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The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm experimentally. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.
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The thermodynamic and elastic properties of a flexible polymer in the presence of dipole interactions are studied via Monte Carlo simulations. The structural coil-globular, solid-globular, and solid-solid transitions are mapped in the hyperphase diagram, parameterized by the dipole concentration, $eta$, and temperature, $T$. Polymer flexibility is usually quantified by the persistent length, $ell_p$, which is defined as the length on which the bond-bond correlation is lost. Non-monotonic flexibility of polymeric complexes as a function of $eta$ has been interpreted as a cooperative effect under the Worm-Like Chain model. Instead of the usual exponential behavior, $langle Cleft(kright)ranglepropto e^{-k/ell_p}$, here we show that the bond-bond correlation follows a power law decay, $langle Cleft(kright)rangleapprox c_0k^{-omega}$. The power law regime holds even at the coil-globular transition, where a Gaussian limit is expected, originated from non-leading terms due to monomer-monomer connectivity. The exponent $omega$ monotonically converges to the mbox{SAW} limit for large $eta$, if the isotherm pathway is constructed at the coil phase. The deviation from ideality in better probed at the chain segment size, and the expected $Theta-$condition at the $(T,eta)$ pathway near the coil-globular transition is not observed.
It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of twist due to a subtle counteraction of geometric expansion with elastic contraction. Using x-ray scanning and by locating each filament in the bundle, we show the remarkable persistence of order even as the twist is increased well above 360 degrees, by measuring the spatial correlation function across the bundle crosssection. We introduce a model which analyzes the combined effects of elasticity including filament stretching, and radial and hoop compression necessary to explain this generic preservation of order observed with Hookean filaments.
We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times -- leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential and an algebraic decay. Analytical calculations and numerical simulations show, that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.
We study a shot noise of a wide channel gated high-frequency transistor at temperature of 4.2K near pinch-off. In this regime, a transition from the metallic to the insulating state is expected to occur, accompanied by the increase of the partition noise. The dependence of the noise spectral density on current is found to be slightly nonlinear. At low currents, the differential Fano factor is enhanced compared to the universal value 1/3 for metallic diffusive conductors. We explain this result by the effect of thermal fluctuations in a nonlinear regime near pinch-off, without calling for the enhanced partition noise.
We investigate a two-component, cylindrical, quasi-one-dimensional quantum plasma subjected to a {em radial} confining harmonic potential and an applied magnetic field in the symmetric gauge. It is demonstrated that such a system as can be realized in semiconducting quantum wires offers an excellent medium for observing the quantum pinch effect at low temperatures. An exact analytical solution of the problem allows us to make significant observations: surprisingly, in contrast to the classical pinch effect, the particle density as well as the current density display a {em determinable} maximum before attaining a minimum at the surface of the quantum wire. The effect will persist as long as the equilibrium pair density is sustained. Therefore, the technological promise that emerges is the route to the precise electronic devices that will control the particle beams at the nanoscale.
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