Mechanism design for land acquisition

We consider the issue of designing Bayesian incentive-compatible, efficient, individually rational and balanced mechanisms for Land Acquisition. This is a problem of great practical importance in developing countries. Several sellers, each with one unit of land, are located at the nodes of a graph. Two sellers are contiguous if they are connected by an edge in the graph. The buyer realizes a positive value only if he can purchase plots that constitute a path of given length. Our main result is that there is a robust set of priors for which successful mechanisms exist when there are at least two distinct feasible sets of contiguous sellers. The analysis also identifies the role of critical sellers who lie on all such feasible sets.     

A Kenmotsu Metric as a *-conformal Yamabe Soliton with Torse Forming Potential Vector Field

Acta Mathematica Sinica, English Series - The purpose of the present paper is to deliberate *-conformal Yamabe soliton, whose potential vector field is torse-forming on Kenmotsu manifold. Here, we...     

A Dissipative Reaction Network Drives Transient Solid–Liquid and Liquid–Liquid Phase Cycling of Nanoparticles

Transient states maintained by energy dissipation are an essential feature of dynamic systems where structures and functions are regulated by fluxes of energy and matter through chemical reaction networks. Perfected in biology, chemically fueled dissipative networks incorporating nanoscale components allow the unique properties of nanomaterials to be bestowed with spatiotemporal adaptability and chemical responsiveness. We report the transient dispersion of gold nanoparticles in water, powered by dissipation of a chemical fuel. A dispersed state that is generated under non-equilibrium conditions permits fully reversible solid–liquid or liquid–liquid phase transfer. The molecular basis of the out-of-equilibrium process is reversible covalent modification of nanoparticle-bound ligands by a simple inorganic activator. Activator consumption by a coupled dissipative reaction network leads to autonomous cycling between phases. The out-of-equilibrium lifetime is tunable by adjusting the pH value, and reversible phase cycling is reproducible over several cycles.     

Incoherently coupled screening photovoltaic spatial solitons in biased photovoltaic photorefractive crystals

Propagation characteristics and stability properties of two-component composite screening photovoltaic spatial solitons have been analyzed in this paper. Employing paraxial ray approximation, we have identified a very large family of new two-component composite screening photovoltaic solitons in photovoltaic-photorefractive crystals. These composite solitons can exist only when the carrier beams have the same polarization, wavelength and are mutually incoherent. We have identified a wide parameter space involving spatial width and power where these composite solitons can exist as a stationary entity. The identified regions of existence of solitons give a deeper understanding of these solitons and reveal some interesting properties. We have shown that composite solitons with different widths cannot propagate as a stationary entity. A relevant example has been provided where the crystal is LiNbO₃ or BaTiO₃. In addition, we have shown that in the new family of solitons, a degenerate pair with equal peak power possesses bistable property. Both paraxial theory and numerical simulation show that the identified family of composite solitons is stable.     

Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse

We have shown the possibility of tunable spectral switching in the far field with an apertured chirped cosh-Gaussian pulse by varying its cosh parameter (Ω). We have also shown that the switching frequency and both blue and red shifted frequencies can be also tuned by varying Ω. Possible application of our results in optical space communications has been highlighted.     

Far-field spectral behaviour and spectral switching of super-Gaussian pulses

We have presented the far-field spectral behaviour of a super-Gaussian pulse diffracted through a rectangular aperture. It has been found that the on-axis modified power spectrum is always blue shifted, whose value increases with the increase in the value of the super-Gaussian parameter (m). For off-axis case, at some critical angle of diffraction, the diffraction induced far-field power spectrum is split into two lines of equal height. The far-field power spectrum is blue shifted when the diffraction angle is greater than the critical angle, whereas it is red shifted when the diffraction angle is less than the critical angle, i.e., spectral switching occurs. The critical angle for switching significantly increases with the increase in the super-Gaussian parameter (m). An important finding is that the switching frequency, the blue and red shift frequencies can be tuned by varying m.     

Dispersion managed dissipative solitons with higher order nonlinearity and frequency-selective feedback

We present the generation and interaction dynamics of dispersion managed soliton in a dissipative cubic-quintic nonlinear optical fiber coupled with frequency-selective feedback. Analytically, perturbative variational method is used to obtain evolution equations for different soliton parameters that are subsequently solved to study the propagation characteristics of the dispersion managed dissipative solitons (DMDS). The DMDSs show breather like characteristics and are found to be robust against certain level of initial noise. Both the standard Gaussian and more generic super-Gaussian pulse profile are shown to yield stable DMDS. Interaction of two DMDSs of same phase may lead to a bound state. By varying the temporal separation and phase difference between the DMDSs the bound state can be switched between low to high speed regime.