Oscillatory instability of fully 3D flow in a cubic diagonally lid-driven cavity

A transition to unsteadiness of a flow inside a cubic diagonally lid-driven cavity with no-slip boundaries is numerically investigated by a series of direct numerical simulations (DNS) performed on 100^3 and 200^3 stretched grids. It is found that the observed oscillatory instability is setting in via a subcritical symmetry-breaking Hopf bifurcation. The instability evolves on two vortices in a coupled manner. Critical values of Reynolds number Recr=2320 and non-dimensional angular oscillating frequency omegacr=0.249 for transition from steady to oscillatory flow are accurately estimated. Characteristic patterns of the 3D oscillatory flow are presented

Fluttering-induced flow in a closed chamber

We study the emergence of fluid flow in a closed chamber that is driven by dynamical deformations of an elastic sheet. The sheet is compressed between the sidewalls of the chamber and partitions it into two separate parts, each of which is initially filled with an inviscid fluid. When fluid exchange is allowed between the two compartments of the chamber, the sheet becomes unstable, and its motion displaces the fluid from rest. We derive an analytical model that accounts for the coupled, two-way, fluid-sheet interaction. We show that the system depends on four dimensionless parameters: the normalized excess length of the sheet compared to the lateral dimension of the chamber, $\Delta$; the normalized vertical dimension of the chamber; the normalized initial volume difference between the two parts of the chamber, $v_{\text{du}}(0)$; and the structure-to-fluid mass ratio, $\lambda$. We investigate the dynamics at the early times of the system's evolution and then at moderate times. We obtain the growth rates and the frequency of vibrations around the second and the first buckling modes, respectively. Analytical solutions are derived for these linear stability characteristics within the limit of the small-amplitude approximation. At moderate times, we investigate how the sheet escapes from the second mode. Given the chamber's dimensions, we show that the initial energy of the sheet is mostly converted into hydrodynamic energy of the fluid if $\lambda\ll 1$, and into kinetic energy of the sheet if $\lambda\gg 1$. In both cases most of the initial energy is released at time $t_{\text{p}}\simeq \ln[c \Delta^{1/2}/v_{\text{du}}(0)]/\sigma$, where $\sigma$ is the growth rate and $c$ is a constant.Comment: 25 pages, 12 figure

Time domain Dielectric Spectroscopy Study of Human Cells. II. Normal and Malignant White Blood Cells

open access articleThe dielectric properties of human lymphocyte suspensions were studied by time domain dielectric spectroscopy (TDDS). Nine populations of malignant and normal lymphocytes were investigated. Analysis of the dielectric parameters of cell structural parts were performed in the framework of Maxwell^Wagner mixture formula and the double-shell model of cell. The specific capacitance of the cell membranes was estimated by the Hanai^Asami^Koisumi formula. It was shown that the dielectric permittivity, capacitance and conductivity values of cell membranes are higher for normal lymphocytes than for the malignant ones. The difference of the same parameters for normal B- and T-cells is also discussed

Inverse melting of the vortex lattice

Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by the formation of nonequilibrium states which conceal the thermodynamic phase transition, or by intermediate phases, as was recently shown in a polymeric system. Here we report a first-order inverse melting of the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low temperatures, the material disorder causes significant pinning of the vortices, which prevents observation of their equilibrium properties. Using a newly introduced 'vortex dithering' technique we were able to equilibrate the vortex lattice. As a result, direct thermodynamic evidence of inverse melting transition is found, at which a disordered vortex phase transforms into an ordered lattice with increasing temperature. Paradoxically, the structurally ordered lattice has larger entropy than the disordered phase. This finding shows that the destruction of the ordered vortex lattice occurs along a unified first-order transition line that gradually changes its character from thermally-induced melting at high temperatures to a disorder-induced transition at low temperatures.Comment: 13 pages, 4 figures, Nature, In pres

Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao

The Impact of Ca2+ on Intracellular Distribution of Hemoglobin in Human Erythrocytes

The membrane-bound hemoglobin (Hb) fraction impacts red blood cell (RBC) rheology and metabolism. Therefore, Hb–RBC membrane interactions are precisely controlled. For instance, the signaling function of membrane-bound deoxy-Hb and the structure of the docking sites in the cytosolic domain of the anion exchanger 1 (AE-1) protein are well documented; however, much less is known about the interaction of Hb variants with the erythrocyte’s membrane. Here, we identified factors other than O2 availability that control Hb abundance in the membrane-bound fraction and the possible variant-specific binding selectivity of Hb to the membrane. We show that depletion of extracellular Ca2+ by chelators, or its omission from the extracellular medium, leads to membrane-bound Hb release into the cytosol. The removal of extracellular Ca2+ further triggers the redistribution of HbA0 and HbA2 variants between the membrane and the cytosol in favor of membrane-bound HbA2. Both effects are reversible and are no longer observed upon reintroduction of Ca2+ into the extracellular medium. Fluctuations of cytosolic Ca2+ also impact the pre-membrane Hb pool, resulting in the massive transfer of Hb to the cellular cytosol. We hypothesize that AE-1 is the specific membrane target and discuss the physiological outcomes and possible clinical implications of the Ca2+ regulation of the intracellular Hb distribution

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while {\dddot H} and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.Comment: 19 pages, 3 figures, text slightly improved and references added. Accepted for publication in Classical and Quantum Gravit