The logistic differential equation is used to analyze cancer cell population, in the presence of a correlated Gaussian white noise. We study the steady state properties of tumor cell growth and discuss the effects of the correlated noise. It is found that the degree of correlation of the noise can cause tumor cell extinction.

Correlated noise in a logistic growth model.

A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also used to study the effect of the taper angle $${\phi}$$
 . Flow parameters such as the velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed for different values of the shape parameter n, the taper angle $${\phi}$$
 , the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.

The micropolar fluid model for blood flow through a tapered artery with a stenosis

Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter exist momentarily before expanding. We analyzed the flow of matter to extract pressures in excess of 1034 pascals, the highest recorded under laboratory-controlled conditions. Using these analyses, we rule out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equations of state with phase transitions at densities less than three times that of stable nuclei, but not equations of state softened at higher densities because of a transformation to quark matter.

Determination of the Equation of State of Dense Matter

Transport of a Brownian particle moving along the axis of a three-dimensional asymmetric periodic tube is investigated in the presence of asymmetric unbiased forces. The reduction of the coordinates may involve not only the appearance of entropic barrier but also the effective diffusion coefficient. It is found that in the presence of entropic barrier, the asymmetry of the tube shape and the asymmetry of the unbiased forces are the two ways of inducing a net current. The current is a peaked function of temperature which indicates that the thermal noise may facilitate the transport even in the presence of entropic barrier. An optimized radius exists at the bottleneck at which the current takes its maximum value. Competition between the two opposite driving factors may induce current reversal.

Current in a three-dimensional periodic tube with unbiased forces

Pure multiplicative noise-induced stochastic resonance, which appears in an anti-tumor system modulated by a seasonal external field, is studied by using theoretical analyses of the generalized potential and numerical simulations. For optimally selected values of the multiplicative noise intensity stochastic resonance is observed, which is manifested by the quasisymmetry of two potential minima. Theoretical results and numerical simulations are in good quantitative agreement.

Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability.

Numerical simulations of pulsating blood flow through models of stenotic and tapered arteries have been performed to investigate the distributions of the wall shear stress. In this paper, a mathematical model of a rigid tapered artery with axially symmetric stenosis is established. The incompressible Navier-Stokes equations are solved numerically by using the finite difference method. The effects of tapering and stenosis are considered. The results show that stenosis disturbs the flow field at the vicinity of the stenosis, especially at the throat and downstream, and easily leads to the formation of a flow separation region in the post-stenotic region.

Numerical Study of Pulsating Flow Through a Tapered Artery with Stenosis

The efficiency of a Brownian particle moving in a periodic potential in the presence of asymmetric unbiased fluctuations is investigated. We found that even on the quasistatic limit there is a regime where the efficiency can be a peaked function of temperature, which proves that thermal fluctuations facilitate the efficiency of energy transformation, contradicting the earlier findings [H. Kamegawa et al., Phys. Rev. Lett. 80, 5251 (1998)]. It is also found that the mutual interplay between temporal asymmetry and spatial asymmetry may induce optimized efficiency at finite temperatures. The ratchet is not most efficient when it gives maximum current.

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations.

We present a detailed study of the transport and the efficiency of a ratchet system in a periodic potential in the presence of correlated noises. The current and the efficiency of the system are investigated. It is found that, when the potential is spatially symmetric, the correlation between the two noises can induce a net transport. The efficiency shows many interesting features as a function of the applied force, the noise intensity, the external load, etc. The efficiency can be maximized as a function of noise intensity (or temperature), which shows that the thermal fluctuation can facilitate the efficiency of energy transformation.

Efficiency and current in a correlated ratchet.

We present a study of the transport of a Brownian particle moving in a periodic symmetric potential in the presence of asymmetric unbiased fluctuations. The particle is considered to move in a medium with periodic space dependent friction. By tuning the parameters of the system, the direction of the current exhibits reversals, both as a function of temperature as well as the amplitude of rocking force. We found that the mutual interplay between the opposite driving factors is the necessary term for current reversals.

Guo-Tao Liu

Papers

Correlated noise in a logistic growth model.

Numerical Study of Pulsating Flow Through a Tapered Artery with Stenosis

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations.

Efficiency and current in a correlated ratchet.

Current reversals in an inhomogeneous system with asymmetric unbiased fluctuations