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M-N-C catalysts, incorporating non-precious metal ions (e.g., M = Fe or Co) within a nitrogen-doped carbon support, are the focus of broad interest for electrochemical O(2) reduction and aerobic oxidation reactions. The present study explores the mechanistic relationship between the O(2) reduction mechanism under electrochemical and chemical conditions. Chemical O(2) reduction is investigated via aerobic oxidation of a hydroquinone, in which the O–H bonds supply the protons and electrons needed for O(2) reduction to water. Mechanistic studies have been conducted to elucidate whether the M-N-C catalyst couples two independent half-reactions (IHR), similar to electrode-mediated processes, or mediates a direct inner-sphere reaction (ISR) between O(2) and the organic molecule. Kinetic data support the latter ISR pathway. This conclusion is reinforced by rate/potential correlations that reveal significantly different Tafel slopes, implicating different mechanisms for chemical and electrochemical O(2) reduction.

Objective: Investigate the performance of multiparametric MRI radiomic features, alone or combined with current standard-of-care methods, for pulmonary nodule classification. Assess the impact of segmentation variability on feature reproducibility and reliability. Methods: Radiomic features were extracted from 74 pulmonary nodules of 68 patients who underwent nodule resection or biopsy after MRI exam. The MRI features were compared with histopathology and conventional quantitative imaging values (maximum standardized uptake value [SUVmax] and mean Hounsfield unit [HU]) to determine whether MRI radiomic features can differentiate types of nodules and associate with SUVmax and HU using Wilcoxon rank sum test and linear regression. Diagnostic performance of features and four machine learning (ML) models were evaluated with area under the receiver operating characteristic curve (AUC) and 95% confidence intervals (CIs). Concordance correlation coefficient (CCC) assessed the segmentation variation impact on feature reproducibility and reliability. Results: Elevn diffusion-weighted features distinguished malignant from benign nodules (adjusted p < 0.05, AUC: 0.73–0.81). No features differentiated cancer types. Sixty-seven multiparametric features associated with mean CT HU and 14 correlated with SUVmax. All significant MRI features outperformed traditional imaging parameters (SUVmax, mean HU, apparent diffusion coefficient [ADC], T1, T2, dynamic contrast-enhanced imaging values) in distinguishing malignant from benign nodules with some achieving statistical significance (p < 0.05). Adding ADC and smoking history improved feature performance. Machine learning models demonstrated strong performance in nodule classification, with extreme gradient boosting (XGBoost) having the highest discrimination (AUC = 0.83, CI=[0.727, 0.932]). We found good to excellent inter- and intrareader feature reproducibility and reliability (CCC≥0.80). Conclusion: Eleven MRI radiomic features differentiated malignant from benign lung nodules, outperforming traditional quantitative methods. MRI radiomic ML models demonstrated good nodule classification performances with XGBoost superior to three others. There was good to excellent inter- and intrareader feature reproducibility and reliability. Advances in knowledge: Our study identified MRI radiomic features that successfully differentiated malignant from benign lung nodules and demonstrated high performance of our MR radiomic feature-based ML models for nodule classification. These new findings could help further establish thoracic MRI as a non-invasive and radiation-free alternative to standard practice for pulmonary nodule assessment.

Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated solitary-wave solutions to the steady gravity-capillary Whitham equation with weak surface tension. Through the application of the center manifold theorem, the nonlocal equation for the solitary wave profiles is reduced to a four-dimensional system of ODEs inheriting reversibility. Along particular parameter curves, relating directly to the classical gravity-capillary water wave problem, the associated linear operator is seen to undergo either a reversible $0^{2+}(i k_0)$ bifurcation or a reversible $(i s)^2$ bifurcation. Through a normal form transformation, the reduced system of ODEs along each relevant parameter curve is seen to be well approximated by a truncated system retaining only second-order or third-order terms. These truncated systems relate directly to systems obtained in the study of the full gravity-capillary water wave equation and, as such, the existence of generalized and modulated solitary waves for the truncated systems is guaranteed by classical works, and they are readily seen to persist as solutions of the gravity-capillary Whitham equation due to reversibility. Consequently, this work illuminates further connections between the gravity-capillary Whitham equation and the full two-dimensional gravity-capillary water wave problem., 35 pages, 4 figures. Some mathematical typos fixed

We study the bifurcation of periodic travelling waves of the capillary–gravity Whitham equation. This is a nonlinear pseudo-differential equation that combines the canonical shallow water nonlinearity with the exact (unidirectional) dispersion for finite-depth capillary–gravity waves. Starting from the line of zero solutions, we give a complete description of all small periodic solutions, unimodal as well bimodal, using simple and double bifurcation via Lyapunov–Schmidt reductions. Included in this study is the resonant case when one wavenumber divides another. Some bifurcation formulas are studied, enabling us, in almost all cases, to continue the unimodal bifurcation curves into global curves. By characterizing the range of the surface tension parameter for which the integral kernel corresponding to the linear dispersion operator is completely monotone (and, therefore, positive and convex; the threshold value for this to happen turns out to be $$T = \frac{4}{\pi ^2}$$, not the critical Bond number $$\frac{1}{3}$$), we are able to say something about the nodal properties of solutions, even in the presence of surface tension. Finally, we present a few general results for the equation and discuss, in detail, the complete bifurcation diagram as far as it is known from analytical and numerical evidence. Interestingly, we find, analytically, secondary bifurcation curves connecting different branches of solutions and, numerically, that all supercritical waves preserve their basic nodal structure, converging asymptotically in $$L^2(\mathbb {S})$$ (but not in $$L^\infty $$) towards one of the two constant solution curves.

We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques, we show that for small surface tension (corresponding to Bond numbers between $0$ and ${1}/{3}$) there exists small amplitude solitary waves that decay to asymptotically small periodic waves at spatial infinity. The size of the oscillations in the far field are shown to be small beyond all algebraic orders in the amplitude of the wave. We also present numerical evidence, based on the recent analytical work of Hur \& Johnson, that the asymptotic end states are modulationally stable for all Bond numbers between $0$ and $1/3$.

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions., Comment: 46 pages, 2 figures

The development of processes for electrochemical energy conversion and chemical production could benefit from new strategies to interface chemical redox reactions with electrodes. Here, we employ a diffusible low-potential organic redox mediator, 9,10-anthraquinone-2,7-disulfonic acid (AQDS), to promote efficient electrochemical oxidation of H(2) at an off-electrode heterogeneous catalyst. This unique approach to integrate chemical and electrochemical redox processes accesses power densities up to 228 mW/cm(2) (528 mW/cm(2) with iR-correction). These values are significantly higher than those observed in previous mediated electrochemical H(2) oxidation methods, including those using enzymes or inorganic mediators. The approach described herein shows how traditional catalytic chemistry can be coupled to electrochemical devices.

Summary New methods for interconversion of electrical and chemical energy are crucial to addressing emerging challenges in renewable energy storage and conversion. Dissolved redox mediators provide an effective means to transport electrons (and protons) between an electrode and catalysts that are not in direct physical contact with an electrode. Mediators are widely implemented in biofuel cells, but such devices typically exhibit low power densities. Here, we report the development of a tetrasubstituted quinone mediator that exhibits excellent stability under strongly acidic conditions and supports electrochemical reduction of O2 at an off-electrode heterogeneous cobalt catalyst contained within a packed-bed reactor. Efficient oxidation of the hydroquinone by O2 in the reactor provides the basis for mediator regeneration, and an integrated “flow-cathode” fuel cell system supports high power densities. These results establish the combination of organic mediators with off-electrode heterogeneous catalysts as a versatile platform for development of new electrode-driven chemical redox transformations.

We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evans-Lopatinski determinant analogous to the periodic Evans function of Gardner in the (smooth) viscous case, obtaining a complete spectral stability diagram useful in hydraulic engineering and related applications. In particular, we obtain an explicit low-frequency stability boundary, which, moreover, matches closely with its (numerically-determined) counterpart in the viscous case. This is seen to be related to but not implied by the associated formal first-order Whitham modulation equations., 45 pages, 11 figures

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity, providing nonlocal model equations that may be expected to exhibit some of the interesting high-frequency phenomena present in the Euler equations that standard "long-wave" theories fail to capture. Of particular interest here is the existence and stability of periodic traveling wave solutions in such models. Using numerical bifurcation techniques we construct global bifurcation diagrams for each system and compare the global structure of branches, together with the possibility of bifurcation branches terminating in a "highest" singular (peaked/cusped) wave. We also numerically approximate the stability spectrum along these bifurcation branches and compare the stability predictions of these models. Our results confirm a number of analytical results concerning the stability of asymptotically small waves in these models and provide new insights into the existence and stability of large amplitude waves., Comment: 36 pages, 19 figures

Quantum dots (QDs) are useful for demonstrating the particle-in-a-box (PIB) model utilized in quantum chemistry, and can readily be applied to a discussion of both thermodynamics and kinetics in an undergraduate laboratory setting. Modifications of existing synthetic procedures were used to create QDs of different sizes and compositions (CdS passivated with polymer, and CdSe passivated with oleic acid/trioctylphosphine). These were investigated by spectroscopy, to which standard 3D PIB mathematical models were applied to determine their effective size. The data were compared to those from other methods for students to see the validity of the PIB model. For CdSe QDs, an empirical formula was applied to the spectroscopic data. In the case of CdS, the synthesized QDs were studied with X-ray diffraction, from which one can also estimate the size of the QDs. Finally, the QDs were utilized as the light-harvesting layer in photovoltaic cells by attachment to a layer of surface-modified titania (TiO2) nanoparticl...

Fluid resuscitation, to restore intravascular volume and improve oxygen delivery, is a crucial step in early resuscitation efforts of patients with sepsis or septic shock. The 2016 Surviving Sepsis Campaign guidelines suggest the use of dynamic versus static measures of fluid responsiveness and fluid resuscitation with at least 30 mL/kg of intravenous crystalloid within the first 3 hours followed by fluid administration if hemodynamic factors continue to improve. Despite these recommendations, risks to this practice may exist as multiple studies have demonstrated an association between a positive fluid balance and/or administration of large fluid volume and increase in mortality. These studies are limited by variations in their methodologic design; therefore, cause and effect cannot yet be determined. Future multicenter, randomized, controlled studies that evaluate fluid balance and fluid volume need to be conducted to clarify the role of fluid administration to patients with sepsis to maximize benefits and minimize risk.

We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable (with asymptotic phase) with exponential rates of decay when subject to $NT$-periodic, i.e., subharmonic, perturbations. However, both the allowable size of perturbations and the exponential rates of decay depend on $N$, and, in particular, they tend to zero as $N\to\infty$, leading to a lack of uniformity in such subharmonic stability results. In this work, we build on recent work by the authors and introduce a methodology that allows us to achieve a stability result for subharmonic perturbations which is uniform in $N$. Our work is motivated by the dynamics of such waves when subject to perturbations which are localized (i.e. integrable on the line), which has recently received considerable attention by many authors., Comment: 24 pages. Updated exposition and incorporated referee comments

We study the linear dynamics of spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. Such $T$-periodic solutions are nonlinearly stable to $NT$-periodic, i.e. subharmonic, perturbations for each $N\in\mathbb{N}$ with exponential decay rates of perturbations of the form $e^{-\delta_N t}$. However, both the exponential rates of decay $\delta_N$ and the allowable size of the initial perturbations tend to $0$ as $N\to\infty$, so that this result is non-uniform in $N$ and, in fact, empty in the limit $N=\infty$. The primary goal of this paper is to introduce a methodology, in the context of the LLE, by which a uniform stability result for subharmonic perturbations may be achieved, at least at the linear level. The obtained uniform decay rates are shown to agree precisely with the polynomial decay rates of localized, i.e. integrable on the real line, perturbations of such spectrally stable periodic solutions of the LLE. This work both unifies and expands on several existing works in the literature concerning the stability and dynamics of such waves, and sets forth a general methodology for studying such problems in other contexts., Comment: 36 pages, 2 figures. Minor typos fixed, some exposition updated

BACKGROUND AND OBJECTIVES Hepatocellular carcinoma (HCC) in patients with hepatitis B virus (HBV) exhibit lower tumor microRNA-26a (miR-26a) expression which is associated with worse outcomes. It is unknown if similar miR-26a loss occurs in HCC developed in other liver diseases. We examined tumor miR-26a expression and its impact on recurrence and mortality in a North American HCC cohort. METHODS MiR-26a levels from tumor and surrounding nontumor liver tissue in 186 subjects were collected. We defined lower tumor expression of miR-26a as

We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant vorticity. When the surface tension coefficient is large, we show that a periodic traveling wave of sufficiently small amplitude is unstable to long wavelength perturbations if the wave number is greater than a critical value, and stable otherwise, similarly to the Benjamin-Feir instability of gravity waves. In the case of weak surface tension, we find intervals of stable and unstable wave numbers, whose boundaries are associated with the extremum of the group velocity, the resonance between the first and second harmonics, the resonance between long and short waves, and a resonance between dispersion and the nonlinearity. For each constant vorticity we show that a periodic traveling wave of sufficiently small amplitude is unstable if the wave number is greater than a critical value, and stable otherwise. Moreover it can be made stable for a sufficiently large vorticity. The results agree with those based upon numerical computations or formal multiple-scale expansions for the physical problem., Comment: 17 pages, 4 figures. References updated

We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. Of particular interest is the existence of a highest, cusped, traveling wave solution, which we obtain as a limiting case at the end of the main bifurcation branch of $2\pi$-periodic traveling wave solutions continuing from the zero state. Unlike the unidirectional Whitham equation, containing only one branch of the full Euler dispersion relation, where such a highest wave behaves like $|x|^{1/2}$ near its crest, the cusped waves obtained here behave like $|x\log|x||$. Although the linear operator involved in this equation can be easily represented in terms of an integral operator, it maps continuous functions out of the H\"older and Lipschitz scales of function spaces by introducing logarithmic singularities. Since the nonlinearity is also of higher order than that of the unidirectional Whitham equation, several parts of our proofs and results deviate from those of the corresponding unidirectional equation, with the analysis of the logarithmic singularity being the most subtle component. This paper is part of a longer research programme for understanding the interplay between nonlinearities and dispersion in the formation of large-amplitude waves and their singularities., Comment: 34 pages, 5 figures

We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion beam at an oblique angle of incidence. Structurally, the linearized operators associated with these fronts have unstable essential spectrum---corresponding to instability of the spatially asymptotic states---and stable point spectrum---corresponding to stability of the transition profile of the front. We show that these waves are linearly orbitally asymptotically stable in appropriate exponentially weighted spaces. While the technical device of exponential weights allows us to accommodate the unstable essential spectrum of individual waves in our linear analysis, it does not shed light on the long-time pattern formation that is observed experimentally and in numerical simulations. To begin to address this issue, we consider a periodic array of unstable front and back solutions. While not an exact solution of the governing equation, this periodic pattern mimics experimentally observed phenomena. Our numerical experiments suggest that the convecting instabilities associated with each individual wave are damped as they pass through transition layers and that this stabilization mechanism underlies the pattern formation seen in experiments., Comment: 31 pages, 14 Figures. Minor update in exposition

We show that periodic traveling waves with sufficiently small amplitudes of the Whitham equation, which incorporates the dispersion relation of surface water waves and the nonlinearity of the shallow water equations, are spectrally unstable to long-wavelengths perturbations if the wave number is greater than a critical value, bearing out the Benjamin–Feir instability of Stokes waves; they are spectrally stable to square integrable perturbations otherwise. The proof involves a spectral perturbation of the associated linearized operator with respect to the Floquet exponent and the small-amplitude parameter. We extend the result to related, nonlinear dispersive equations.

Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation., Comment: 25 pages, 3 figures

We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time behavior is governed by an associated second-order formal Whitham modulation system. A key point is to identify the way in which initial perturbations translate to initial data for this formal system, a task accomplished by detailed estimates on the linearized solution operator about the background wave. Notably, our approach gives both a common theoretical treatment and a complete classification in terms of "phase-coupling" or "-decoupling" of general systems of conservation or balance laws, encompassing cases that had previously been studied separately or not at all. At the same time, our refined description of solutions gives the new result of nonlinear asymptotic stability with respect to localized perturbations in the phase-decoupled case, further distinguishing behavior in the different cases. An interesting technical aspect of our analysis is that for systems of conservation laws the Whitham modulation description is of system rather than scalar form, as a consequence of which renormalization methods such as have been used to treat the reaction-diffusion case in general do not seem to apply., 63 pages

Our previous work has shown that antigens adjuvanted with ligands specific for Toll-like receptor 4 (TLR4) and TLR7/8 encapsulated in poly(lactic-co-glycolic) acid (PLGA)-based nanoparticles (NPs) induce robust and durable immune responses in mice and macaques. We investigated the efficacy of these NP adjuvants in inducing protective immunity against simian immunodeficiency virus (SIV). Rhesus macaques (RMs) were immunized with NPs containing TLR4 and TLR7/8 agonists mixed with soluble recombinant SIVmac239-derived envelope (Env) gp140 and Gag p55 (protein) or with virus-like particles (VLPs) containing SIVmac239 Env and Gag. NP-adjuvanted vaccines induced robust innate responses, antigen-specific antibody responses of a greater magnitude and persistence, and enhanced plasmablast responses compared to those achieved with alum-adjuvanted vaccines. NP-adjuvanted vaccines induced antigen-specific, long-lived plasma cells (LLPCs), which persisted in the bone marrow for several months after vaccination. NP-adjuvanted vaccines induced immune responses that were associated with enhanced protection against repeated low-dose, intravaginal challenges with heterologous SIVsmE660 in animals that carried TRIM5α restrictive alleles. The protection induced by immunization with protein-NP correlated with the prechallenge titers of Env-specific IgG antibodies in serum and vaginal secretions. However, no such correlate was apparent for immunization with VLP-NP or alum as the adjuvant. Transcriptional profiling of peripheral blood mononuclear cells isolated within the first few hours to days after primary vaccination revealed that NP-adjuvanted vaccines induced a molecular signature similar to that induced by the live attenuated yellow fever viral vaccine. This systems approach identified early blood transcriptional signatures that correlate with Env-specific antibody responses in vaginal secretions and protection against infection. These results demonstrate the adjuvanticity of the NP adjuvant in inducing persistent and protective antibody responses against SIV in RMs with implications for the design of vaccines against human immunodeficiency virus (HIV). IMPORTANCE The results of the RV144 HIV vaccine trial, which demonstrated a rapid waning of protective immunity with time, have underscored the need to develop strategies to enhance the durability of protective immune responses. Our recent work in mice has highlighted the capacity of nanoparticle-encapsulated TLR ligands (NP) to induce potent and durable antibody responses that last a lifetime in mice. In the present study, we evaluated the ability of these NP adjuvants to promote robust and durable protective immune responses against SIV in nonhuman primates. Our results demonstrate that immunization of rhesus macaques with NP adjuvants mixed with soluble SIV Env or a virus-like particle form of Env (VLP) induces potent and durable Env-specific antibody responses in the serum and in vaginal secretions. These responses were superior to those induced by alum adjuvant, and they resulted in enhanced protection against a low-dose intravaginal challenge with a heterologous strain of SIV in animals with TRIM5a restrictive alleles. These results highlight the potential for such NP TLR L adjuvants in promoting robust and durable antibody responses against HIV in the next generation of HIV immunogens currently being developed.

International audience; In this note, we announce a complete classification of the stability of periodic roll-wave solutions of the viscous shallow water equations, from their onset at Froude number F approximate to 2 up to the infinite Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F and the boundaries of the region of stable periods, which appears potentially useful in hydraulic engineering applications. In the asymptotic regime F. 2(onset), we provide an analytic expression of the stability boundaries, whereas in the limit F -> infinity, we show that roll waves are always unstable.

International audience; In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized (L1 ) perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.

We consider the stability of periodic travelling-wave solutions to a generalized Korteweg–de Vries (gKdV) equation and prove an index theorem relating the number of unstable and potentially unstable eigenvalues to geometric information on the classical mechanics of the travelling-wave ordinary differential equation. We illustrate this result with several examples, including the integrable KdV and modified KdV equations, the L2-critical KdV-4 equation that arises in the study of blow-up and the KdV-½ equation, which is an idealized model for plasmas.

Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian rate of spatially periodic traveling waves of systems of reaction–diffusion equations. In the case that wave-speed is identically zero for all periodic solutions, we recover and slightly sharpen a well-known result of Schneider obtained by renormalization/Bloch transform techniques; by the same arguments, we are able to treat the open case of nonzero wave-speeds to which Schneiderʼs renormalization techniques do not appear to apply.

We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to exhibit examples of metastable solitary waves for the St. Venant equations, with stable point spectrum indicating coherence of the wave profile but unstable essential spectrum indicating oscillatory convective instabilities shed in its wake. We propose a mechanism based on ``dynamic spectrum'' of the wave profile, by which a wave train of solitary pulses can stabilize each other by de-amplification of convective instabilities as they pass through successive waves. We present numerical time evolution studies supporting these conclusions, which bear also on the possibility of stable periodic solutions close to the homoclinic. For the closely related viscous Jin-Xin model, by contrast, for which the essential spectrum is stable, we show using the stability index of Gardner--Zumbrun that solitary wave pulses are always exponentially unstable, possessing point spectra with positive real part., Comment: 42 pages, 9 figures

In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.