Yair Zarmi

Combined effects of light intensity, light-path and culture density on output rate of Spirulina platensis (Cyanobacteria)

The requirements for efficient utilization of high light fluxes in cultures of Spirulina platensis have previously been elucidated. The most important of these was a short light-path coupled with a highly turbulent flow, facilitating ultrahigh cell densities (i.e. above 100 mg chl l−1). The present study shows that for each irradiance there is an optimal culture density, defined as the concentration that yields the highest output rate of cell mass under the prevailing conditions. In ultrahigh cell density cultures, a linear relationship was observed between the output rate and the irradiance, up to a photon flux density (PFD) of 2500 μmol m−2 s−1. Using a total PFD of 8000 μmol m−2 s−1, a maximal output rate of 16.8 g dry weight m−2 h−1 was obtained, which is the highest reported for a culture of photoautotrophic microorganisms exposed to direct beam radiation. Testing the effect of reduction in light-path on productivity, output rate per unit volume increased 50-fold as the light-path was reduced 27-fold...

Vegetation patterns along a rainfall gradient

A continuum model for vegetation patterns in water limited systems is presented. The model involves two variables, the vegetation biomass density and the soil water density, and takes into account positive feedback relations between the two. The model predicts transitions from bare-soil at low precipitation to homogeneous vegetation at high precipitation through intermediate states of spot, stripe and gap patterns. It also predicts the appearance of ring-like shapes as transient forms toward asymptotic stripes. All these patterns have been identified in observations made on two types of perennial grasses in the Northern Negev. Another prediction of the model is the existence of wide precipitation ranges where different stable states coexist, e.g. a bare soil state and a spot pattern, a spot pattern and a stripe pattern, and so on. This result suggests the interpretation of desertification followed by recovery as an hysteresis loop and sheds light on the irreversibility of desertification. 2003 Elsevier Ltd. All rights reserved.

Efficient use of strong light for high photosynthetic productivity: interrelationships between the optical path, the optimal population density and cell-growth inhibition

The interrelationships between the optical path in flat plate reactors and photosynthetic productivity were elucidated. In preliminary works, a great surge in photosynthetic productivity was attained in flat plate photoreactors with an ultra short (e.g. 1.0 cm) optical path, in which extremely high culture density was facilitated by vigorous stirring and strong light. This surge in net photosynthetic efficiency was associated with a very significant increase in the optimal population density facilitated by the very short optical path (OP). A salient feature of these findings concerns the necessity to address growth inhibition (GI) which becomes increasingly manifested as cell concentration rises above a certain, species-specific, threshold (e.g. 1-2 billion cells of Nannochloropsis sp. ml(-1)). Indeed, ultrahigh cell density cultures may be established and sustained only if growth inhibition is continuously, or at least frequently, removed. Nannochloropsis culture from which GI was not removed, yielded 60 mg(-1) h(-1), yielding 260 mg l(-1) h(-1) when GI was removed. Two basic factors crucial for obtaining maximal photosynthetic productivity and efficiency in strong photon irradiance are defined: (1) areal cell density must be optimal, as high as possible (cell growth inhibition having been eliminated), insuring the average photon irradiance (I(av)) available per cell is falling at the end of the linear phase of the PI(av) curve, relating rate of photosynthesis to I(av), i.e. approximately photon irradiance per cell. (2) The light-dark (L-D) cycle period, which is determined by travel time of cells between the dark and the light volumes along the optical path, should be made as short as practically feasible, so as to approach, as much as possible the photosynthetic unit turnover time. This is obtainable in flat plate reactors by reducing the OP to as small a magnitude as is practically feasible.

Allelic richness following population founding events--a stochastic modeling framework incorporating gene flow and genetic drift.

Allelic richness (number of alleles) is a measure of genetic diversity indicative of a populations long-term potential for adaptability and persistence. It is used less commonly than heterozygosity as a genetic diversity measure, partially because it is more mathematically difficult to take into account the stochastic process of genetic drift for allelic richness. This paper presents a stochastic model for the allelic richness of a newly founded population experiencing genetic drift and gene flow. The model follows the dynamics of alleles lost during the founder event and simulates the effect of gene flow on maintenance and recovery of allelic richness. The probability of an alleles presence in the population was identified as the relevant statistical property for a meaningful interpretation of allelic richness. A method is discussed that combines the probability of allele presence with a populations allele frequency spectrum to provide predictions for allele recovery. The models analysis provides insights into the dynamics of allelic richness following a founder event, taking into account gene flow and the allele frequency spectrum. Furthermore, the model indicates that the “One Migrant per Generation” rule, a commonly used conservation guideline related to heterozygosity, may be inadequate for addressing preservation of diversity at the allelic level. This highlights the importance of distinguishing between heterozygosity and allelic richness as measures of genetic diversity, since focusing merely on the preservation of heterozygosity might not be enough to adequately preserve allelic richness, which is crucial for species persistence and evolution.

Wind energy as a solar‐driven heat engine: A thermodynamic approach

An upper bound on annual average energy in the Earth’s winds is calculated via the formalism of finite‐time thermodynamics. The Earth’s atmosphere is viewed as the working fluid of a heat engine where the heat input is solar radiation, the heat rejection is to the surrounding universe, and the work output is the energy in the Earth’s winds. The upper bound for the annual average power in the Earth’s winds is found to be 17 W/m2, which can be contrasted with the actual estimated annual average wind power of 7 W/m2. Our thermodynamic model also predicts the average extreme temperatures of the Earth’s atmosphere and can be applied to wind systems on other planets.

The Bertrand theorem revisited

The Bertrand theorem, which states that the only power-law central potentials for which the bounded trajectories are closed are 1/r2 and r2, is analyzed using the Poincare–Lindstedt perturbation method. This perturbation method does not generate secular terms and correctly incorporates the effect of nonlinearities on the nature of periodic solutions. The requirement that the orbits be closed implies that the theorem holds in each order of the expansion.

Minimal normal forms in harmonic oscillations with small nonlinear perturbations

The freedom of choice of the zeroth-order approximation in the perturbative expansion of solutions to oscillatory problems with small nonlinearities is exploited within the framework of the method of normal forms. A priori, the normal form may contain an infinite number of resonant terms. It is shown that in a large class of problems of interest, the normal form can be simplified so that the number of such terms is small, or to have other desired properties. Conservative as well as dissipative systems are discussed.

Weakly nonlinear oscillations: A perturbative approach

The perturbative analysis of a one-dimensional harmonic oscillator subject to a small nonlinear perturbation is developed within the framework of two popular methods: normal forms and multiple time scales. The systems analyzed are the Duffing oscillator, an energy conserving oscillatory system, the cubically damped oscillator, a system that exhibits damped oscillations, and the Van der Pol oscillator, which represents limit-cycle systems. Special emphasis is given to the exploitation of the freedom inherent in the calculation of the higher-order terms in the expansion and to the comparison of the application of the two methods to the three systems.

Nonlinear dynamics: A tutorial on the method of normal forms

We consider a variety of nonlinear systems, described by linear differential equations, subjected to small nonlinear perturbations. Approximate solutions are sought in terms of expansions in a small parameter. The method of normal forms is developed and shown to be capable of constructing a series expansion in which the individual terms in the series correctly incorporate the essential aspects of the full solution. After an extensive introduction, we discuss a series of examples. Most of our attention is given to autonomous systems with imaginary eigenvalues for the unperturbed problem. But, we also analyze a system of equations with negative eigenvalues; one zero and one negative eigenvalue; two nonautonomous problems and phase locking in a coupled-oscillator system. We conclude with a brief section on an integral formulation of the method.

Time dependence of operators in anharmonic quantum oscillators: Explicit perturbative analysis

An explicit, order-by-order perturbative solution, valid over extended time scales, for the time dependence of operators of anharmonic oscillators, is developed within the framework of the method of normal forms. The freedom of choice of the zeroth-order term and, concurrently in the higher-order corrections, is exploited to develop a minimal normal form (MNF). The expansion for the eigenvalues of the perturbed Hamiltonian in a standard form is independent of the choice. However, the simple form obtained for the time dependence of the perturbative solution is more suitable than any other choice for application to high-lying excited states, as it offers a renormalized form for the propagator.