Hyperbolic Metamaterials via Hierarchical Block Copolymer Nanostructures

Hyperbolic metamaterials (HMMs) offer unconventional properties in the field of optics, enabling the opportunity for confinement and propagation of light at the nanoscale. In-plane orientation of the optical axis, in the direction coinciding with the anisotropy of the HMMs, is desirable for a variety of novel applications in nanophotonics and imaging. Here, we introduce a method for creating localized HMMs with in-plane optical axis based on block copolymers (BCPs) blend instability. The dewetting of BCP thin film over topographically defined substrates generates droplets composed of highly ordered lamellar nanostructures in hierarchical configuration. The hierarchical nanostructures represent a valuable platform for the subsequent pattern transfer into a Au/air HMM, exhibiting hyperbolic behavior in a broad wavelength range in the visible spectrum. A computed Purcell factor as high as 32 at 580 nm supports the strong reduction in the fluorescence lifetime of defects in nanodiamonds placed on top of the HMM.

Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations

The dual-phase-lag heat transfer models attract a lot of interest of researchers in the last few decades. These are used in problems arising from non-classical thermal models, which are based on a non-Fourier type law. We study uniqueness of solutions to some inverse source problems for fractional partial differential equations of the Dual-Phase-Lag type. The source term is supposed to be of the form h(t)f(x) with a known function h(t). The unknown space dependent source f(x) is determined from the final time observation. New uniqueness results are formulated in Theorem 1 (for a general fractional Jeffrey-type model). Here, the variational approach was used. Theorem 2 derives uniqueness results under weaker assumptions on h(t) (monotonically increasing character of h(t) was removed) in a case of dominant parabolic behavior. The proof technique was based on spectral analysis. Section Modified Model for τq>τT shows that an analogy of Theorem 2 for dominant hyperbolic behavior (fractional Cattaneo–Vernotte equation) is not possible.

COMPRESSIBILITY BEHAVIOUR OF COMPACTED SOILS – HYPERBOLIC MODELLING

Compacted soils constitute most engineering projects such as earth dams,embankments, pavements, and engineered slopes because of their high shear strengthand low compressibility. The compressibility behavior of compacted soils is a key soilparameter in the design of earth structures but it is not determined correctly owing topartly saturated state. The compressibility of compacted soils can be better evaluatedunder the framework of hyperbolic behavior. One dimensional Consolidation tests oncompacted specimens were conducted using conventional oedometer apparatus underconstant water content condition. Tests were conducted by compact the soil specimensat respective optimum moisture contents for eight different soil samples, of varyinggrain size characteristics and consistency limits, collected from Tirupati Region. Themain objective of this study is to examine the compressibility behavior of compactedsoils to propose a phenomenological model. It is observed that the compressibilitybehavior can be captured by hyperbolic modeling with model parameters involved inthe behavior being initial void ratio, e0, representing the initial state of soil and otherhyperbolic constants linked to this state. The data of 6 samples were used fordeveloping the model and the data of remaining two samples were used for predictingthe observed response from the model proposed. The data of published literature hasalso been used to predict the experimental behavior to bring out the merits of themodel proposed.

Amontons’ laws and the friction in miniature elements

This research demonstrates that Amontons’ laws, which state that the friction force is proportional to the (normal) applied load and is independent of the apparent contact area, begin to break down when the sliding solids have dimensions of several millimetres and loads of tens of millinewtons. The method used to test the hypothesis involved sliding a cylinder into another cylinder. The results indicated that the static friction coefficient as a function of the load exhibited hyperbolic behavior at low loads; the friction force was not proportional to the load. While the static friction coefficient as a function of the apparent contact area exhibited linear behavior, the friction force was dependent on the apparent contact area. The tests were conducted without lubrication and the materials used were steel on SAE 40 bronze and steel on polytetrafluroethylene.

Vortex filamentation and fragmentation phenomena in flapping motion and effect of aspect ratio and frequency on global strain, rotation, and enstrophy

In the present study, flow field around rigid flat plate wings executing main flapping motion has been studied using phase-locked two-dimensional particle image velocimetry measurements. Experiments have been conducted in water as a fluid medium for an asymmetric upper–lower stroke single degree of freedom main flapping motion. Two different aspect ratio (1.5 and 1.0) rectangular wings at 1.5 and 2.0 Hz flapping frequency in hovering flight mode (advance ratio, J = 0), zero wing pitch angle, and chord-based Reynolds number of the order of 104 have been studied. Velocity field and vorticity field with λ2 criterion information have been obtained for the complete stroke in great detail to reveal the minute aspects of flow dynamics. The flow features during the downstroke and upstroke have been observed to be consistent for all four cases investigated. The predominant characteristic of the flow during downstroke and upstroke has been referred to as vortex filamentation and fragmentation phenomena. Quantities such as circulation, rate of strain, rate of rotation, and enstrophy have been studied to identity the effect of minor change in aspect ratio and flapping frequency. It is found that for higher aspect ratio wing hyperbolic behavior is predominant except for end of downstroke and beginning of upstroke where elliptic behavior is observed. For lower aspect ratio, wing elliptic behavior is predominant except for end of upstroke and beginning of downstroke where hyperbolic behavior is seen. The hyperbolic behavior became stronger at higher frequency. From enstrophy distribution it is evident that higher frequencies play a more dominant role than aspect ratio in determining the budget.

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

We construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to the action of K-essence theories. This approach is applied to anisotropic cosmological Bianchi type VI(h=-1) model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. The classical Einstein field equations give us a hidden symmetry, corresponding to the equality between two radii B=C, which permits us to solve exactly the equations of motion. One relation between the scale factors (A,C) via the solutions is found. With this hidden symmetry, then we solve the FRW model, finding that the scale factor goes to B radii. Also the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology is solved, building a wavepacket when the scalar fields have a hyperbolic behavior, obtaining some qualitative results when we analyze the projection plane to the wall formed by the probability density. Bohm’s formalism for this cosmological model is revisited too.