Growth Cone Pathfinding: a competition between deterministic and stochastic events

Background  

Growth cone migratory patterns show evidence of both deterministic and stochastic search modes.     

Excited-state absorption and 1064-nm end-pumped laser emission of Nd:YVO4 single-crystal fiber grown by laser-heated pedestal growth

We present an investigation of the excited-state absorption and laser emission of a 1.0-at. %-Nd3+-doped YVO4 single-crystal fiber grown by the low-cost and versatile laser-heated pedestal growth technique. Efficient laser emission at 1064 nm was achieved when the fiber was pumped, in an end-pump cavity, by a Ti:sapphire laser at 808 nm. A continuous-wave threshold of 10 mW was observed with an efficiency of 42% with respect to the absorbed pump power and the maximum output power of 200 mW. These results are excellent when compared with those of a commercial bulk crystal adapted to the same cavity (48% efficiency, 250-mW maximum output power). Thus the fibers are characterized as strong candidates for the construction of compact lasers that can also be pumped by low-cost diode lasers.     

On the Physical Origin of Long-Ranged Fluctuations in Fluids in Thermal Nonequilibrium States

Thermodynamic fluctuations in systems that are in nonequilibrium steady states are always spatially long ranged, in contrast to fluctuations in thermodynamic equilibrium. In the present paper we consider a fluid subjected to a stationary temperature gradient. Two different physical mechanisms have been identified by which the temperature gradient causes long-ranged fluctuations. One cause is the presence of couplings between fluctuating fields. Secondly, spatial variation of the strength of random forces, resulting from the local version of the fluctuation-dissipation theorem, has also been shown to generate long-ranged fluctuations. We evaluate the contributions to the long-ranged temperature fluctuations due to both mechanisms. While the inhomogeneously correlated Langevin noise does lead to long-ranged fluctuations, in practice, they turn out to be negligible as compared to nonequilibrium temperature fluctuations resulting from the coupling between temperature and velocity fluctuations.     

A new superhard material: Osmium diboride OsB2

Superhard materials have many industrial applications, wherever resistance to abrasion and wear are important. The synthesis of new superhard materials is one of the great challenges to scientists. We re-examined the phase diagram of the binary osmium-boron system and confirmed the existence of two hexagonal phases, OsB_1.1, Os₂B₃, and an orthorhombic phase, OsB₂. Almost nothing is known about the physical properties of osmium borides. Microhardness measurements show that OsB₂ is extremely hard. Ab initio calculations show that this is due to formation of covalent bonds between boron atoms. OsB₂ is also a low compressibility material. It can be used as hard coating.     

On Metastability in FPU

We present an analytical study of the Fermi–Pasta–Ulam (FPU) α–model with periodic boundary conditions. We analyze the dynamics corresponding to initial data with one low frequency Fourier mode excited. We show that, correspondingly, a pair of KdV equations constitute the resonant normal form of the system. We also use such a normal form in order to prove the existence of a metastability phenomenon. More precisely, we show that the time average of the modal energy spectrum rapidly attains a well defined distribution corresponding to a packet of low frequencies modes. Subsequently, the distribution remains unchanged up to the time scales of validity of our approximation. The phenomenon is controlled by the specific energy.     

Measuring the 13C/12C isotope ratio in atmospheric CO2 by means of laser absorption spectrometry: a new perspective based on a 2.05-microm diode laser

The potential use of high sensitivity laser absorption spectroscopy for measuring the 13C/12C isotope ratio in atmospheric CO2 has been demonstrated, using a GaSb-based diode laser at 2.05 microm. In this spectral region, the overlapping between relatively strong 12CO2 and 13CO2 absorption features gives rise to several line pairs which are well suitable for a spectroscopic determination of the isotope ratio. Preliminary results have demonstrated that a short-term precision better than 1 per thousand can be easily obtained, for a CO2 concentration of 1000 ppm. We extensively discuss the influence of a possible non-linearity in the detectors' response on the delta-value and suggest an instrumental development that would allow to eliminate this effect.     

Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and B^{-\frac12,\frac12}₄{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS _ν ) has a unique global solution with initial data u₀ = (u₀^h, u₀³){u_0 = (u_0^h, u_0^3)} which satisfies ||u₀^h||_B exp(\fracCn⁴ ||u₀³||_B⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or ||u₀^h||_{B^{-\frac12,\frac12}4} exp(\fracCn⁴ ||u₀³||_{B^{-\frac12,\frac12}4}⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c ₀ sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, [(L^p_t)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L²_{t, f})\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L ¹ function f(t).     

The unification of inflation and late-time acceleration in the frame of <Emphasis Type="Italic">k</Emphasis>-essence

By using the formulation of the reconstruction, we explicitly construct models of k-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.     

Evolution of hole depth and shape in ultrashort pulse deep drilling in silicon

We report on the temporal evolution of the percussion drilling process in deep laser drilling. Ultrashort laser pulses at 1030 nm and a duration of 8 ps were used to machine silicon while simultaneously imaging the silhouette of the hole using an illumination wavelength above the band edge. We investigate the influence of the processing parameters fluence and pulse energy on the depth and shape of the hole demonstrating different phases of the drilling process. In the first phase, a tapered hole is formed with highly reproducible shape and depth. In the following, the evolution of the hole shape is irregular and imperfections like bulges, changes of the drilling direction and the formation of multiple hole ends occur. In the final phase, the maximum depth stays constant while the volume still increases due to enlargement of the hole diameter and the possible formation of multiple hole ends. Deviations from the ideal hole shape occur primarily in the lower part of the hole. Their extent can be reduced by increasing the amount of applied pulse energy. Moreover, the pulse energy is chiefly determining the maximum achievable hole depth, which is largely independent of the focusing conditions and corresponding fluence.     

Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.