A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which "chaotic advection" occurs in the mixer. An optimization of mixer geometries is a non trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper an algorithm is presented that applies the concept of finite-time Lyapunov exponents to obtain a quantitative measure of the chaotic advection of the flow and hence the performance of micromixers. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and non-interacting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by a comparison of the improved geometrical structure of the staggered herringbone mixer with available literature data.Comment: 9 pages, 8 figure

Low Resistance Polycrystalline Diamond Thin Films Deposited by Hot Filament Chemical Vapour Deposition

Polycrystalline diamond thin films with outgrowing diamond (OGD) grains were deposited onto silicon wafers using a hydrocarbon gas (CH4) highly diluted with H2 at low pressure in a hot filament chemical vapour deposition (HFCVD) reactor with a range of gas flow rates. X-ray diffraction (XRD) and SEM showed polycrystalline diamond structure with a random orientation. Polycrystalline diamond films with various textures were grown and (111) facets were dominant with sharp grain boundaries. Outgrowth was observed in flowerish character at high gas flow rates. Isolated single crystals with little openings appeared at various stages at low gas flow rates. Thus, changing gas flow rates had a beneficial influence on the grain size, growth rate and electrical resistivity. CVD diamond films gave an excellent performance for medium film thickness with relatively low electrical resistivity and making them potentially useful in many industrial applications

Foot Bone in Vivo: Its Center of Mass and Centroid of Shape

This paper studies foot bone geometrical shape and its mass distribution and establishes an assessment method of bone strength. Using spiral CT scanning, with an accuracy of sub-millimeter, we analyze the data of 384 pieces of foot bones in vivo and investigate the relationship between the bone's external shape and internal structure. This analysis is explored on the bases of the bone's center of mass and its centroid of shape. We observe the phenomenon of superposition of center of mass and centroid of shape fairly precisely, indicating a possible appearance of biomechanical organism. We investigate two aspects of the geometrical shape, (i) distance between compact bone's centroid of shape and that of the bone and (ii) the mean radius of the same density bone issue relative to the bone's centroid of shape. These quantities are used to interpret the influence of different physical exercises imposed on bone strength, thereby contributing to an alternate assessment technique to bone strength.Comment: 9 pages, 4 figure

Applications of Nature-Inspired Algorithms for Dimension Reduction: Enabling Efficient Data Analytics

In [1], we have explored the theoretical aspects of feature selection and evolutionary algorithms. In this chapter, we focus on optimization algorithms for enhancing data analytic process, i.e., we propose to explore applications of nature-inspired algorithms in data science. Feature selection optimization is a hybrid approach leveraging feature selection techniques and evolutionary algorithms process to optimize the selected features. Prior works solve this problem iteratively to converge to an optimal feature subset. Feature selection optimization is a non-specific domain approach. Data scientists mainly attempt to find an advanced way to analyze data n with high computational efficiency and low time complexity, leading to efficient data analytics. Thus, by increasing generated/measured/sensed data from various sources, analysis, manipulation and illustration of data grow exponentially. Due to the large scale data sets, Curse of dimensionality (CoD) is one of the NP-hard problems in data science. Hence, several efforts have been focused on leveraging evolutionary algorithms (EAs) to address the complex issues in large scale data analytics problems. Dimension reduction, together with EAs, lends itself to solve CoD and solve complex problems, in terms of time complexity, efficiently. In this chapter, we first provide a brief overview of previous studies that focused on solving CoD using feature extraction optimization process. We then discuss practical examples of research studies are successfully tackled some application domains, such as image processing, sentiment analysis, network traffics / anomalies analysis, credit score analysis and other benchmark functions/data sets analysis

The phylogenetically-related pattern recognition receptors EFR and XA21 recruit similar immune signaling components in monocots and dicots

During plant immunity, surface-localized pattern recognition receptors (PRRs) recognize pathogen-associated molecular patterns (PAMPs). The transfer of PRRs between plant species is a promising strategy for engineering broad-spectrum disease resistance. Thus, there is a great interest in understanding the mechanisms of PRR-mediated resistance across different plant species. Two well-characterized plant PRRs are the leucine-rich repeat receptor kinases (LRR-RKs) EFR and XA21 from Arabidopsis thaliana (Arabidopsis) and rice, respectively. Interestingly, despite being evolutionary distant, EFR and XA21 are phylogenetically closely related and are both members of the sub-family XII of LRR-RKs that contains numerous potential PRRs. Here, we compared the ability of these related PRRs to engage immune signaling across the monocots-dicots taxonomic divide. Using chimera between Arabidopsis EFR and rice XA21, we show that the kinase domain of the rice XA21 is functional in triggering elf18-induced signaling and quantitative immunity to the bacteria Pseudomonas syringae pv. tomato (Pto) DC3000 and Agrobacterium tumefaciens in Arabidopsis. Furthermore, the EFR:XA21 chimera associates dynamically in a ligand-dependent manner with known components of the EFR complex. Conversely, EFR associates with Arabidopsis orthologues of rice XA21-interacting proteins, which appear to be involved in EFR-mediated signaling and immunity in Arabidopsis. Our work indicates the overall functional conservation of immune components acting downstream of distinct LRR-RK-type PRRs between monocots and dicots