The processing method applied to the side surface is different from the method applied to the light pass surface in neodymium phosphate glass (Nd:glass), and thus subsurface defects remain after processing. The subsurface defects in the side surface influence the gain uniformity of Nd:glass, which is a key factor to evaluate the performance of amplifiers. The scattering characteristics of side subsurface defects were simulated by finite difference time domain (FDTD) Solutions software. The scattering powers of the glass fabricated by a computer numerical control (CNC) machine without cladding were tested at different incident angles. The trend of the curve was similar to the simulated result, while the smallest point was different with the complex true morphology. The simulation showed that the equivalent residual reflectivity of the cladding glass can be more than 0.1% when the number of defects in a single gridding is greater than 50.

miR-124, a brain-specific microRNA, was originally considered as a key regulator in neuronal differentiation and the development of the nervous system. Here we showed that miR-124 expression was suppressed in patients with epilepsy and rats after drug induced-seizures. Intrahippocampal administration of a miR-124 duplex led to alleviated seizure severity and prolonged onset latency in two rat models (pentylenetetrazole- and pilocarpine-induced seizures), while miR-124 inhibitor led to shortened onset latency in pilocarpine-induced seizure rat models. Moreover, the result of local field potentials (LFPs) records further demonstrated miR-124 may have anti-epilepsy function. Inhibition of neuronal firing by miR-124 was associated with the suppression of mEPSC, AMPAR- and NMDAR-mediated currents, which were accompanied by decreased surface expression of NMDAR. In addition, miR-124 injection resulted in decreased activity and expression of cAMP-response element-binding protein1 (CREB1). a key regulator in epileptogenesis. A dual-luciferase reporter assay was used to confirm that miR-124 targeted directly the 3′UTR of CREB1 gene and repressed the CREB1 expression in HEK293T cells. Immunoprecipitation studies confirmed that the CREB1 antibody effectively precipitated CREB1 and NMDAR1 but not GLUR1 from rat brain hippocampus. These results revealed a previously unknown function of miR-124 in neuronal excitability and provided a new insight into molecular mechanisms underlying epilepsy.

This paper is devoted to time domain numerical solutions of two-dimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls for the development of advanced interface treatments for popular Maxwell solvers. We will investigate such interface treatments by considering two typical Maxwell solvers – one based on collocation formulation and another based on Galerkin formulation. To restore the accuracy reduction of the collocation finite-difference time-domain (FDTD) algorithm near an interface, the physical jump conditions relating discontinuous wave solutions on both sides of the interface must be rigorously enforced. For this purpose, a novel matched interface and boundary (MIB) scheme is proposed in this work, in which new jump conditions are derived so that the discontinuous and staggered features of electric and magnetic field components can be accommodated. The resulting MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses the staircase approximation errors completely over the Yee lattices. In the discontinuous Galerkin time-domain (DGTD) algorithm – a popular GalerkinMaxwell solver, a proper numerical flux can be designed to accurately capture the jumps in the electromagnetic waves across the interface and automatically preserves the discontinuity in the explicit time integration. The DGTD solution to Maxwell interface problems is explored in this work, by considering a nodal based high order discontinuous Galerkin method. In benchmark TM and TE tests with analytical solutions, both MIBTD and DGTD schemes achieve the second order of accuracy in solving circular interfaces. In comparison, the numerical convergence of the MIBTD method is slightly more uniform, while the DGTD method is more flexible and robust.

An extended microbridge test (eMBT) was proposed to assess the adhesion of metallic coatings on metallic substrates. Through loading on the backside of narrow striped freestanding coatings, a two-dimensional stable interfacial delamination was introduced. A cross-sectional scanning electron microscope (SEM) was used to examine the interfacial fracture process. A large deflection solution for elastic deformation of the coating was derived, and an approximate model was established for the estimate of interfacial crack extension force G. The eMBT samples of electroplated Ni coatings on C45 carbon steel substrate were tested, and the measured interfacial fracture toughness was about 5.28 J/m2. Cross-sectional SEM examination showed that the interface crack extended along the interface plane, and therefore the interfacial fracture proceeded by the debonding of Ni/steel interface.

Recently, the magnetostrictive microcantilever (MSMC) as a high performance biosensor platform was introduced. The MSMC is a wireless acoustic wave (AW) sensor and exhibits a high Q value. More importantly, the MSMC works well in liquid. In this paper, the detection of Bacillus anthracis spores using MSMCs with filamentous phage as the bioprobe is reported. The phased-coated MSMC biosensors were exposed to cultures containing target spores with increasing concentrations ranging from 5 × 104 to 5 × 108 spores/mL. By monitoring the shift in the resonance frequency of the MSMCs, the spores were detected in a real-time manner and a detection limit of 105 spores/mL was obtained for the MSMCs used in this research. Higher sensitivity is expected for the MSMCs with smaller size.

By using conventional solution casting method, a flexible ceramic [CaCu3Ti4O12 (CCTO)]-Polymer [P(VDF-TrFE)] composite has been fabricated. The CCTO ceramic powders with a relative uniform size were prepared by traditional powder processing method. The dielectric properties of these films with different CCTO fractions were determined. The process was optimized to achieve high dielectric constant. A dielectric constant about 510 at room temperature and 1240 at 95 °C at 1 kHz for 6 layer hot compression was obtained.

We embed truncations of the epi-graph of quasi-convex functions defined on linear subspaces E ⊂ MN × n of real matrices into MN × n to bound quasi-convex sets by the graph of the functions. We also characterize subspaces E on which all quasi-convex functions are convex and show, by using the Tarski–Seidenberg theorem in real algebraic geometry, that if dim (E) > N + n − 1, then there exist non-trivial quasi-convex functions on E.

We establish an approximation theorem for a sequence oflinear elastic strains approaching a compact set in L 1 by thesequence of linear strains of mapping bounded in Sobolev space W 1,p . We apply this result to establish equalities forsemiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.

We classify the Morse indices for rank-convex quadratic forms defined on the space of linear elastic strains in two- and three-dimensional linear elasticity. For the higher-dimensional case n > 3, we give a universal lower bound of the largest possible Morse index and various upper bound of this index. We show in the three-dimensional case that the Morse index is at most 1, and in this case the nullity cannot exceed 2. Examples are given that show that the estimates can be reached. We apply the results to study the critical points for smooth rank-one convex functions defined on the space of linear strains. We also examine an example and construct a quasiconvex function that vanishes in a finite set in the direct sum of the null subspace and the negative subspace of the rank-one quadratic form.

For every 0 < k < min{m,n} and any linear subspace E of real m × n matrices whose non-zero elements have rank greater than k, we show that there is a maximal extension Emax satisfying the same rank condition, and that the dimension of Emax is not less than (m – k)(n – k). We apply this result to the study of quasiconvex functions defined on the complement E⊥ of E in the form F(X) = f(PE⊥(X)), where PE⊥ is the orthgonal projection to E⊥.

The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.

In the shape from shading problem of computer vision oneattempts to recover the three-dimensional shape of an object orlandscape from the shading on a single image. Under theassumptions that the surface is dusty, distant, and illuminatedonly from above, the problem reduces to that of solving theeikonal equation |Du|=f on a domain in $\mathbb{R}^2$ . Despitevarious existence and uniqueness theorems for smooth solutions,we show that this problem is unstable, which is catastrophic forgeneral numerical algorithms.

We show the instability of solutions of the Dirichlet problem for Hamilton-Jacobi equations under quite general conditions.

We prove that connected subsets of M2×2 without rank-one connections are Lipschitz graphs of mappings from subsets of a fixed two-dimensional subspace to its orthogonal complement. Under a weaker condition that the set does not have rank-one connections locally, we are able to establish some global results on the set. We also establish some results on Lipschitz extensions of the functions thus obtained.

We construct nontrivial, non-negative quasiconvex functions denned on M2×2 with p-th order growth such that the zero sets of the functions are Lipschitz graphs of mappings from subsets of a fixed two-dimensional subspace to its orthogonal complement. We assume that the graphs do not have rank-one connections with the Lipschitz constants sufficiently small. In particular, we are able to construct quasiconvex functions which are homogeneous of degree p (p > 1) and ‘conjugating’ invariant.

We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in ℝ2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 X 2 matrices.