A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.

A model of seasonal foliage dynamics of the subtropical mangrove species Rhizophora stylosa Griff.growing at the northern limit of its distribution

Background： Progress of forest production in response to the environment requires a quantitative understanding of leaf area development. Therefore, it is necessary to investigate the dynamics of seasonal crown foliage in order to understand the productivity of mangroves, which play an important role in the subtropical and tropical coastlines of the world. Method： Crown foliage dynamics of the mangrove Rhizophora styloso were studies to reveal patterns of leaf recruitment, survival and seasonal leaf area growth. Results： Flushing of leaves occurred throughout the year, but both flushing and leaf area growth pattern of leaves varied with season. Maximum flushing occurred in summer, but leaf areas did not differ significantly with season. The half-expansion period is longer, and the intrinsic rate of increase was lower in winter. Summer flushed leaves grew faster at their initial stage and reached their maximum area over a shorter period of time. The difference in temperature and air vapor pressure deficit （VPD） between summer and winter contributed to the present dynamics of foliage patterns. The mean leaf longevity was estimated to be 13.1 month. The crown foliage area was almost stable throughout the year. Conclusions： Homeostatic control of the crown foliage area may be accompanied by the existence of ecophysiological mechanisms in R. stylosa. Integrating crown foliage dynamics into forest models represents an important step towards incorporating physiological mechanisms into the models for predicting growth responses to environmental changes and for understanding the complex responses of tree growth and litter production.

Hamiltonian Representation of Higher Order Partial Differential Equations with Boundary Energy Flows

This paper presents a system representation that can be applied to the description of the interaction between systems connected through common boundaries. The systems consist of partial differential equations that are first order with respect to time, but spatially higher order. The representation is derived from the instantaneous multisymplectic Hamiltonian formalism;therefore, it possesses the physical consistency with respect to energy. In the interconnection, particular pairs of control inputs and observing outputs, called port variables, defined on the boundaries are used. The port variables are systematically introduced from the representation.

Symplectic Numerical Approach for Nonlinear Optimal Control of Systems with Inequality Constraints

This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.