Distribution, abundance and damages caused by European beavers (Castor fiber) in Polish forests

Borowski, Z., Borkowski, J

Relaxation into equilibrium under pure Schr\"odinger dynamics

We consider bipartite quantum systems that are described completely by a state vector $|\Psi(t)>$ and the fully deterministic Schr\"odinger equation. Under weak constraints and without any artificially introduced decoherence or irreversibility, the smaller of the two subsystems shows thermodynamic behaviour like relaxation into an equilibrium, maximization of entropy and the emergence of the Boltzmann energy distribution. This generic behaviour results from entanglement.Comment: 5 pages, 9 figure

On the concept of pressure in quantum mechanics

Heat and work are fundamental concepts for thermodynamical systems. When these are scaled down to the quantum level they require appropriate embeddings. Here we show that the dependence of the particle spectrum on system size giving rise to a formal definition of pressure can, indeed, be correlated with an external mechanical degree of freedom, modelled as a spatial coordinate of a quantum oscillator. Under specific conditions this correlation is reminiscent of that occurring in the classical manometer.Comment: 7 pages, 3 figure

The dynamical balance, transport and circulation of the Antarctic Circumpolar Current

The physical ingredients of the ACC circulation are reviewed. A picture of thecirculation is sketched by means of recent observations of the WOCE decade. Wepresent and discuss the role of forcing functions (wind stress, surfacebuoyancy flux) in the balance of the (quasi)-zonal flow, the meridionalcirculation and their relation to the ACC transport. Emphasis will be on theinterrelation of the zonal momentum balance and the meridional circulation, theimportance of diapycnal mixing and eddy processes. Finally, new model conceptsare described: a model of the ACC transport dependence on wind stress andbuoyancy flux, based on linear wave theory; and a model of the meridionaloverturning of the Southern Ocean, based on zonally averaged dynamics with eddyparameterization

Using The-Math-You-Need modules in a general education, oceanography course

The Math You Need (TMYN) is a series of on-line tutorials designed for students to increase their mathematical abilities while taking geology and other science courses. The aim of the program is to increase the quantitative abilities of students while demonstrating mathematical applications in an effort to make students more comfortable with and aware of the utility of mathematics. Over two semesters, we implemented targeted-TMYN modules into a general-education oceanography course that is typically populated by non-science majors with a wide variety of mathematical skills before calculus. Students participate voluntarily in TMYN modules with extra credit given for their successful completion. Every class day in the course involves exercises and/or a laboratory that applies oceanographic concepts into which we frequently weave elementary mathematics; also, quantitative questions appear on course exams. For example, understanding rates is particularly fundamental, so exercises frequently concentrate on rate calculations and re-arrangement of simple rate equations and this in-class instruction is complemented by appropriate TMYN modules. To reinforce the importance and utility of mathematics, the instructor continually makes connections between course material and TMYN tutorials. Pedagogical results are mostly positive. Because participation in TMYN modules is voluntary, two-thirds of students participate partially or wholly in the modules; the complementary fraction do not access a single module. We use pre- and post-tests to recognize gains in student mathematical competence. About one third of students either have lower or no change in performance whereas the balance exhibit varying gains. Some students’ scores saltate markedly by doubling, whereas other students achieve more modest gains. Not surprisingly, larger gains tend to be seen by students that have completed more modules with better scores, but this tendency is not absolute. TMYN modules are looked upon favorably by students. The preponderance of students think that TMYN modules improved their mathematical abilities and helped with the class. We plan continued use of TMYN modules with the goal of augmenting student participation, in anticipation of associated improvement in quantitative skills

Predictions from a stochastic polymer model for the MinDE dynamics in E.coli

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations -- both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.Comment: 16 page

Characterizing mixed mode oscillations shaped by noise and bifurcation structure

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and reset and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.Comment: 22 page