Asynchronous exponential growth of semigroups of nonlinear operators

AbstractThe property of asynchronous exponential growth is analyzed for the abstract nonlinear differential equation z′(t) = Az(t) + F(z(t)), t ⩾ 0, z(0) = x ϵ X, where A is the infinitesimal generator of a semigroup of linear operators in the Banach space X and F is a nonlinear operator in X. Asynchronous exponential growth means that the nonlinear semigroup S(t), t ⩾ 0 associated with this problem has the property that there exists λ > 0 and a nonlinear operator Q in X such that the range of Q lies in a one-dimensional subspace of X and limt → ∞ e−λtS(t)x = Qx for all x ϵ X. It is proved that if the linear semigroup generated by A has asynchronous exponential growth and F satisfies ∥F(x)∥ ⩽ f(∥x∥) ∥x∥, where f: R+ → R+ and ∝∞(f(r)r) dr < ∞, then the nonlinear semigroup S(t), t ⩾ 0 has asynchronous exponential growth. The method of proof is a linearization about infinity. Examples from structured population dynamics are given to illustrate the results

Nonlinear hyperbolic systems with nonlocal boundary conditions

AbstractA system of nonlinear hyperbolic equations with boundary conditions of renewal type is studied as a general mathematical model for structured biological populations

Primordial nucleosynthesis and hadronic decay of a massive particle with a relatively short lifetime

In this paper we consider the effects on big bang nucleosynthesis (BBN) of the hadronic decay of a long-lived massive particle. If high-energy hadrons are emitted near the BBN epoch ($t \sim 10^{-2}$ -- $10^2 \sec$), they extraordinarily inter-convert the background nucleons each other even after the freeze-out time of the neutron to proton ratio. Then, produced light element abundances are changed, and that may result in a significant discrepancy between standard BBN and observations. Especially on the theoretical side, now we can obtain a lot of experimental data of hadrons and simulate the hadronic decay process executing the numerical code of the hadron fragmentation even in the high energy region where we have no experimental data. Using the light element abundances computed in the hadron-injection scenario, we derive a constraint on properties of such a particle by comparing our theoretical results with observations.Comment: 33 pages, 14 postscript figures, reference added, typo corrected, to appear in Phys. Rev.

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

SO(10) unified models and soft leptogenesis

Motivated by the fact that, in some realistic models combining SO(10) GUTs and flavour symmetries, it is not possible to achieve the required baryon asymmetry through the CP asymmetry generated in the decay of right-handed neutrinos, we take a fresh look on how deep this connection is in SO(10). The common characteristics of these models are that they use the see-saw with right-handed neutrinos, predict a normal hierarchy of masses for the neutrinos observed in oscillating experiments and in the basis where the right-handed Majorana mass is diagonal, the charged lepton mixings are tiny. In addition these models link the up-quark Yukawa matrix to the neutrino Yukawa matrix Y^\nu with the special feature of Y^\nu_{11}-> 0 Using this condition, we find that the required baryon asymmetry of the Universe can be explained by the soft leptogenesis using the soft B parameter of the second lightest right-handed neutrino whose mass turns out to be around 10^8 GeV. It is pointed out that a natural way to do so is to use no-scale supergravity where the value of B ~1 GeV is set through gauge-loop corrections.Comment: 26 pages, 2 figures. Added references, new appendix of a relevant fit and improved comment

Magnetic Flux of EUV Arcade and Dimming Regions as a Relevant Parameter for Early Diagnostics of Solar Eruptions - Sources of Non-Recurrent Geomagnetic Storms and Forbush Decreases

This study aims at the early diagnostics of geoeffectiveness of coronal mass ejections (CMEs) from quantitative parameters of the accompanying EUV dimming and arcade events. We study events of the 23th solar cycle, in which major non-recurrent geomagnetic storms (GMS) with Dst <-100 nT are sufficiently reliably identified with their solar sources in the central part of the disk. Using the SOHO/EIT 195 A images and MDI magnetograms, we select significant dimming and arcade areas and calculate summarized unsigned magnetic fluxes in these regions at the photospheric level. The high relevance of this eruption parameter is displayed by its pronounced correlation with the Forbush decrease (FD) magnitude, which, unlike GMSs, does not depend on the sign of the Bz component but is determined by global characteristics of ICMEs. Correlations with the same magnetic flux in the solar source region are found for the GMS intensity (at the first step, without taking into account factors determining the Bz component near the Earth), as well as for the temporal intervals between the solar eruptions and the GMS onset and peak times. The larger the magnetic flux, the stronger the FD and GMS intensities are and the shorter the ICME transit time is. The revealed correlations indicate that the main quantitative characteristics of major non-recurrent space weather disturbances are largely determined by measurable parameters of solar eruptions, in particular, by the magnetic flux in dimming areas and arcades, and can be tentatively estimated in advance with a lead time from 1 to 4 days. For GMS intensity, the revealed dependencies allow one to estimate a possible value, which can be expected if the Bz component is negative.Comment: 27 pages, 5 figures. Accepted for publication in Solar Physic

Primordial Nucleosynthesis as a Test of the Friedmann Equation in the Early Universe

In the standard hot big bang model, the expansion of the early universe is given by the Friedmann equation with an energy density dominated by relativistic particles. Since in a variety of models this equation is altered, we introduce modifications in the Friedmann equation and show that we can constrain them using big bang nucleosynthesis data. When there is no neutrino/antineutrino asymmetry these modifications are tightly bounded but in presence of an asymmetry the bounds become much looser. As an illustration, we apply our results to a model where the second and third families couple to gravity differently than the first family (non-universal gravity).Comment: 6 figures. Revised version. Matches with the accepted one for publication in PR

Thermal leptogenesis in a model with mass varying neutrinos

In this paper we consider the possibility of neutrino mass varying during the evolution of the Universe and study its implications on leptogenesis. Specifically, we take the minimal seesaw model of neutrino masses and introduce a coupling between the right-handed neutrinos and the dark energy scalar field, the Quintessence. In our model, the right-handed neutrino masses change as the Quintessence scalar evolves. We then examine in detail the parameter space of this model allowed by the observed baryon number asymmetry. Our results show that it is possible to lower the reheating temperature in this scenario in comparison with the case that the neutrino masses are unchanged, which helps solve the gravitino problem. Furthermore, a degenerate neutrino mass patten with $m_i$ larger than the upper limit given in the minimal leptogenesis scenario is permitted.Comment: 18 pages, 7 figures, version to appear in PR

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model

Characterization of large area avalanche photodiodes in X-ray and VUV-light detection

The present manuscript summarizes novel studies on the application of large area avalanche photodiodes (LAAPDs) to the detection of X-rays and vacuum ultraviolet (VUV) light. The operational characteristics of four different LAAPDs manufactured by Advanced Photonix Inc., with active areas of 80 and 200 mm^2 were investigated for X-ray detection at room temperature. The best energy resolution was found to be in the 10-18% range for 5.9 keV X-rays. The LAAPD, being compact, simple to operate and with high counting rate capability (up to about 10^5/s), proved to be useful in several applications, such as low-energy X-ray detection, where they can reach better performance than proportional counters. Since X-rays are used as reference in light measurements, the gain non-linearity between 5.9 keV X-rays and light pulses was investigated. The gain ratio between X-rays and VUV light decreases with gain, reaching 10 and 6% variations for VUV light produced in argon (~128 nm) and xenon (~172 nm), respectively, for a gain 200, while for visible light (~635 nm) the variation is lower than 1%. The effect of temperature on the LAAPD performance was investigated. Relative gain variations of about -5% per Celsius degree were observed for the highest gains. The excess noise factor was found to be independent on temperature, being between 1.8 and 2.3 for gains from 50 to 300. The energy resolution is better for decreasing temperatures due mainly to the dark current. LAAPDs were tested under intense magnetic fields up to 5 T, being insensitive when used in X-ray and visible-light detection, while for VUV light a significant amplitude reduction was observed at 5 T.Comment: 25 pages, 40 figures, submitted to JINS