Racah Institute of Physics

Fluorescent molecules are much in demand for biosensors, solar cells, LEDs and VCSEL diodes, therefore, considerable efforts have been expended in designing and tailoring fluorescence to specific technical applications. However, naturally occurring fluorescence of diverse types has been reported from a wide array of living organisms: most famously, the jellyfish Aequorea victoria, but also in over 100 species of coral and in the cuticle of scorpions, where it is the rule, rather than the exception. Despite the plethora of known insect species, comparatively few quantitative studies have been made of insect fluorescence. Because of the potential applications of natural fluorescence, studies in this field have relevance to both physics and biology. Therefore, in this paper, we review the literature on insect fluorescence, before documenting its occurrence in the longhorn beetles Sternotomis virescens, Sternotomis variabilis var. semi rufescens, Anoplophora elegans and Stellognatha maculata, the tiger beetles Cicindela maritima and Cicindela germanica and the weevil Pachyrrhynchus gemmatus purpureus. Optical features of insect fluorescence, including emitted wavelength, molecular ageing and naturally occurring combinations of fluorescence with bioluminescence and colour-producing structures are discussed.

Planar spirals offer a highly scalable geometry appropriate for wireless power trasfer via strongly coupled inductive resonators. We numerically derive a set of geometric scale and material independent coupling terms, and analyze a simple model to identify design considerations for a variety of different materials. We use our model to fabricate integrated planar resonators of handheld sizes, and optimize them to achieve high Q factors, comparable to much larger systems, and strong coupling over significant distances with approximately constant efficiency.

A thin water film evaporating from a cleaved mica substrate undergoes a first-order phase transition between two values of film thickness. During evaporation, the interface between the two phases develops a fingering instability similar to that observed in the Saffman-Taylor problem. The dynamics of the droplet interface is dictated by an infinite number of conserved quantities: all harmonic moments decay exponentially at the same rate. A typical scenario is the nucleation of a dry patch within the droplet domain. We construct solutions of this problem and analyze the toplogical transition occuring when the boundary of the dry patch meets the outer boundary. We show a duality between Laplacian growth and evaporation, and utilize it to explain the behaviour near the transition. We construct a family of problems for which evaporation and Laplacian growth are limiting cases and show that a necessary condition for a smooth topological transition, in this family, is that all boundaries share the same pressure. * [email protected] 1 arXiv:1206.3762v2 [cond-mat.soft] 31 Jul 2012

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.

We calculate the expected spectrum and light curves of the early afterglow. For short GRBs the peak of the afterglow will be delayed, typically, by a few dozens of seconds after the burst. The x-ray and γ-ray characteristics of this delayed emission provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. Detection of this delayed emission will prove the internal shock scenario as producing the GRB, and will pinpoint the initial Lorentz factor γ 0 . In the optical band, the dominant emission arises from the reverse shock. This shock, carries an energy comparable to that of the forward shock. It radiates this energy at much lower frequencies, producing a short optical flash of 15th magnitude or brighter.

We discuss the spectrum arising from synchrotron emission by fast cooling (FC) electrons, when fresh electrons are continually accelerated by a strong blast wave, into a power law distribution of energies. The FC spectrum was so far described by four power law segments divided by three break frequencies ν sa < ν c < ν m . This is valid for a homogeneous electron distribution. However, hot electrons are located right after the shock, while most electrons are farther down stream and have cooled. This spatial distribution changes the optically thick part of the spectrum, introducing a new break frequency, ν ac < ν sa , and a new spectral slope, F ν ∝ ν 11/8 for ν ac < ν < ν sa . The familiar F ν ∝ ν 2 holds only for ν < ν ac . This ordering of the break frequencies is relevant for typical gamma-ray burst (GRB) afterglows in an ISM environment. Other possibilities arise for internal shocks or afterglows in dense circumstellar winds. We discuss possible implications of this spectrum for GRBs and their afterglows, in the context of the internal-external shock model. Observations of F ν ∝ ν 11/8 would enable us to probe scales much smaller than the typical size of the system, and constrain the amount of turbulent mixing behind the shock.

On December 27, 2004, a giant flare from SGR 1806−20 was detected on earth. Its thermal spectrum and temperature suggest that the flare resulted from an energy release of about 10 47 erg/sec close to the surface of a neutron star in the form of radiation and/or pairs. This plasma expanded under its own pressure producing a fireball and the observed gamma-rays escaped once the fireball became optically thin. The giant flare was followed by a bright radio afterglow, with an observable extended size, implying an energetic relativistic outflow. We revisit here the evolution of relativistic fireballs and we calculate the Lorentz factor and energy remaining in relativistic outflow once the radiation escapes. We show that pairs that arise naturally in a pure pairs-radiation fireball do not carry enough energy to account for the observed afterglow. We consider various alternatives and we show that if the relativistic outflow that causes the afterglow is related directly to the prompt flare, then the initial fireball must be loaded by baryons or Poynting flux. While we focus on parameters applicable to the giant flare and the radio afterglow of SGR 1806−20 the calculations presented here might be also applicable to GRBs.

Planets form in disks around young stars. Interactions with these disks cause them to migrate and thus affect their final orbital periods. We suggest that the connection between planets and disks may be deeper and involve a symbiotic evolution. By contributing to the outward transport of angular momentum, planets promote disk accretion. Here we demonstrate that planets sufficiently massive to open gaps could be the primary agents driving disk accretion. Those having masses below the gap opening threshold drift inward more rapidly than the disk material and can only play a minor role in its accretion. Eccentricity growth during gap formation may involve an even more intimate symbiosis. Given a small initial eccentricity, just a fraction of a percent, the orbital eccentricity of a massive planet may grow rapidly once a mass in excess of the planet's mass has been repelled to form a gap around the planet's orbit. Then, as the planet's radial excursions approach the gap's width, subsequent eccentricity growth slows so that the planet's orbit continues to be confined within the gap.

Many small bodies in the solar system are believed to be rubble piles, a collection of smaller elements separated by voids. We propose a model for the structure of a self-gravitating rubble pile. Static friction prevents its elements from sliding relative to each other. Stresses are concentrated around points of contact between individual elements. The effective dimensionless rigidity,μ rubble , is related to that of a monolithic body of similar composition and size,μ byμ rubble ∼μ 1/2 ǫ

We present analytic approximations to the optically thin synchrotron and synchrotron self-Compton (SSC) spectra when Klein-Nishina (KN) effects are important and pair production and external radiation fields can be neglected. This theory is useful for analytical treatment of radiation from astrophysical sources, such as gamma-ray bursts (GRBs), active galactic nuclei and pulsar wind nebula, where KN effects may be important. We consider a source with a continuous injection of relativistic electrons with a power-law energy distribution above some typical injection energy. We find that the synchrotron-SSC spectra can be described by a broken power-law, and provide analytic estimates for the break frequencies and power-law indices. In general, we show that the dependence of the KN cross-section on the energy of the upscattering electron results in a hardening of the energy distribution of fast cooling electrons and therefore in a hardening of the observed synchrotron spectrum. As a result the synchrotron spectrum of fast cooling electrons, below the typical injection energy, can be as hard as F ν ∝ ν 0 , instead of the classical ν −1/2 when KN effects are neglected. The synchrotron energy output can be dominated by electrons with energy above the typical injection energy. We solve self-consistently for the cooling frequency and find that the transition between synchrotron and SSC cooling can result in a discontinuous variations of the cooling frequency and the synchrotron and SSC spectra. We demonstrate the application of our results to theory by applying them to prompt and afterglow emission models of GRBs.

We develop a framework based on energy kicks for the evolution of higheccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass ratio µ ≪ 1. We use this framework to explore mean-motion resonances between the test particle and the secondary mass. This approach leads to (i) a redefinition of resonance orders to reflect the importance of interactions at periapse; (ii) a pendulum-like equation describing the librations of resonance orbits; (iii) an analogy between these new fixed points and the Lagrangian points as well as between librations around the fixed points and the well known tadpole and horseshoe orbits; (iv) a condition a ∼ µ −2/5 for the onset of chaos at large semimajor axis a; (v) the existence of a range µ < ∼ 5 × 10 −6 in secondary mass for which a test particle initially close to the secondary cannot escape from the system, at least in the planar problem; (vi) a simple explanation for the presence of asymmetric librations in exterior 1 : N resonances.

The extremely bright optical flash that accompanied GRB 080319B suggested, at first glance, that the prompt γ-rays in this burst were produced by Synchrotron self Compton (SSC). We analyze here the observed optical and γ spectrum. We find that the very strong optical emission poses, due to self absorption, very strong constraints on the emission processes and put the origin of the optical emission at a very large radius, almost inconsistent with internal shock. Alternatively it requires a very large random Lorentz factor for the electrons. We find that SSC could not have produced the prompt γ-rays. We also show that the optical emission and the γ rays could not have been produced by synchrotron emission from two populations of electron within the same emitting region. Thus we must conclude that the optical and the γrays were produced in different physical regions. A possible interpretation of the observations is that the γ-rays arose from internal shocks but the optical flash resulted from external shock emission. This would have been consistent with the few seconds delay observed between the optical and γ-rays signals.

The standard model of Gamma-Ray Bursts afterglows is based on synchrotron radiation from a blast wave produced when the relativistic ejecta encounters the surrounding medium. We reanalyze the refreshed shock scenario, in which slower material catches up with the decelerating ejecta and reenergizes it. This energization can be done either continuously or in discrete episodes. We show that such scenario has two important implications. First there is an additional component coming from the reverse shock that goes into the energizing ejecta. This persists for as long as the re-energization itself, which could extend for up to days or longer. We find that during this time the overall spectral peak is found at the characteristic frequency of the reverse shock. Second, if the injection is continuous, the dynamics will be different from that in constant energy evolution, and will cause a slower decline of the observed fluxes. A simple test of the continuously refreshed scenario is that it predicts a spectral maximum in the far IR or mm range after a few days.

Studies of the cosmic gamma-ray bursts (GRBs) and their host galaxies are now starting to provide interesting or even unique new insights in observational cosmology. Observed GRB host galaxies have a median magnitude R ∼ 25 mag, and show a range of luminosities, morphologies, and star formation rates, with a median redshift z ∼ 1.0. They represent a new way of identifying a population of star-forming galaxies at cosmological redshifts, which is mostly independent of the traditional selection methods. They seem to be broadly similar to the normal field galaxy populations at comparable redshifts and magnitudes, and indicate at most a mild luminosity evolution over the redshift range they probe. Studies of GRB optical afterglows seen in absorption provide a powerful new probe of the ISM in dense, central regions of their host galaxies, which is complementary to the traditional studies using QSO absorption line systems. Some GRB hosts are heavily obscured, and provide a new way to select a population of cosmological sub-mm sources. A census of detected optical tranistents may provide an important new way to constrain the total obscured fraction of star formation over the history of the universe. Finally, detection of GRB afterglows at high redshifts (z > 6) may provide a unique way to probe the primordial star formation, massive IMF, early IGM, and chemical enrichment at the end of the cosmic reionization era.

Planetesimal accretion during planet formation is usually treated as collisionless. Such accretion from a uniform and dynamically cold disk predicts protoplanets with slow retrograde rotation. However, if the building blocks of protoplanets, planetesimals, are small, of order of a meter in size, then they are likely to collide within the protoplanet's sphere of gravitational influence, creating a prograde accretion disk around the protoplanet. The accretion of such a disk results in the formation of protoplanets spinning in the prograde sense with the maximal spin rate allowed before centrifugal forces break them apart. As a result of semi-collisional accretion, the final spin of a planet after giant impacts is not completely random but is biased toward prograde rotation. The eventual accretion of the remaining planetesimals in the post giant-impact phase might again be in the semi-collisional regime and delivers a significant amount of additional prograde angular momentum to the terrestrial planets. We suggest that in our Solar System, semi-collisional accretion gave rise to the preference for prograde rotation observed in the terrestrial planets and perhaps the largest asteroids.

We show that external shocks cannot produce a variable GRB, unless they are produced by an extremely narrow jets (angular opening of < ∼ 10 −4 ) or if only a small fraction of the shell emits the radiation and the process is very inefficient. Internal shocks can produce the observed complex temporal structure provided that the source itself is variable. In this case, the observed temporal structure reflects the activity of the "inner engine" that drives the bursts. This sets direct constraints on it.

We derive self similar solutions for ultra-relativistic shock waves propagating into cold material of powerlaw density profile in radius ρ ∝ r −k . We treat both implosions and explosions in three geometries: planar, cylindrical and spherical. For spherical explosions these are the first type solutions of Blandford and McKee for k < 4 and the second type solutions found by Best and Sari for k > 5 − 3/4. In addition we find new, hollow (with evacuated interior), first type solutions that may be applicable for 4 < k < 17/4. This "sequence" with increasing k of first type solutions, hollow first type solutions, and then second type solutions is reminiscent of the non-relativistic sequence. However, while in the non relativistic case there is a range of k which corresponds to a "gap" -a range in k with neither first nor second type solutions which separates the hollow first type solutions and the second type solutions, here there is an "overlap": a range of k for which current considerations allow for both hollow first and second type solutions. Further understanding is needed to determine which of the two solutions apply in this overlap regime. We provide similar exploration for the other geometries and for imploding configurations. Interestingly, we find a gap for imploding spherical shocks and exploding planar shocks and an overlap for imploding planar solutions. Cylindrical configurations have no hollow solutions and exhibit direct transition from first type to second type solutions, without a gap or an overlap region.

We investigate the GeV emission from gamma-ray bursts (GRBs), using the results from the Energetic Gamma Ray Experimental Telescope (EGRET), and in view of the Gamma-ray Large Area Space Telescope (GLAST). Assuming that the conventional prompt and afterglow photons originate from synchrotron radiation, we compare an accompanying inverse-Compton component with EGRET measurements and upper limits on GeV fluence, taking Klein-Nishina feedback into account. We find that EGRET constraints are consistent with the theoretical framework of the synchrotron self-Compton model for both prompt and afterglow phases, and discuss constraints on microphysical parameters in both phases. Based on the inverse-Compton model and using EGRET results, we predict that GLAST would detect GRBs with GeV photons at a rate 20 yr −1 from each of the prompt and afterglow phases. This rate applies to the high-energy tail of the prompt synchrotron emission and to the inverse-Compton component of the afterglow. Theory predicts that in a large fraction of the cases where synchrotron GeV prompt emission would be detected by GLAST, inverse-Compton photons should be detected as well at high energies ( 10 GeV). Therefore GLAST will enable a more precise test of the high-energy emission mechanism. Finally, we show that the contribution of GRBs to the flux of the extragalactic gamma-ray background measured with EGRET is at least 0.01% and likely around 0.1%.