Connection Rules Research Articles

Quantum box energies as a route to the ground state levels of self-assembled InAs pyramidal dots

A theoretical investigation of the ground state electronic structure of InAs/GaAs quantum confined structures is presented. Energy levels of cuboids and pyramidal shaped dots are calculated using a single-band, constant-confining-potential model that in former applications has proved to reproduce well both the predictions of very sophisticated treatments and several features of many experimental photoluminescence spectra. A connection rule between their ground state energies is found which allows the calculation of the energy levels of pyramidal dots using those of cuboids of suitably chosen dimensions, whose solution requires considerably less computational effort. The purpose of this work is to provide experimentalists with a versatile and simple method to analyze their spectra. As an example, this rule is then applied to successfully reproduce the position of the ground state transition peaks of some experimental photoluminescence spectra of self-assembled pyramidal dots. Furthermore the rule is used to predict the dimensions of a pyramidal dot, starting from the knowledge of the ground state transition energy and an estimate for the aspect ratio Q.

Approximate methods for the solution of quantum wires and dots: Connection rules between pyramidal, cuboidal, and cubic dots

Energy eigenvalues of the electronic ground state are calculated for rectangular and triangular GaAs/Ga0.6Al0.4As quantum wires as well as for cuboidal and pyramidal quantum dots of the same material. The wire (dot) geometries are approximated by a superposition of perpendicular independent finite one-dimensional potential wells. A perturbation is added to the system to improve the approximation. Excellent agreement with more complex treatments is obtained. The method is applied to investigate the ground state energy dependence on volume and aspect ratio for finite barrier cubic, cuboidal, and pyramidal quantum dots. It is shown that the energy eigenvalues of cubes are equal to those of cuboids of the same volume and aspect ratio similar to one. In addition, a relationship has been found between the volumes of pyramidal quantum dots (often the result of self-assembling in strain layered epitaxy) and cuboidal dots with the same ground state energy and aspect ratios close to one.

DENSITY PROFILE OF THE INCIPIENT INFINITE PERCOLATION CLUSTER

Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d=2 and d=6-∊ dimensions and with earlier simulations. We also present and explain results for bus–bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

Connection Rules versus Differential Equations for Envelope Functions in Abrupt Heterostructures

Connection Rules versus Differential Equations for Envelope Functions in Abrupt Heterostructures

A simulation approach to reliability analysis of weapon systems

We report a modeling simulation approach to analyse weapon systems reliability. The introduced functional diagram generalises the logic diagram allowing the replication on the functioning mode of system components. To handle the functional diagram, the availability and connection rules are also introduced. Based on the functional diagram, a simulation model is outlined and a case study, the propulsion system of a Mine Hunter, is included.

Superstructures of Functional Colloids: Chemistry on the Nanometer Scale

AbstractChemistry is classically concerned with the connection of atoms and molecules into new functional units. The rules of connection are yet to be extended to the generation and connection of larger objects, whose dimensions are measured in nanometers. However, linking objects of this size through molecules approaching each other randomly is inefficient, instead the principle of self‐assembly is decisive, in which lyotropic structure formation or amphiphilic interaction play a significant role. As a result of the nature of the energetic driving forces, the objects generated in this way are often well‐defined aggregate structures or highly symmetric volume phases. In contrast to “molecular chemistry”, the linking of larger objects also disregards the inherent borders of classical fields of chemistry: for example, the nanoscale association of inorganic colloids with polymers affords hybrid materials that combine the physical properties of both partners. In such a way, catalytic, optical, and electronic features of inorganic colloids might be combined with the mechanical characteristics of polymers such as film formation, elasticity, and melt processibility.

Copolymerization with Chain Transfer Monomer. 2. Molecular Weight Distribution

The full molecular weight distribution formed in a batch free-radical copolymerization with chain transfer monomer is considered theoretically. A Monte Carlo simulation algorithm is proposed on the basis of the random sampling technique. Illustrative calculations are conducted for the cases with equal reactivity of all types of double bonds. It was found that even when the probability of possessing a branch point is the same for all units, the formed molecular weight distribution is highly dependent on the chain connection rule. Bimolecular termination by combination may contribute to form extremely large polymer molecules by forming cross-linkages between primary chains. Under the idealized conditions, homogeneously branched polymer molecules are formed, and the analytical solution for the molecular weight distribution can be obtained.

Mesoscopic Description of Heterojunctions

Starting from the microscopic current associated with the single-electron wave functions and using Wannier functions suitably generalized for nonperiodic heterostructures we construct mesoscopic (either discrete or continuous) conserved currents associated with states having components only in the considered band. This provides a rigorous basis to the approximate envelope function approaches. As an application we analyze general one-dimensional heterojunctions, mapping explicitly the microscopic asymptotic states onto mesoscopic (one-band envelope) ones. This proves that, apart from the effective masses and the band offsets, the connection rules are characterized in general by three parameters, the values of which are unconstrained, confirming the results of phenomenological analyses.

Two rules for callosal connectivity in striate cortex of the rat.

In the rat, callosal cells occupy lateral as well as medial portions of striate cortex. In the region of the border between areas 17 and 18, which contains a representation of the vertical meridian of the visual field, cells projecting through the corpus callosum are concentrated throughout the depth of the cortex. In contrast, in medial portion of striate cortex, where peripheral portions of the visual field are represented, callosal cells are preferentially found in infragranular layers. These differences in topography and laminar distribution suggest that these callosal regions, referred to as medial and lateral callosal regions in the present study, subserve different functions. We explored this possibility by analyzing the patterns of callosal linkages in these two callosal regions. We charted the location of retrogradely labeled cells within striate cortex of one hemisphere after placing restricted injections of one or more fluorescent tracers into selected sites in the contralateral striate cortex. We found the medial and lateral callosal regions have distinctly different topographic organizations. Injections into medial striate cortex of one hemisphere produced labeled cells predominantly in mirror-symmetric loci in medial portions of contralateral striate cortex. The arrangement of these connections suggests that they mediate direct interactions between cortical regions representing visual fields located symmetrically on opposite sides of the vertical meridian of the visual field. In contrast, the mapping in the lateral callosal region is reversed: injections into the 17/18a border produced labeled fields located medial to the contralateral 17/18a border, while injections slightly medial to the 17/18a border produced labeled fields located at the contralateral 17/18a border.(ABSTRACT TRUNCATED AT 250 WORDS)

Form of kinetic energy in effective-mass Hamiltonians for heterostructures.

We first prove that the class of effective-mass Hamiltonians H=${\mathit{T}}_{\mathrm{\ensuremath{\alpha}}}$+V with ${\mathit{T}}_{\mathrm{\ensuremath{\alpha}}}$=1/2${\mathit{m}}^{\mathrm{\ensuremath{\alpha}}}$${\mathit{pm}}^{\mathrm{\ensuremath{-}}1\mathrm{\ensuremath{-}}2\mathrm{\ensuremath{\alpha}}}$${\mathit{pm}}^{\mathrm{\ensuremath{\alpha}}}$, where m=m(x) is a twice differentiable (${\mathrm{C}}_{2}$) function and p=-id/dx can be mapped by an unitary transformation onto the constant-mass case with still a local potential that we give explicitly. The value of \ensuremath{\alpha} is thus irrelevant. We then consider the case when m(x) is only piecewise ${\mathrm{C}}_{2}$, that is, the case of heterojunctions. We show that the general connection rule for the envelope function and its derivative at an unstrained heterojunction depends on a Hermitian 2\ifmmode\times\else\texttimes\fi{}2 matrix which is intrinsic to the junction. Hence, the latter should be described by four parameters (three in the case of time-reversal invariant systems). The parameter values may be obtained from the scattering data for Bloch waves, which can be either measured or computed. Up to two Tamm states, localized at the interface, are allowed.

Analysis of connectivity in the cat cerebral cortex

The mammalian cerebral cortex is innervated by a large number of corticocortical connections. The number of connections makes it difficult to understand the organization of the cortical network. Nonetheless, conclusions about the organization of cortical systems drawn from examining connectional data have often been made in a speculative and informal manner, unsupported by any analytic treatment. Recently, progress has been made toward more systematic ways of extracting organizing principles from data on the network of connections between cortical areas of the monkey. In this article, we extend these approaches to the cortical systems of the cat. We collated information from the neuroanatomical literature about the corticocortical connections of the cat. This collation incorporated 1139 reported corticocortical connections between 65 cortical areas. We have previously used an optimization technique (Scannell and Young, 1993) to analyze this database in order to represent the connectional organization of cortical systems in the cat. Here, we report the connectional database and analyze it in a number of further ways. First, we employed rules from Felleman and Van Essen (1991) to investigate hierarchical relations among the areas. Second, we compared quantitatively the results of the optimization method with the results of the hierarchical method. Third, we examined quantitatively whether simple connection rules, which may reflect the development and evolution of the cortex, can account for the experimentally identified corticocortical connections in the database. The results showed, first, that hierarchical rules, when applied to the cat visual system, define a largely consistent hierarchy. Second, in both auditory and visual systems, the ordering of areas by hierarchical analysis and by optimization analysis was statistically significantly related. Hence, independent analyzes concur broadly in their ordering of areas in the cortical hierarchies. Third, the majority of corticocortical connections, and much of the pattern of connectivity, were accounted for by a simple "nearest-neighbor-or-next-door-but-one" connection rule, which may suggest one of the mechanisms by which the development of cortical connectivity is controlled.

Connection rules and electron transmissivity at an interface between materials with different electronic properties

We derive approximate connection rules for conduction-electron waves at an abrupt interface between two materials with different electronic properties. We avoid the arbitrariness in the connection rules for effective-mass wave functions by taking the Bloch functions into account in an approximate way that is appropriate for the non-epitaxial interfaces that we wish to study. The result is particularly relevant for the physics of superconductor-semiconductor heterostructures because the basic property governing their behaviour is the transmissivity of the interface. The application of the result to measurements on niobium-silicon heterostructures shows that the situation has been reached in which the transmissivity is mainly limited by the large Fermi wave vector mismatch of metal and semiconductor.

Connectional topography in the zebrafish olfactory system: random positions but regular spacing of sensory neurons projecting to an individual glomerulus.

It is unknown how neuronal connections are specified in the olfactory system. To define rules of connectivity in this system, we investigated whether the projection of sensory neurons from the olfactory epithelium to the olfactory bulb is topographically ordered. By backtracking with 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (DiI), we find that neurons projecting into a single identified glomerulus are widely dispersed over the olfactory epithelium. Their positions in the sensory surface do not predict their glomerulus specificity and are probably random. A statistical analysis reveals that neurons connected to the same glomerulus are spaced at distances of several cell diameters from each other. The convergence of projections to one point in the target area from neurons that are widely and evenly distributed in the sensory surface constitutes an unusual type of connectional topography that contrasts with the precise topological (neighborhood-preserving) maps found in other sensory systems. It may maximize the probability to detect odorants that activate a single glomerular unit.

Normal Forms for Linear Mode Conversion and Landau-Zener Transitions in One Dimension

Standard eikonal methods for the asymptotic analysis of coupled linear wave equations may fail when two eigenvalues of a matrix (the dispersion matrix) associated with the wave operator are both small in the same region of wave phase space. In this region the two eikonal modes associated with the two small eigenvalues are coupled, leading to a process called linear mode conversion or Landau-Zener coupling. A theory of linear mode conversion is presented in which geometric structure is emphasized. This theory is then used to identify the most generic type of mode conversion which occurs in one dimension. Finally, a general solution for this generic mode conversion problem is derived by transforming an arbitrary equation exhibiting generic mode conversion into an easily solvable normal form. This solution is given as a connection rule, with which one may continue standard eikonal wave solutions through mode conversion regions.

Dependence of valence-subband dispersion relations on heterointerface boundary conditions in InxGa1−xAsyP1−y/InP narrow quantum wells

In the framework of envelope function approximation, the dependence on heterointerface boundary conditions of valence-band dispersion relations in InP-based quantum-well structures is investigated. Under conventional boundary conditions, the root-finding calculation for the eigenvalue problem of quantum well structures is carried out while taking into account a large difference in the effective-mass parameters (the Luttinger parameters) among the constituting bulk materials. In spite of a decreasing interband mixing between heavy- and light-hole states due to strain and the quantum size effect, hole subband structure of a compressive-strained quantum well with a narrow well width is found to form an anomalous dispersion curve. It is clarified that the requirement for envelope continuity at interfaces is responsible for anomaly in the dispersion curves through off-diagonal terms with an additional δ-function-like interface potential in the valence-band effective-mass Hamiltonian. We present the results of dispersion relations and envelope functions related to a newly derived connection rule based on the tight-binding bond-orbital description, under which the envelopes are free from continuity restrictions at the interfaces regardless of any difference in the effective-mass parameters.

Comment on "Connection rules for envelope functions at semiconductor-heterostructure interfaces"

It is shown that the results of calculations using a scattering-matrix approach based on empirical pseudopotentials support the use of the usual envelope-function interface connection rules at GaAs/AlAs heterojunctions, contrary to the claims of the above-cited paper, provided one uses an energy-dependent effective mass.

Coupling between Gamma - and X-type envelope functions at GaAs/Al(Ga)As interfaces.

Connection rules for envelope functions related to the Γ- and X-point conduction-band valleys in GaAs/Al(Ga)As systems are formulated in terms of a transfer matrix. The transfer-matrix elements are calculated using a method in which wave functions, which are obtained using empirical pseudopotentials, are matched at the interface. The nonzero transfer-matrix elements appear to depend weakly on energy which enables us to give a simple prescription for connection rules for envelope functions in which Γ-X coupling is incorporated

Transplantation of neurons reveals processing areas and rules for synaptic connectivity in the cricket nervous system

In order to assess the nature of spatial cues in determining the characteristic projection sites of sensory neurons in the CNS, we have transplanted sensory neurons of the cricket Acheta domesticus to ectopic locations. Thoracic campaniform sensilla (CS) function as proprioceptors and project to an intermediate layer of neuropil in thoracic ganglia while cercal CS transduce tactile information and project into a ventral layer in the terminal abdominal ganglion (TAG). When transplanted to ectopic locations, these afferents retain their modality-specific projection in the host ganglion and terminate in the layer of neuropil homologous to that of their ganglion of origin. Thus, thoracic CS neurons project to intermediate neuropil when transplanted to the abdomen and cercal CS neurons project to a ventral layer of neuropil when transplanted to the thorax. We conclude that CS can be separated into two classes based on their characteristic axonal projections within each segmental ganglion. We also found that the sensory neurons innervating tactile hairs project to ventral neuropil in any ganglion they encounter after transplantation. Ectopic sensory neurons can form functional synaptic connections with identified interneurons located within the host ganglia. The new contacts formed by these ectopic sensory neurons can be with normal targets, which arborize within the same layer of neuropil in each segmental ganglion, or with novel targets, which lack dendrites in the normal ganglion and are thus normally unavailable for synaptogenesis. These observations suggest that a limited set of molecular markers are utilized for cell-cell recognition in each segmentally homologous ganglion. Regenerating sensory neurons can recognize novel postsynaptic neurons if they have dendrites in the appropriate layer of neuropil. We suggest that spatial constraints produced by the segmentation and the modality-specific layering of the nervous system have a pivotal role in determining synaptic specificity.

Machine identification of buds in images of plant shoots

Tissue cultures find increasingly widespread applications for cloning of many plants. Commercial propagation by tissue cultures is limited to ornamental plants, because the cost of skilled labor required cannot compete with conventional propagation methods. To cut down the cost, some automation is essential. A cost-effective approach is to chop the plantlets into segments on a conveying production line while using machine vision for identifying and locating the number and positions of propagation organs in images of the plantlet segments. Plantlet segments without propagation organs will be rejected, while segments with viable buds will be selected for subculturing. To this end, a machine-vision-controlled automatic subculturing system for potato tissue cultures is proposed as a simpler and more cost-effective solution than the popular trend of imitating the manual sub-culturing task by a robot. A simple and relatively fast image-processing algorithm particularly suitable for classification of potato tissue cultures, was developed. In lieu of the general Medial Axis Transform approach, this specialized algorithm takes advantage of the inherent difference between the geometrical shape and gray scale levels of the stems and the leaves as well as of the rather simple connectivity rules of attachment between them. The results indicate that machine inspection and classification of tissue culture plantlets is possible, but considerably more work needs to be done before this technique is fully developed for automating tissue culture processes.

Quantum mechanics of electrons in crystals with graded composition.

We construct the effective Hamiltonian describing the motion of electrons in compositionally graded crystals which is valid throughout a given energy band and part way into the gaps. Near the edges of a simple or degenerate band this effective Hamiltonian reduces to an effective mass Hamiltonian with position dependent effective mass. Next, we examine more general states---not restricted to the vicinity of a band edge---in crystals with composition and applied potential variation in one direction. We obtain a WKB-type solution for the envelope functions, as well as the appropriate turning point connection rules.