Lithium garnet oxide dispersed polymer composite membrane for rechargeable lithium batteries

Free-standing composite polymer membranes comprising of high molecular weight poly (ethylene oxide) (PEO) complexed with lithium perchlorate (LiClO₄) and Li₆La₂BaTa₂O₁₂ (LLBTO) garnet oxide as filler were developed via standard solution-casting method. The as-synthesized composite membranes were investigated through powder x-ray diffraction (PXRD), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and impedance spectroscopy techniques for their phase, thermal, morphological, and electrical properties, respectively. The lithium ion conductivity of polymer composite membranes consisting of PEO₈/LiClO₄ with various weight percents (5, 10, 15, 20, 25, and 30) of LLBTO were evaluated. We demonstrated a significant enhancement in Li⁺ conductivity with the addition of LLBTO to the polymer-lithium salt complex. Among the investigated membranes, the composite containing 20 LLBTO wt% garnet oxide exhibits maximized room temperature (30 °C) Li⁺ conductivity of 2.03 × 10^?4 S cm^?1 and electrochemical stability greater than 4.5 V.     

Facile Exfoliation of Single‐Crystalline Copper Alkylphosphates to Single‐Layer Nanosheets and Enhanced Supercapacitance

Manipulation of low‐dimensional solids through soft chemical routes is an elegant way to realize newer materials. A new family of single‐crystalline transition‐metal layered organophosphates, with about 185 000 metal phosphate layers in a single crystal, can be exfoliated to a single‐layer nanosheet by a facile and rapid solvent assisted method. This exfoliation aids the formation of high‐surface‐area pyrophosphates with enhanced supercapacitance.     

Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

We construct the hydrodynamic equations for suspensions of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions: (i) Nematic SPP suspensions are always absolutely unstable at long wavelengths. (ii) SPP suspensions support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wave number regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable. (iv) The variance in the number N of particles, divided by the mean , diverges as (2/3 ) in polar-ordered SPP suspensions.     

Solution of the boussinesq equations by the finite element method

A finite element procedure is presented for the calculation of two-dimensional transient convective/conductive heat transfer in a fluid region. The governing equations are expressed in terms of the primitive variables; the flow is assumed to be laminar, and the fluid incompressible within the Boussinesq approximation. Three typical problems are examined: flow through a sudden enlargement, natural convection in rectangular enclosures, and natural convection between horizontal concentric cylinders. An assessment of the characteristics of the flow regime is made in association with varying dimensionless Prandtl and Rayleigh numbers, as well as cavity aspects ratios. The upper limit for the Rayleigh number in the present paper is 10⁷. Wherever possible, the results are compared with existing solutions obtained by other numerical methods.     

Systematics of some levels in even-even nuclei

Morinaga’s study of the lowest odd-parity states in even-even nuclei has been extended to even-parity odd-spin and odd-parity even-spin states. These states show good agreement with the curve E=67 A^?3/4 Mev.     

Generalized Hardy-Sobolev Inequalities and Exponential Decay of the Entropy of g(x)[(u)\dot]=Dug(x)\dot{u}=\Delta u

Provided the non-negative function g ? L_loc¹(W)g \in L_{\rm loc}^1(\Omega) allows for a generalized Hardy-Sobolev inequality, existence and uniqueness of global weak solutions of the possibly degenerate parabolic PDE g(x)[(u)\dot]=Dug(x)\dot{u}=\Delta u , subject to homogeneous Dirichlet boundary conditions, is proved. The maximum/minimum principle holds. The associated entropy decays exponentially as t with a rate not exceeding 2/C, where C is the constant arising in the generalized Hardy-Sobolev inequality.