Numerical simulations of winter cold damage to citrus fruits using the WRF model

To numerically assess winter cold damages of citrus fruits, a cold duration of sub-zero temperature was simulated using a high resolution configuration (500&thinsp;m horizontal grid spacing) of the WRF numerical weather prediction system. Japanese citrus is often cultivated on slopes made of a small hill and a valley. Hence, a high resolution spatial configuration is needed to simulate cold durations at complex micro-topographies. In this study, detailed cold duration maps for sub-zero temperatures were produced to assess the spatial difference of cold duration, as an example of a winter cold surge attack in west Japan in 2011. Our findings suggest that the recorded temperature (by automatic observation of the Japan Meteorological Agency), which was observed at a flat coastal plain, may underestimate cold damage risk for citrus fruit on narrow slopes, valleys and hilly areas.</p

A skeleton structure of self-replicating dynamics

A skeleton dynamics for the self-replicating patterns (SRP) of reaction diffusion system is presented. Self­replicating dynamics can be regarded as a transient process from a localized trigger to a stable Turing pattern or oscillatory Turing pattern. It looks like a reverse process of usual coarsening phenomena, i.e., the number of unit localized pattern increases until the domain is filled by them completely. SRP was found in several chemical reaction models, for instance, the Gray-Scott model as well as in real experi­ments. The most difficult point to describe SRP lies in the fact that it is truly a transient phenomenon in the sense that it can be captured neither as a definite object in dynamical system theory like an attractor nor an orbit itinerating among saddle points in the phase space. To our knowledge, it is not known that what kind of dynamical framework is suitable to clarify the behavior of SRP. The aim is to give a new point of view to describe such a transient dynamics of SRP on a finite interval. Especially we concen­trate on the basic mechanism causing SRP from a bifurcational view point by employing a new model system and its finite-dimensional con:.partment model which shares common qualitative features with the Gray-Scott model. By a careful anatomy of global bifurcation diagrams, the skeleton dynamics of SRP comes from a hierarchy structure of the subcritical bifurcating loops of oscillatory branches of pulse type. It should be noted that these loops themselves do not constitute the skeleton dynamics of SRP, but the ruins of them do it. In other words, the aftereffect of the hierarchy structure manifests the dynamics of SRP. The most important ingredient of an organizing center from which the whole hierarchy structure of SRP emerges is Bogdanov-Takens-Turing singularity as well as the existence of stable equilibrium point, which indicates universality of the above structure in the class of nonlinearities sharing this character

Chaotic pulses for discrete reaction diffusion systems

Existence and dynamics of chaotic pulses on a one-dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on one-dimensional lattice, i.e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, is found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, it is found that the route from standing pulse to chaotic pulse is of intermittent type. If two chaotic pulses collide with appropriate timing, they form a periodic oscillating pulse called a molecular pulse. Interaction among many chaotic pulses is also studied numerically