Time-dependent Plume Front Positioning and Its Dynamics Coupled With Seasonal River Efflux

The time-dependent plume front fluctuation concerning different tidal phases and its dynamics coupled with seasonal river efflux in the shelf off Kochi, south west coast of India, were investigated using Finite Volume Community Ocean Model (FVCOM). The region is linked with a monsoonal estuary, featured by mixed semi-diurnal tide (1 m) and exhibited a highly complicated plume pattern. The rivalry between river efflux with tidal phases create plume fronts in the shelf, whose gradients fortified or weakened by mixing dynamics. Eventhough the incessant river efflux in the summer monsoon impart significant momentum in the shelf, the range of frontal fluctuation was curtailed to 2 km by strong monsoon currents. During transient phase of the season (fall inter-monsoon), the tidal forcings on plume positioning overwhelm the shelf currents, such that the plume front fluctuate between 6-17 km (range increased to ~11 km) from the inlet. In low tides, the region near to the inlets was almost homogenized (Rd<1). While, it gets more stratified in high tides due to the transport of high saline ambient water towards the inlet and also by the decreasing kinetic energy (Rd>1). The location of frontal zones suitable for the propagation of nonlinear waves (F≤1)will change in respect to the competition between river efflux and tide-topography interaction. The strong stratified plume front regions with increased Brunt Vaisala Frequency (BVF) in summer monsoon behave as active zones of non linear wave propagation only when the plume front decelerates from supercritical to subcritical. During dry season, the F≤1 was satisfied at limited locations, but the absence of BVFmax zone (frequency >0.3 s-1) revealed that the amplitude of such nonlinear waves would be considerably small. The study divulge that tidally pulsating plume front fluctuates between 3-18 km from inlet and also highlights that the propagation of nonlinear waves with considerable amplitude will depend on both the plume front velocity and the Brunt Vaisala Frequency of the water column.

Topology optimization of an acoustic diode?

By using topology optimization, we consider the problem of designing a passive acoustic device that allows for one-way flow of sound waves; such a device is often colloquially referred to as an acoustic diode. The Helmholtz equation is used to model the time harmonic linear wave propagation together with a Dirichlet-to-Neumann (DtN) type boundary condition, and the finite element method is used for discretization. The objective of this study is to maximize the wave propagation in one direction (from left to right) and minimize the wave propagation in the reverse direction (from right to left) for planar incoming waves. The method of moving asymptotes (MMA) solves the optimization problem, and a continuation approach is used for the penalizing intermediate design variables. The results for the optimized waveguide show that more than 99.8% of the power of planar incoming waves get transmitted from left to right while less than 0.3% gets transmitted in the reverse direction for planar incoming waves in the specified frequency range. Since a true diode is a non-reciprocal device and here we used a linear acoustic wave model, which is basically reciprocal, we discuss details about how it appears to be possible to obtain a one-way waveguiding effect using this linear model.

On new closed form solutions: The (2+1)-dimensional Bogoyavlenskii system

This paper studies the new closed form solutions to (2+1)-dimensional Bogoyavlenskii system that describes interaction of a Riemann wave propagation. The extended Fan sub-equation technique is used to investigate some new traveling wave solutions to the higher-dimensional coupled model. The obtained closed form solutions are named as shock, kink, shock and periodic soliton solutions. Clearly, the outcomes of the study confirm the strength of the current approach. Moreover, the obtained results are helpful for the understanding of non-linear wave propagation and are of great interest to present-day scientists and can be employed to deal with more complex models arising in diverse disciplines of contemporary science.

Time reversed optical waves by arbitrary vector spatiotemporal field generation

Lossless linear wave propagation is symmetric in time, a principle which can be used to create time reversed waves. Such waves are special “pre-scattered” spatiotemporal fields, which propagate through a complex medium as if observing a scattering process in reverse, entering the medium as a complicated spatiotemporal field and arriving after propagation as a desired target field, such as a spatiotemporal focus. Time reversed waves have previously been demonstrated for relatively low frequency phenomena such as acoustics, water waves and microwaves. Many attempts have been made to extend these techniques into optics. However, the much higher frequencies of optics make for very different requirements. A fully time reversed wave is a volumetric field with arbitrary amplitude, phase and polarisation at every point in space and time. The creation of such fields has not previously been possible in optics. We demonstrate time reversed optical waves with a device capable of independently controlling all of light’s classical degrees of freedom simultaneously. Such a class of ultrafast wavefront shaper is capable of generating a sequence of arbitrary 2D spatial/polarisation wavefronts at a bandwidth limited rate of 4.4 THz. This ability to manipulate the full field of an optical beam could be used to control both linear and nonlinear optical phenomena.

Linear-Gaussian systems and signal processing

Linear systems theory, based on the mathematics of vector spaces, is the backbone of all “classical” DSP and a large part of statistical machine learning. The basic idea -- that linear algebra applied to a signal can of substantial practical value -- has counterparts in many areas of science and technology. In other areas of science and engineering, linear algebra is often justified by the fact that it is often an excellent model for real-world systems. For example, in acoustics the theory of (linear) wave propagation emerges from the concept of linearization of small pressure disturbances about the equilibrium pressure in classical fluid dynamics. Similarly, the theory of electromagnetic waves is also linear. Except when a signal emerges from a justifiably linear system, in DSP and machine learning we do not have any particular correspondence to reality to back up the choice of linearity. However, the mathematics of vector spaces, particularly when applied to systems which are time-invariant and jointly Gaussian, is highly tractable, elegant and immensely useful.