New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials

We have generated, using an sl(2,R) formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problems for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable.Comment: 14 pages, 5 tables, LaTeX2

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

Electrically modulated photoluminescence in ferroelectric liquid crystal

Electrical modulation and switching of photoluminescence (PL) have been demonstrated in pure deformed helix ferroelectric liquid crystal (DHFLC) material. The PL intensity increases and peak position shifts towards lower wavelength above a threshold voltage which continues up to a saturation voltage. This is attributed to the helix unwinding phenomenon in the DHFLC on the application of an electric field. Moreover, the PL intensity could be switched between high intensity (field-on) and low intensity (field-off) positions. These studies would add a new dimension to ferroelectric liquid crystal's application in the area of optical devices.Comment: 4 figure

Emergence of a non-scaling degree distribution in bipartite networks: a numerical and analytical study

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We derive the exact analytical expression for the degree-distribution of all these different types of attachments while assuming that edges are incorporated sequentially, i.e., a single edge is added to the growing network in a time step. We also provide an approximate expression for the case when more than one edge are added in a time step. We show that depending on the relative weight between random and preferential attachment, the degree-distribution of this type of network falls into one of four possible regimes which range from a binomial distribution for pure random attachment to an u-shaped distribution for dominant preferential attachment

EPR and Structural Characterization of Water-Soluble Mn2+-Doped Si Nanoparticles.

Water-soluble poly(allylamine) Mn2+-doped Si (SiMn) nanoparticles (NPs) were prepared and show promise for biologically related applications. The nanoparticles show both strong photoluminescence and good magnetic resonance contrast imaging. The morphology and average diameter were obtained through transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM); spherical crystalline Si NPs with an average diameter of 4.2 ± 0.7 nm were observed. The doping maximum obtained through this process was an average concentration of 0.4 ± 0.3% Mn per mole of Si. The water-soluble SiMn NPs showed a strong photoluminescence with a quantum yield up to 13%. The SiMn NPs had significant T1 contrast with an r1 relaxivity of 11.1 ± 1.5 mM-1 s-1 and r2 relaxivity of 32.7 ± 4.7 mM-1 s-1 where the concentration is in mM of Mn2+. Dextran-coated poly(allylamine) SiMn NPs produced NPs with T1 and T2 contrast with a r1 relaxivity of 27.1 ± 2.8 mM-1 s-1 and r2 relaxivity of 1078.5 ± 1.9 mM-1 s-1. X-band electron paramagnetic resonance spectra are fit with a two-site model demonstrating that there are two types of Mn2+ in these NP's. The fits yield hyperfine splittings (A) of 265 and 238 MHz with significant zero field splitting (D and E terms). This is consistent with Mn in sites of symmetry lower than tetrahedral due to the small size of the NP's

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds

Surface Engineering for Phase Change Heat Transfer: A Review

Among numerous challenges to meet the rising global energy demand in a sustainable manner, improving phase change heat transfer has been at the forefront of engineering research for decades. The high heat transfer rates associated with phase change heat transfer are essential to energy and industry applications; but phase change is also inherently associated with poor thermodynamic efficiencies at low heat flux, and violent instabilities at high heat flux. Engineers have tried since the 1930's to fabricate solid surfaces that improve phase change heat transfer. The development of micro and nanotechnologies has made feasible the high-resolution control of surface texture and chemistry over length scales ranging from molecular levels to centimeters. This paper reviews the fabrication techniques available for metallic and silicon-based surfaces, considering sintered and polymeric coatings. The influence of such surfaces in multiphase processes of high practical interest, e.g., boiling, condensation, freezing, and the associated physical phenomena are reviewed. The case is made that while engineers are in principle able to manufacture surfaces with optimum nucleation or thermofluid transport characteristics, more theoretical and experimental efforts are needed to guide the design and cost-effective fabrication of surfaces that not only satisfy the existing technological needs, but also catalyze new discoveries