Geometry Of Interaction Research Articles

Nonlinear diffraction in orientation-patterned semiconductors.

This work represents experimental demonstration of nonlinear diffraction in an orientation-patterned semiconducting material. By employing a new transverse geometry of interaction, three types of second-order nonlinear diffraction have been identified according to different configurations of quasi-phase matching conditions. Specifically, nonlinear Čerenkov diffraction is defined by the longitudinal quasi-phase matching condition, nonlinear Raman-Nath diffraction satisfies only the transverse quasi-phase matching condition, and nonlinear Bragg diffraction fulfils the full vectorial quasi-phase matching conditions. The study extends the concept of transverse nonlinear parametric interaction toward infrared frequency conversion in semiconductors. It also offers an effective nondestructive method to visualise and diagnose variations of second-order nonlinear coefficients inside semiconductors.

Quantum mechanics study of repulsive π–π interaction and flexibility of phenyl moiety in the iron azodioxide complex

In this study, repulsive π–π interactions within iron azodioxide complex Fe[Ph(O)NN(O)Ph]3 were quantum mechanically characterized using DFT, MP2 and CCSD(T) methods. Flexibility of six phenyl moieties in this complex structure was also investigated by structural optimization approach using the DFT methods. Our MP2 and CCSD(T) calculations of the closest pair provided interaction energy of 6.62 and 8.29kcal/mol respectively, which indicate a strongest repulsion among these intra-molecular π–π interactions. Interaction energy of the particular π–π pair calculated from 24 hybrid DFT methods ranges from 4.56kcal/mol from BHandH method to 15.15kcal/mol from O3LYP method. Cares should be exercised when interpreting interaction energy and geometry optimization from DFT simulation of systems containing π–π interaction. Comparison between the DFT results and the benchmark CCSD(T) results shows that the DFT calculations of π–π interaction are reasonable but still need to be interpreted with caution. Furthermore, MP2 interaction energy of −44.69kcal/mol between two substituted π systems/phenyl rings Ph(O)N-moieties suggested that above energetically unfavorable π–π interaction can be compensated by the covalent bond N–N in a single ligand Ph(O)NN(O)Ph, which allows for a reasonable stability across the complex molecules. Optimizations of the entire complex molecule using B3LYP and M06HF methods produced a large variation of π–π distances and orientations, which implied that the complex molecule may perform catalysis at room temperature.

Patterns in the Pythagorean Configuration and Some Extensions: The Power of Interactive Geometry Software.

In this paper I describe classroom experiences with pre-service secondary mathematics teachers (PSMTs) investigating and extending patterns embedded in the Pythagorean configuration. This geometric figure is a fruitful source of mathematical tasks to help students, including PSMTs, further develop habits of mind such as visualization, experimenting, looking for and noticing patterns, conjecturing, inventing, constructing mathematical arguments, and posing problems. By carrying out these tasks, the PSMTs were also engaged in a plethora of mathematical practices recommended by the Common Core State Standards Initiative (CCSSI). The use of the Geometer’s Sketchpad facilitated the accomplishment of most of these activities. As students of mathematics, these PSMTs were engaged in activities to reinforce some of their mathematical habits of mind and experienced learning new mathematical ideas and processes through practices that exemplify typical mathematical thinking. As future teachers, they were engaged in tasks so they can, in turn, design or adapt instructional tasks to develop further their own students’ habits of minds and engage them in learning mathematics through the mathematical practices advocated by the CCSSI.

Spectra and Eigenstates of Spin Chain Hamiltonians

We prove that translationally invariant Hamiltonians of a chain of n qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $${n \rightarrow \infty}$$ we show that any translationally invariant Hamiltonian of a chain of n qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixed-size sub-blocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e., Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly, in the limit $${n \rightarrow \infty}$$ we show that any nearest-neighbour Hamiltonian of a chain of n qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a non-interacting one. The comparison applies to chains of qubits with translationally invariant nearest-neighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented that suggests that the translational invariance condition may be dropped in the case of nearest-neighbour chains.

Van der Waals Interactions on the Mesoscale: Open-Science Implementation, Anisotropy, Retardation, and Solvent Effects.

The self-assembly of heterogeneous mesoscale systems is mediated by long-range interactions, including van der Waals forces. Diverse mesoscale architectures, built of optically and morphologically anisotropic elements such as DNA, collagen, single-walled carbon nanotubes, and inorganic materials, require a tool to calculate the forces, torques, interaction energies, and Hamaker coefficients that govern assembly in such systems. The mesoscale Lifshitz theory of van der Waals interactions can accurately describe solvent and temperature effects, retardation, and optically and morphologically anisotropic materials for cylindrical and planar interaction geometries. The Gecko Hamaker open-science software implementation of this theory enables new and sophisticated insights into the properties of important organic/inorganic systems: interactions show an extended range of magnitudes and retardation rates, DNA interactions show an imprint of base pair composition, certain SWCNT interactions display retardation-dependent nonmonotonicity, and interactions are mapped across a range of material systems in order to facilitate rational mesoscale design.

Application of Technology in Teaching Mathematics: A Concept Paper for Measuring Determinants of Acceptance among School Teachers

In the context of Bangladesh, there is no substantial research going beyond level of belief of mathematics teachers of technology use in teaching learning process. While belief influences to motivation, perception, intention, awareness and acceptance therefore, is has been assumed in this study that there must be some determinants of acceptance among school teachers in Bangladesh. Calculators and other technological tools, such as computer algebra systems, interactive geometry software, applets, spreadsheets, and interactive presentation devices, are vital components of a high-quality mathematics education. With guidance from effective mathematics teachers, students at different levels can use these tools to support and extend mathematical reasoning and sense making, gain access to mathematical content and problem-solving contexts, and enhance computational fluency. In a well-articulated mathematics program, students can use these tools for computation, construction, and representation as they explore problems. The use of technology also contributes to mathematical reflection, problem identification, and decision making. Unfortunately, in Bangladesh bringing technology in mathematics teaching is less studied and overlooked. This has led this particular research to conduct this study.

Assessment of pile response due to deep excavation in close proximity—A case study based on DTL3 Tampines West Station

AbstractGround movements during deep excavations and tunnelling, especially in urban areas, may potentially have major impact on adjacent buildings, structures and utilities. This impact on buildings and structures needs to be assessed by considering the horizontal and vertical displacements induced by deep excavations to determine the necessary mitigation measures. One major factor affecting the degree of severity the impact due to deep excavation may have on the buildings and structures is the type of foundation systems. While methodology in determining the damage category for the buildings on shallow foundation has been quite well established, the methodology for assessing the impact on the pile foundation is not straightforward due to the geometry and complexity of soil structure interaction. Often simplified two-dimensional (2D) or comprehensive three-dimensional (3D) finite element analyses would be carried out for the stage excavation to predict the displacement and stresses in the piles. Suitable ...

Elasto-optic effect anisotropy in calcium tungstate crystals.

The anisotropy of piezo- and elasto-optic effects in calcium tungstate CaWO4 crystals was studied by the indicatory surfaces method. On the basis of the maximum surfaces of the elasto-optic effect, the geometry of acousto-optic interaction with maximum efficiency was found.

Interaction between mobile dislocations and perfect dislocation loops in Fe-Ni-Cr austenitic alloy systems

The classical molecular dynamics method is employed to simulate the interaction of screw and edge dislocations with interstitial perfect dislocation loops (of 2 and 5 nm in diameter) in the austenitic model alloy Fe70Ni10Cr20 at temperatures of T = 300–900 K. Perfect loops can be created from Frank loops during the plastic deformation of irradiated austenitic steels applied in nuclear reactors. As a result, the dislocation-defect interaction mechanisms are established and classified. The loop absorption mechanisms, which are related to the formation of free channels capable of enhancing radiation-induced steel embrittlement, are revealed. The effectivenesses of loop absorption observed during their interaction with screw and edge dislocations, as well as unpinning stresses required for a dislocation to overcome the defect acting as an obstacle, are compared versus the material temperature, defect size, and interaction geometry.

Helix-Helix Interactions: Is the Medium the Message?

In this issue of Structure, Zhang and colleagues compare the helix-helix interaction spaces of an extensive database of soluble and membrane proteins. Intriguingly, the resultant clusters show similar helix interaction geometries between the protein classes, differing in detail only by patterns of local interactions and inter-helical distances.

Electronic structure and partial charge distribution of Doxorubicin in different molecular environments.

The electronic structure and partial charge of doxorubicin (DOX) in three different molecular environments-isolated, solvated, and intercalated in a DNA complex-are studied by first-principles density functional methods. It is shown that the addition of solvating water molecules to DOX, together with the proximity to and interaction with DNA, has a significant impact on the electronic structure as well as on the partial charge distribution. Significant improvement in estimating the DOX-DNA interaction energy is achieved. The results are further elucidated by resolving the total density of states and surface charge density into different functional groups. It is concluded that the presence of the solvent and the details of the interaction geometry matter greatly in determining the stability of DOX complexation. Ab initio calculations on realistic models are an important step toward a more accurate description of the long-range interactions in biomolecular systems.

Geometry of Resource Interaction – A Minimalist Approach

The Resource $\lambda$-calculus is a variation of the $\lambda$-calculus where arguments can be superposed and must be linearly used. Hence it is a model for linear and non-deterministic programming languages, and the target language of Ehrhard-Taylor expansion of $\lambda$-terms. In a strictly typed restriction of the Resource $\lambda$-calculus, we study the notion of path persistence, and we define a Geometry of Interaction that characterises it, is invariant under reduction, and counts addends in normal forms.

Spatial and spectral image distortions caused by diffraction of an ordinary polarised light beam by an ultrasonic wave

We consider the problem of determining the spatial and spectral image distortions arising from anisotropic diffraction by ultrasonic waves in crystals with ordinary polarised light . By neglecting the small-birefringence approximation, we obtain analytical solutions that describe the dependence of the diffraction angles and wave mismatch on the acousto-optic (AO) interaction geometry and crystal parameters. The formulas derived allow one to calculate and analyse the magnitude of diffraction-induced spatial and spectral image distortions and to identify the main types of distortions: chromatic compression and trapezoidal deformation. A comparison of the values of these distortions in the diffraction of ordinary and extraordinary polarised light shows that they are almost equal in magnitude and opposite in signs, so that consistent diffraction ( or ) in two identical AO cells rotated through in the plane of diffraction can compensate for these distortions.

Highly accurate local pseudopotentials of Li, Na, and Mg for orbital free density functional theory

We present a method to make highly accurate pseudopotentials for use with orbital-free density functional theory (OF-DFT) with given exchange-correlation and kinetic energy functionals, which avoids the compounding of errors of Kohn–Sham DFT and OF-DFT. The pseudopotentials are fitted to reference (experimental or highly accurate quantum chemistry) values of interaction energies, geometries, and mechanical properties, using a genetic algorithm. This can enable routine large-scale ab initio simulations of many practically relevant materials. Pseudopotentials for Li, Na, and Mg resulting in accurate geometries and energies of different phases as well as of vacancy formation and bulk moduli are presented as examples.

Varying the Number of Heads in Phosphorylated Smooth Muscle Myosin Filaments Provides Evidence for Attachment Limited Kinetics of in vitro Actin-Sliding Velocities

Previously we have shown that the ATP-dependence of EDC-stabilized fluorescent smooth muscle myosin (SMM) filament motility is very similar to solution ATPase values (KATP = 8.5 and 9.2 µM, respectively). This suggests both processes are influenced by the same kinetic step, acto-myosin attachment not detachment, presumably linked to Pi release. This mechanism predicts that velocities will be linearly related to the number of working heads. Therefore, we prepared SMM- rod co-filaments that contain fewer molecules per filament length as well as longer SMM filaments that contain more molecules per filament to determine the relationship between the number of heads and velocity. SMM:rod co-filaments (at 50:50, 25:75, and 15:25 ratios) were approximately the same length as normal SMM filaments (∼0.6 µm), and the number of molecules incorporated was directly related to the ratio of SMM to rods. As the number of heads decreased, the maximal velocity at saturating ATP also decreased, and the KATP was lower for all of the co-filaments compared to the normal filaments. These findings provide evidence that the velocity of SMM filaments is influenced by attachment limited kinetics. The longer SMM filaments (average length of 2.3 ± 0.81 µm) will allow us to visualize the geometry of acto-myosin interactions during motion. Also, the relationship between velocity and filament length will be determined at various [ATP]. The long filaments also better demonstrate our previously described “parking” behavior where filaments move to the end of actin filaments but remain attached for long periods even at saturating [ATP] (Haldeman et al, JBC, 2014). Interestingly, most of the SMM filament hangs off the end of the actin suggesting the parking is mediated by a small fraction of the heads.

Three-dimensional clustering of Janus cylinders by convex curvature and hydrophobic interactions.

The three-dimensional (3D) clustering of Janus cylinders is controlled by simply tuning the cylinder geometry and hydrophobic interactions. Janus cylinders were prepared by combining two approaches: micromolding and initiated chemical vapor deposition (iCVD). Hydrophilic cylinders with a flat- or convex-top curvature were prepared by micromolding based on surface tension-induced flow. The iCVD process then provides a hydrophobic domain through the simple and precise deposition of a polymer film on the top surface, forming monodisperse Janus microcylinders. We use these Janus cylinders as building blocks to form 2D or 3D clusters via hydrophobic interactions in methanol. We investigate how cylinder geometry or degree of hydrophobic interaction affects the resulting cluster geometries. The convex-top Janus cylinders lead to 3D clustering through tip-to-tip interactions, and the flat-top Janus cylinders lead to 2D clustering through face-to-face attraction. The number of Janus cylinders in 3D clusters is tuned by controlling the degree of hydrophobic (or hydrophilic) interaction.

New Method to Calculate Spatial Distribution of Acousto-Optic Figure of Merit in Crystals

We propose a novel method to calculate acousto-optic gure of merit in crystals. Calculations are performed in laboratory coordinate system where Z′-axis is collinear with wave vector of ultrasound and the Fresnel equation is considered as an equation on the third component of refractive index vector. The method is applicable to both uniaxial and biaxial crystals. In this paper, we compared obtained values of acousto-optic gure of merit with values from literature data for uniaxial crystals such as paratellurite, lithium niobate, tellurium and for biaxial crystals such as lead and strontium tetraborates. Calculations in paratellurite were carried out for slow-shear acoustic wave propagating along [110] crystal axis. In lithium niobate crystal, we perform comparison with results for geometry of acousto-optic interaction where acoustic wave vector forms 88◦ angle with X crystal axis and 150.4◦ angle with Z crystal axis. In tellurium crystal, we investigate geometries applied in infrared de ectors. In SrB4O7 and PbB4O7 crystals we analyze acousto-optic characteristics of slow-shear mode propagating along [100] crystal axis. Spatial distributions of acousto-optic gure of merit and acoustic frequency for the mentioned acousto-optic interaction geometries are presented.

Synthesis, characterization and thermal degradation studies on some oxovanadium(IV) carbodithioates

Some oxovanadium(IV) carbodithioates of general formulae [VO(MorphcdtH)2B]SO4, [VO(4-RPipzcdtH)2B]SO4, [VO(4-EtPipzcdt)2B] (Morphcdt = morpholinecarbodithioate, Pipzcdt = piperazinecarbodithioate, R = M, Et and B = nil or Py) have been prepared and characterized by elemental analysis, TG/DSC, FTIR, electrospray mass spectral, conductance, NMR, solution electronic absorption spectral and variable temperature magnetic susceptibility measurement studies. All the complexes exhibit 1:1 electrolytic nature except [VO(4-EtPipzcdt)2B] which is a non electrolyte. Square pyramidal geometry and presence of superexchange interactions through bridging carbodithioate ligands for antiferromagnetic behaviour of complexes [VO(MorphcdtH)2]SO4, [VO(4-RPipzcdtH)2]SO4 and [VO(4-EtPipzcdt)2] have been proposed. Exchange interaction parameter, 2J = −124 to −83 cm−1 has been evaluated. Octahedral geometry for the pyridine adducts of oxovanadium(IV) carbodithioates has been proposed. Some of the complexes have also been screened for their antimicrobial activities against some pathogenic gram-negative bacteria, Escherichia coli, Enterobacter, Pseudomonasaeruginosa, Salmonella typhi, Shigella flexneri and gram-positive Staphylococcus epidermidis and Salmonella typhimurium using twofold serial dilution method. Minimum inhibitory concentration has been determined to fall in the range 31.25–250 μg mL−1.

System Reliability Assessment of Existing Jacket Platforms in Malaysian Waters

Reliability of offshore platforms has become a very important issue in the Malaysian Oil and Gas Industry as, majority of the jacket platforms in Malaysian waters to date, have exceeded their design life. Reliability of a jacket platform can be assessed through reliability index and probability of failure. Conventional metocean consideration uses 100 year return period wave height associated with 100 year return period current velocity and wind speed. However, recent study shows that for Malaysian waters, the proposed metocean consideration should be 100 year return period wave height associated with 10 year return period current velocity and wind speed. Hence, this research investigated the effect of different metocean consideration, to system-based reliability of jacket platforms in Malaysian waters. Prior to that, the effect of different metocean consideration to the pushover analysis has also been studied. Besides, the significance of Pile Soil Interaction (PSI), wave direction and platform geometry were analyzed in a sensitivity study. Pushover analysis was performed on three jacket platforms representing three water regions in Malaysia to obtain Reserve Strength Ratio (RSR) as an indicator of the reliability of the jackets. Utilizing sensitivity study parameters mentioned above, seven different case studies were undertaken to study their significance on RSR. The RSR values of each case study were compared and incorporated as resistance model of reliability analysis. Besides, platform specific response model of each jacket has been generated using response surface technique which was later incorporated into the limit state function for reliability analysis. Reliability analysis using First Order Reliability Method (FORM) has been conducted in MATLAB to obtain the reliability index and probability of failure. Results from the reliability analysis were compared to analyze the effect of different metocean consideration. In this study, an updated and detailed methodology of system reliability analysis for offshore jacket platforms is presented. Relationship curves for the safety indices were generated as the outcome of this study. Probability of Failure is found to be inversely functional to RSR. The newly proposed metocean consideration eliminates the conservativeness in currently practiced metocean values. Parameters like metocean considerations and PSI greatly affect the RSR, hence affects Reliability index and Probability of Failure.

Combinatorics

Combinatorics is a fundamental mathematical discipline which focuses on the study of discrete objects and their properties. The current workshop brought together researchers from diverse fields such as Extremal and Probabilistic Combinatorics, Discrete Geometry, Graph theory, Combinatorial Optimization and Algebraic Combinatorics for a fruitful interaction. New results, methods and developments and future challenges were discussed. This is a report on the meeting containing abstracts of the presentations and a summary of the problem session.