Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity

Let $J \in C(\mathbb{R})$, $J\ge 0$, \int_{\tiny\mathbb{R}} J = 1 and consider the nonlocal diffusion operator $\mathcal{M}[u] = J \star u - u$. We study the equation $\mathcal{M} u + f(x,u) = 0$, $u \ge 0$, in $\mathbb{R}$, where $f$ is a KPP-type nonlinearity, periodic in $x$. We show that the principal eigenvalue of the linearization around zero is well defined and that a nontrivial solution of the nonlinear problem exists if and only if this eigenvalue is negative. We prove that if, additionally, $J$ is symmetric, then the nontrivial solution is unique

High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc

We study the octet SS-PP correlator within resonance chiral theory up to the one-loop level, i.e., up to next-to-leading order in the 1/Nc expansion. We will require that our correlator follows the power behaviour prescribed by the operator product expansion at high euclidian momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high-energy behaviour will be demanded for the whole correlator, not for individual absorptive channels. The amplitude is progressively improved by considering more and more complicated operators in the hadronic lagrangian. Matching the resonance chiral theory result with chiral perturbation theory at low energies produces the estimates L_8(mu)^{SU(3)} = (1.0+-0.4)10^-3 and C_{38}(mu)^{SU(3)} = (8+-5) 10^-6 for mu=770 MeV. The effect of alternative renormalization schemes is also discussed in the article.Comment: 40 pages, 18 figure

Statistical Properties of Avalanches in Networks

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some probability, then stimulate subsequent firings of the nodes to which it is connected, resulting in a cascade of firings. This type of process is relevant to a wide variety of situations, including neuroscience, cascading failures on electrical power grids, and epidemology. We find that the statistics of avalanches can be characterized in terms of the largest eigenvalue and corresponding eigenvector of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches. Our results apply to individual networks (rather than network ensembles) and provide expressions for the distributions of size and duration of avalanches starting at particular nodes in the network. These findings might find application in the analysis of branching processes in networks, such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of size and duration of neuronal avalanches), are robust to complex underlying network topologies.Comment: 11 pages, 7 figure

Network connectivity during mergers and growth: optimizing the addition of a module

The principal eigenvalue $\lambda$ of a network's adjacency matrix often determines dynamics on the network (e.g., in synchronization and spreading processes) and some of its structural properties (e.g., robustness against failure or attack) and is therefore a good indicator for how ``strongly'' a network is connected. We study how $\lambda$ is modified by the addition of a module, or community, which has broad applications, ranging from those involving a single modification (e.g., introduction of a drug into a biological process) to those involving repeated additions (e.g., power-grid and transit development). We describe how to optimally connect the module to the network to either maximize or minimize the shift in $\lambda$, noting several applications of directing dynamics on networks.Comment: 7 pages, 5 figure

Photoluminescence characterization of single heterojunction quantum well structures

A photoluminescence emission band at 830 nm has been detected in single heterojunction quantum well structures (modulation‐doped structures) in the range of 250–400 K. This emission band is observed neither in heterojunction structures without a two‐dimensional electron gas (2DEG), nor in n+ AlGaAs and GaAs. The intensity of the emission band increases as the mobility of the samples with 2DEG and shows excitonic behavior in its variation with incident laser excitation intensity. This photoluminescence emission was observed in samples grown by both molecular beam epitaxy and by organometallic vapor phase epitaxy. This effect may be useful as a rough identification of high quality, modulation‐doped heterostructures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71007/2/APPLAB-50-1-43-1.pd

Linear and nonlinear optical responses in the chiral multifold semimetal RhSi

Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and non-linear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of different kinds of multifold fermions. The characteristic features of the CPGE, which displays a sign change at 0.4 eV and a large non-quantized response peak of around 160 $\mu \textrm{A V}^{-2}$ at 0.7 eV, are explained by assuming that the chemical potential crosses a flat hole band at the Brillouin zone center. Our theory predicts that, in order to observe a quantized CPGE in RhSi, it is necessary to increase the chemical potential as well as the quasiparticle lifetime. More broadly our methodology, especially the development of the broadband terahertz emission spectroscopy, could be widely applied to study photo-galvanic effects in noncentrosymmetric materials and in topological insulators in a contact-less way and accelerate the technological development of efficient infrared detectors based on topological semimetals.Comment: Accepted in npj Quantum Materials; Abstract update

Study of Pure Annihilation Decays B_{d,s} \to D^{0} \bar D^{0}

With heavy quark limit and hierarchy approximation $\lambda_{QCD}\ll m_D\ll m_B$, we analyze the $B\to D^0\bar D^0$ and $B_s\to D^0\bar D^0$ decays, which occur purely via annihilation type diagrams. As a roughly estimation, we calculate their branching ratios and CP asymmetries in Perturbative QCD approach. The branching ratio of $B\to D^0\bar D^0$ is about $3.8\times10^{-5}$ that is just below the latest experimental upper limit. The branching ratio of $B_s\to D^0\bar D^0$ is about $6.8\times10^{-4}$, which could be measured in LHC-b. From the calculation, it could be found that this branching ratio is not sensitive to the weak phase angle $\gamma$. In these two decay modes, there exist CP asymmetries because of interference between weak and strong interaction. However, these asymmetries are too small to be measured easily.Comment: 13 pages, 4 figure

Non-characteristic Half-lives in Radioactive Decay

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation

The GALEX/S4G UV-IR color-color diagram: Catching spiral galaxies away from the Blue Sequence

We obtained GALEX FUV, NUV, and Spitzer/IRAC 3.6$\mu$m photometry for > 2000 galaxies, available for 90% of the S4G sample. We find a very tight "GALEX Blue Sequence (GBS)" in the (FUV-NUV) versus (NUV-[3.6]) color-color diagram which is populated by irregular and spiral galaxies, and is mainly driven by changes in the formation timescale ($\tau$) and a degeneracy between $\tau$ and dust reddening. The tightness of the GBS provides an unprecedented way of identifying star-forming galaxies and objects that are just evolving to (or from) what we call the "GALEX Green Valley (GGV)". At the red end of the GBS, at (NUV-[3.6]) > 5, we find a wider "GALEX Red Sequence (GRS)" mostly populated by E/S0 galaxies that has a perpendicular slope to that of the GBS and of the optical red sequence. We find no such dichotomy in terms of stellar mass (measured by $\rm{M}_{[3.6]}$), since both massive ($M_{\star} > 10^{11} M_{\odot}$) blue and red sequence galaxies are identified. The type that is proportionally more often found in the GGV are the S0-Sa's and most of these are located in high-density environments. We discuss evolutionary models of galaxies that show a rapid transition from the blue to the red sequence on timescale of $10^{8}$years.Comment: 7 pages, 4 figures, 1 table. Accepted for publication in ApJ

Inflation and nonequilibrium renormalization group

We study de spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques.Comment: 6 pages, 1 figure, submitted to J. Phys.