Analytical Study of Diffusive Relativistic Shock Acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.Comment: 4 pages, 2 figures, PRL accepted, minor change

Deep Chandra observation and numerical studies of the nearest cluster cold front in the sky

We present the results of a very deep (500 ks) Chandra observation, along with tailored numerical simulations, of the nearest, best resolved cluster cold front in the sky, which lies 90 kpc (19 arcmin) to the north-west of M 87. The northern part of the front appears the sharpest, with a width smaller than 2.5 kpc (1.5 Coulomb mean free paths; at 99 per cent confidence). Everywhere along the front, the temperature discontinuity is narrower than 4–8 kpc and the metallicity gradient is narrower than 6 kpc, indicating that diffusion, conduction and mixing are suppressed across the interface. Such transport processes can be naturally suppressed by magnetic fields aligned with the cold front. Interestingly, comparison to magnetohydrodynamic simulations indicates that in order to maintain the observed sharp density and temperature discontinuities, conduction must also be suppressed along the magnetic field lines. However, the northwestern part of the cold front is observed to have a non-zero width. While other explanations are possible, the broadening is consistent with the presence of Kelvin–Helmholtz instabilities (KHI) on length-scales of a few kpc. Based on comparison with simulations, the presence of KHI would imply that the effective viscosity of the intracluster medium is suppressed by more than an order of magnitude with respect to the isotropic Spitzer-like temperature dependent viscosity. Underneath the cold front, we observe quasi-linear features that are ∼10 per cent brighter than the surrounding gas and are separated by ∼15 kpc from each other in projection. Comparison to tailored numerical simulations suggests that the observed phenomena may be due to the amplification of magnetic fields by gas sloshing in wide layers below the cold front, where the magnetic pressure reaches ∼5–10 per cent of the thermal pressure, reducing the gas density between the bright features

Self-Similar Collisionless Shocks

Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and that a previously suggested model for the generation of large scale magnetic fields through a hierarchical merger of current-filaments should be generalized. A numerical experiment testing our analysis is outlined (Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth

The spectrum of particles accelerated in relativistic, collisionless shocks

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s = (3beta_u - 2beta_u*beta_d^2 + beta_d^3) / (beta_u - beta_d) for isotropic diffusion, where beta_u (beta_d) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta_u,beta_d), and yields s=38/9 in the ultra-relativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and for constraining non-isotropic diffusion results. It implies that the spectrum is highly sensitive to the form of the diffusion function for particles travelling along the shock front.Comment: 4 pages, 1 figur

Evaluation of a two-way SMS messaging strategy to reduce neonatal mortality: rationale, design and methods of the Mobile WACh NEO randomised controlled trial in Kenya

Abstract: Introduction Globally, approximately half of the estimated 6.3 million under-5 deaths occur in the neonatal period (within the first 28 days of life). Kenya ranks among countries with the highest number of neonatal deaths, at 20 per 1000 live births. Improved identification and management of neonates with potentially life-threatening illness is critical to meet the WHO’s target of ≤12 neonatal deaths per 1000 live births by 2035. We developed an interactive (two-way) short messaging service (SMS) communication intervention, Mobile Solutions for Neonatal Health (Mobile women’s and children’s health (WACh) NEO), focused on the perinatal period. Mobile WACh NEO sends automated tailored SMS messages to mothers during pregnancy and up to 6 weeks post partum. Messages employ the Information-Motivation-Behaviour Skills framework to promote (1) maternal implementation of essential newborn care (ENC, including early, exclusive breast feeding, cord care and thermal care), (2) maternal identification of neonatal danger signs and care-seeking, and (3) maternal social support and self-efficacy. Participants can also send SMS to the study nurse, enabling on-demand remote support. Methods and analysis We describe a two-arm unblinded randomised controlled trial of the Mobile WACh NEO intervention. We will enrol 5000 pregnant women in the third trimester of pregnancy at 4 facilities in Kenya and randomise them 1:1 to receive interactive SMS or no SMS (control), and conduct follow-up visits at 2 and 6 weeks post partum. Neonatal mortality will be compared between arms as the primary outcome. Secondary outcomes include care-seeking, practice of ENC and psychosocial health. Exploratory analysis will investigate associations between maternal mental health, practice of ENC, care-seeking and SMS engagement. Ethics and dissemination This study received ethical approval from the University of Washington (STUDY00006395), Women and Infants Hospital (1755292-1) and Kenyatta National Hospital/University of Nairobi (P310/04/2019). All participants will provide written informed consent. Findings will be published in peer-reviewed journals and international conferences

Interlayer Registry Determines the Sliding Potential of Layered Metal Dichalcogenides: The case of 2H-MoS2

We provide a simple and intuitive explanation for the interlayer sliding energy landscape of metal dichalcogenides. Based on the recently introduced registry index (RI) concept, we define a purely geometrical parameter which quantifies the degree of interlayer commensurability in the layered phase of molybdenum disulphide (2HMoS2). A direct relation between the sliding energy landscape and the corresponding interlayer registry surface of 2H-MoS2 is discovered thus marking the registry index as a computationally efficient means for studying the tribology of complex nanoscale material interfaces in the wearless friction regime.Comment: 13 pages, 7 figure

Characterization of Turing diffusion-driven instability on evolving domains

In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linearising the original system along a spatially independent solution). This framework allows for the inclusion of the analysis of the long-time behavior of the solutions of reaction-diffusion systems. Applications to two special types of evolving domains are considered: (i) time-dependent domains which evolve to a final limiting fixed domain and (ii) time-dependent domains which are eventually time periodic. Reaction-diffusion systems have been widely proposed as plausible mechanisms for pattern formation in morphogenesis

Intermediate Asymptotics of the Kerr Quasinormal Spectrum

We study analytically the quasinormal mode spectrum of near-extremal (rotating) Kerr black holes. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature T_{BH} and its horizon's angular velocity \Omega, which is valid in the intermediate asymptotic regime 1<<\omega<<1/T_{BH}.Comment: 4 page

Global stability of enzymatic chain of full reversible Michaelis-Menten reactions

International audienceWe consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi- steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems