, and good agreement is observed.