The motion of a two-dimensional packet of capillary–gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schrödinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary–gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary–gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary–gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.

No abstract

Mechanical moduli of cultured airway smooth muscle cells (Fabry, B., et al. Phys. Rev. Lett. 87:148102, 2001) reveal that the frequency dependence of cell rheological behavior conforms to a weak power-law relationship over a wide range of frequency (10(-2)-10(3) Hz). Such a behavior cannot be accounted for by standard viscoelastic models characterized by a discrete number of time constants that have been commonly used in previous studies of cell viscoelasticity. Fractional calculus, by contrast, provides a natural framework for describing weak power-law relationships and requires no assumptions about the type of material, the time constant distribution or the time/frequency interval in which rheological observations are made. In this study, we developed a rheological model of the cell using methods of fractional calculus. We used a least-squares technique to fit the model to data previously obtained from measurements on airway smooth muscle cells. The fit provided an excellent correspondence to the data, and the estimated values of model parameters were physically plausible. The model leads to a novel and unexpected empirical link between dynamic viscoelastic behavior of the cytoskeleton and the static contractile stress that it bears.

Immobilized cell technology has shown a significant promotional effect on the fermentation of alcoholic beverages such as beer, wine and cider. However, genetic, morphological and physiological alterations occurring in immobilized yeast cells impact on aroma formation during fermentation processes. The focus of this review is exploitation of existing knowledge on the biochemistry and the biological role of flavour production in yeast for the biotechnological production of aroma compounds of industrial importance, by means of immobilized yeast. Various types of carrier materials and immobilization methods proposed for application in beer, wine, fruit wine, cider and mead production are presented. Engineering aspects with special emphasis on immobilized cell bioreactor design, operation and scale-up potential are also discussed. Ultimately, examples of products with improved quality properties within the alcoholic beverages are addressed, together with identification and description of the future perspectives and scope for cell immobilization in fermentation processes.

TaxonAltitude (m) (Mean ± SD) Arrhenath ( 129) Brachyp ( 180) Calamagro ( 3) Calthion ( 18) Chrysopog ( 134) Cynosurion ( 274) Deschamp ( 31) Festucetalia (137)

The influence of different phospholipid types (pure phospholipids 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3‐phosphocholine, POPC, 1,2‐dipalmitoyl‐sn‐glycero‐3‐phosphocholine, DPPC, and one commercial phospholipid mixture, Lipoid H100), sterol types (cholesterol vs. β‐sitosterol), and various sterol concentrations (5–50 mol%) on liposomal membrane fluidity, thermotropic properties, liposome size, zeta potential, and lipid oxidation kinetics using fluorescent lipid probe BODIPY 581/591 C11 (4,4‐difluoro‐5‐[4‐phenyl‐1,3‐butadienyl]‐4‐bora‐3a,4a‐diaza‐s‐indacene‐3‐undecanoic acid) are investigated. DPPC bilayer is more rigid than POPC and phospholipids mixture membranes. Pure DPPC gives the smallest liposomes, while liposomes of Lipoid H100 have the largest diameter. Both sterols reduce membrane fluidity of all liposomes, increase absolute zeta potential, cause significant changes in particle size, and decrease phase transition temperature (Tm) and enthalpy of DPPC. POPC/β‐sitosterol liposomes exhibit the most significant lipid oxidation of the lipophilic probe. Along with beneficial effects of phytosterols on human health, better membrane fluidity, more favorable and stabilizing interactions with phospholipids, smaller vesicle size, and enhanced physical stability in comparison to cholesterol are some of the encouraging results for the use of β‐sitosterol in liposome formulations for potential application in foods, pharmaceutics, and cosmetics. Practical Applications: Adjusting the composition of liposomal membrane (lipid type, sterol type, and concentration) can be used as a tool to control membrane fluidity, permeability, and thermotropic properties, and thus predict release properties, physical, thermal, and oxidative stability. A commercial phospholipid mixture of different natural phospholipids with impurities creates less uniform liposomal membrane that is characterized by higher fluidity in comparison to DPPC. The type of phospholipid has huge influence on MLVs size. β‐sitosterol, which is a phytosterol with beneficial effects on human health can be used as a replacement for cholesterol in liposomal formulations, but with the following in mind: β‐sitosterol reduces fluidity of the phospholipid bilayer to a lesser extent than cholesterol, β‐sitosterol gives smaller MLVs than cholesterol, DPPC/β‐sitosterol SUVs are bigger than 100 nm in diameter (relevant for intravenous administration), MLVs with ≥30 mol% of β‐sitosterol can be considered as physically stable (unlike those with cholesterol), irrespective to the phospholipid type. The influence of different phospholipid types, sterol types, and various sterol concentrations on liposomal membrane fluidity, thermo tropic properties, liposomesize, zeta potential, and lipid oxidation kinetics are investigated.

We analyze self-similar solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg-deVries equation in one spatial variable. By using Lie-group scaling transformation, we determined the similarity solutions. After the introduction of the similarity variables, both problems are reduced to ordinary nonlinear fractional differential equations. In two special cases exact solutions to the ordinary fractional differential equation, which is derived from the diffusion equation, are presented. In several other cases the ordinary fractional differential equations are solved numerically, for several values of governing parameters. In formulating the numerical procedure, we use special representation of a fractional derivative that is recently obtained.

No abstract