Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.

A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Using organoclay to promote morphology refinement and co-continuity in high-density polyethylene/polyamide 6 blends - Effect of filler content and polymer matrix composition

We investigate the gradual changes of the microstructure of two blends of high-density polyethylene (HDPE) and polyamide 6 (PA6) at opposite composition filled with increasing amounts of an organomodified clay. The filler locates preferentially inside the polyamide phase, bringing about radical alterations in the micron-scale arrangement of the polymer phases. When the host polyamide represents the major constituent, a sudden reduction of the average sizes of the polyethylene droplets was observed upon addition of even low amounts of organoclay. A morphology refinement was also noticed at low filler contents when the particles distributes inside the minor phase. In this case, however, keep increasing the organoclay content eventually results in a high degree of PA6 phase continuity. Rheological analyses reveal that the filler loading at which the polyamide assembles in a continuous network corresponds to the critical threshold for its rheological transition from a liquid- to a gel-like behaviour, which is indicative of the structuring of the filler inside the host PA6. On the basis of this finding, a schematic mechanism is proposed in which the role of the filler in driving the space arrangement of the polymer phases is discussed. Finally, we show that the synergism between the reinforcing action of the filler and its ability to affect the blend microstructure can be exploited in order to enhance relevant technological properties of the materials, such as their high temperature structural integrity.

Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

The influence of nutrient supply and cell density on the growth and survival of intervertebral disc cells in 3D culture

The adult human intervertebral disc (IVD) is normally avascular. Changes to the extracellular matrix in degenerative disc disease may promote vascularisation and subsequently alter cell nutrition and disc homeostasis. This study examines the influence of cell density and the presence of glucose and serum on the proliferation and survival of IVD cells in 3D culture. Bovine nucleus pulposus (NP) cells were seeded at a range of cell densities (1.25 × 10(5)-10(6) cells/mL) and cultured in alginate beads under standard culture conditions (with 3.15 g/L glucose and 10 % serum), or without glucose and/or 20% serum. Cell proliferation, apoptosis and cell senescence were examined after 8 days in culture. Under standard culture conditions, NP cell proliferation and cluster formation was inversely related to cell seeding density, whilst the number of apoptotic cells and enucleated "ghost" cells was positively correlated to cell seeding density. Increasing serum levels from 10% to 20% was associated with increased cluster size and also an increased prevalence of apoptotic cells within clusters. Omitting glucose produced even larger clusters and also more apoptotic and senescent cells. These studies demonstrate that NP cell growth and survival are influenced both by cell density and the availability of serum or nutrients, such as glucose. The observation of clustered, senescent, apoptotic or "ghost" cells in vitro suggests that environmental factors may influence the formation of these phenotypes that have been previously reported in vivo. Hence this study has implications for both our understanding of degenerative disc disease and also cell-based therapy using cells cultured in vitro.

The role of organoclay in promoting co-continuous morphology in high-density poly(ethylene)/poly(amide) 6 blends

The effect of organically modified clay on the morphology, rheology and mechanical properties of high-density polyethylene (HDPE) and polyamide 6 (PA6) blends (HDPE/PA6 = 75/25 parts) is studied. Virgin and filled blends were prepared by melt compounding the constituents using a twin-screw extruder. The influence of the organoclay on the morphology of the hybrid was deeply investigated by means of wide-angle X-ray diffractometry, transmission and scanning electron microscopies and quantitative extraction experiments. It has been found that the organoclay exclusively places inside the more hydrophilic polyamide phase during the melt compounding. The extrusion process promotes the formation of highly elongated and separated organoclay-rich PA6 domains. Despite its low volume fraction, the filled minor phase eventually merges once the extruded pellets are melted again, giving rise to a co-continuous microstructure. Remarkably, such a morphology persists for long time in the melt state. A possible compatibilizing action related to the organoclay has been investigated by comparing the morphology of the hybrid blend with that of a blend compatibilized using an ethylene–acrylic acid (EAA) copolymer as a compatibilizer precursor. The former remains phase separated, indicating that the filler does not promote the enhancement of the interfacial adhesion. The macroscopic properties of the hybrid blend were interpreted in the light of its morphology. The melt state dynamics of the materials were probed by means of linear viscoelastic measurements. Many peculiar rheological features of polymer-layered silicate nanocomposites based on single polymer matrix were detected for the hybrid blend. The results have been interpreted proposing the existence of two distinct populations of dynamical species: HDPE not interacting with the filler, and a slower species, constituted by the organoclay-rich polyamide phase, which slackened dynamics stabilize the morphology in the melt state. In the solid state, both the reinforcement effect of the filler and the co-continuous microstructure promote the enhancement of the tensile modulus. Our results demonstrate that adding nanoparticles to polymer blends allows tailoring the final properties of the hybrid, potentially leading to high-performance materials which combine the advantages of polymer blends and the merits of polymer nanocomposites.

Comparison of the ageing behaviour of PM 2124 Al alloy and Al-SiCp metal-matrix composite

The ageing response of 2124 Al-SiC particulate metal-matrix composite (MMC) and unreinforced alloy has been examined using hardness measurements and Arrhenius analysis. The formation of phases during precipitation has been studied using differential scanning calorimetry (DSC). The MMC exhibits accelerated ageing compared to unreinforced alloy, due to enhanced S′ formation. The activation energy for diffusion is lower in the MMC than in the unreinforced alloy. DSC scans show Guinier-Preston B (GPB) zone nucleation to occur at a lower temperature in the MMC, whilst the total volume of GPB zones formed is smaller than in the unreinforced alloy. A model has been proposed to explain the GPB zone formation behaviour, in which ease of GPB zone nucleation varies within the MMC, as a function of ageing time and of position within the matrix. S′ formation is enhanced in the MMC because of improved diffusion and a large increase in density of heterogeneous nucleation sites compared to the unreinforced alloy. © 1994 Chapman & Hall.

Impact of scatterer density on the performances of double-scattering MIMO channels

We investigate a MIMO double-scattering model with both local and remote scatterers, aiming to investigate the effect of scatterer density on channel performances, such as capacity, correlation, and the condition number of the channel matrix in flat and frequency-selective fading channels. The investigations are carried out in terms of scatterer density. It is shown that in flat fading channels the scatterer density has a marginal effect on channel performances when the area of the two scatterer zones is fixed, while a significant impact is observed when the area of the scatterer zones is allowed to change. In frequency-selective fading channels, no matter the area of the scatterer zones is fixed or not, scatterer density can affect the channel capacity to a certain degree that depends on the length of the coding block of the transmitted signals. © 2010 IEEE.