Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

AC electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications

Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK) phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across the semiconductor-electrolyte interface (consisting of the electric double layer (EDL) inside the electrolyte solutions and the space charge layer (SCL) inside the semiconductors) under AC electric fields with arbitrary wave forms. The present electrokinetic boundary conditions allow for evaluation of induced zeta potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Subsequently, we demonstrate the applications of these boundary conditions in analyzing the ACEK phenomena around a semiconducting cylinder. It is concluded that the flow circulations exist around the semiconducting cylinder and are shown to be stronger under an AC field with lower frequency and around a cylinder with higher conductivity.Comment: 29 pages, 4 figure

Friedel Oscillations and Charge-density Waves Pinning in Quasi-one-dimensional Conductors: An X-ray Access

We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.Comment: 4 pages REVTEX, 5 figure

Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily

Supercapacitive Admittance Tomoscopy

A sensor for measuring adsorption on a substrate has been designed including a contactless detection scheme, called supercapacitive admittance tomoscopy (SCAT). The sensor comprises a thin dielectric layer with two parallel band electrodes on the one side and a chemically modified surface on the other onto which the adsorption of molecules occurs. Upon application of a high frequency ac voltage between the two electrodes, a capacitive coupling is established across the dielectric layer, and the admittance measured depends on the surface state of the chemically modified interface. On the basis of this principle, a flow sensor has been developed to measure sensorgrams to follow the dynamics of the adsorption and has been tested for the adsorption of IgG on the modified surface

Size Dependence of Investigations of Hot Electron Cooling Dynamincs in Metal/Adsorbates Nanoparticles

The size dependence of electron-phonon coupling rate has been investigated by femtosecond transient absorption spectroscopy for gold nanoparticles (NPs) wrapped in a shell of sulfate with diameter varying from 1.7 to 9.2 nm. Broad-band spectroscopy gives an overview of the complex dynamics of nonequilibrium electrons and permits the choice of an appropriate probe wavelength for studying the electron-phonon coupling dynamics. Ultrafast experiments were performed in the weak perturbation regime (less than one photon in average per nanoparticle), which allows the direct extraction of the hot electron cooling rates in order to compare different NPs sizes under the same conditions. Spectroscopic data reveals a decrease of hot electron energy loss rates with metal/adsorbates nanosystem sizes. Electron-phonon coupling time constants obtained for 9.2 nm NPs are similar to gold bulk materials (a. 1 ps) whereas an increase of hot electron cooling time up to 1.9 ps is observed for sizes of 1.7 nm. This is rationalized by the domination of surface effects over size (bulk) effects. The slow hot electron cooling is attributed to the adsorbates-induced long-lived nonthermal regime, which significantly reduces the electron-phonon coupling strength (average rate of phonon emission)

Role of Adsorbates on Dynamics of Hot-Electron (type I and II) Thermalization within Gold Nanoparticles

Early stages of hot-electron thermalization in small gold nanoparticles wrapped in an adsorbates shell have been investigated by femtosecond transient absorption spectroscopy. Type-I hot electrons thermalize in 800 fs (to form type-II hot electron) either by scattering with cold conduction band electrons or by chemical interface scattering with adsorbates shell. Type-II hot electrons redistribute the excess energy toward the lattice via electron–phonon coupling in 1.8–3.6 ps depending on pump fluence. The electron–phonon coupling process (type II hot electron) is retarded because of the incomplete internal thermalization of type-I hot electron at early times due to the presence of adsorbates

Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systems

A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition. It is shown that intrachain fluctuations in the order parameter play a crucial role and must be treated exactly. The effect of these fluctuations is determined by a single dimensionless parameter. The three-dimensional transition temperature, the associated specific heat jump, coherence lengths, and width of the critical region, are computed assuming that the single chain Ginzburg-Landau coefficients are independent of temperature. The width of the critical region, estimated from the Ginzburg criterion, is virtually parameter independent, being about 5-8 per cent of the transition temperature. To appear in {\it Physical Review B,} March 1, 1995.Comment: 15 pages, RevTeX, 5 figures in uuencoded compressed tar file

Nanomosaic Network for the Detection of Proteins Without Direct Electrical Contact

A nanomosaic network of metallic nanoparticles for the detection of ultralow concentrations of proteins is reported, which uses two planar microelectrodes embedded in a microchip that permit generation of capacitive coupling to the nanomosaic system without the need for direct electrical contact with the channel. By tailoring the microchannel surface using a sandwich configuration of polyethylene terephthalate/gold nanoparticles/poly(L-lysine), the surface charge can be modified following biomolecular interactions and monitored using a noncontact admittance technique. This nanodevice system behaves like a tunable capacitor and can be employed for the detection of any kind of molecule. The femtomolar detection of an anionic protein, such as b- lactoglobulin in phosphatebuffered saline medium, is taken as an example

Generation of OH radicals at palladium oxide nanoparticle modified electrodes, and scavenging by fluorescent probes and antioxidants

The reduction of palladium oxide nanoparticles in the presence of hydrogen peroxide or dissolved oxygen gives rise to a catalytic reduction current dependent on the hydrogen peroxide concentration or the oxygen concentration. Using terephthalic acid as an OH radical scavenger yielding the fluorescent 2-hydroxyterephthalic acid, we demonstrate that the catalytic current stems from the freshly exposed palladium metal re-oxidation by OH radicals. A kinetic model is presented to account for these catalytic reactions. We also demonstrate that the measurement of the catalytic reduction current in the presence of antioxidant molecules can be used to measure the OH scavenging properties of antioxidants