Geometrical Mechanism Research Articles

Mechanisms in the size segregation of a binary granular mixture

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

EOS of nonequilibrium parton plasma in an expanding flux tube

We investigate a new version of the flux-tube model based on joint action of two different processes responsible for vacuum creation of the parton plasma: the dynamical Schwinger mechanism and the geometrical mechanism linked to the dynamical Casimir effect. These two mechanisms act at different time scales. The Casimir mechanism provides the abundant generation of partons from the sea at the very early stage after the fusion of colliding nuclei and release of color degrees of freedom. Then the created plasma initiates the backreaction mechanism via the standard Schwinger scenario. This process apparently leads to fast thermalization of secondary partons. The model allows for the self-consistent description of preequilibrium evolution of the plasma, fully determined by the total energy and the total number of valence quarks of colliding nuclei. The Equation of State of the created parton plasma is discussed.

Flavour physics of the RS model with KK masses reachable at LHC

The version of the higher-dimensional Randall-Sundrum (RS) model with matter in the bulk, which addresses the gauge hierarchy problem, has additional attractive features. In particular, it provides an intrinsic geometrical mechanism that can explain the origin of the large mass hierarchies among the Standard Model fermions. Within this context, a good solution for the gauge hierarchy problem corresponds to low masses for the Kaluza-Klein (KK) excitations of the gauge bosons. Some scenarios have been proposed in order to render these low masses (down to a few TeV) consistent with precision electroweak measurements. Here, we give specific and complete realizations of this RS version with small KK masses, down to 1 TeV, which are consistent with the entire structure of the fermions in flavour space: (1) all the last experimental data on quark/lepton masses and mixing angles (including massive neutrinos of Dirac type) are reproduced, (2) flavour changing neutral current constraints are satisfied and (3) the effective suppression scales of non-renormalizable interactions (in the physical basis) are within the bounds set by low energy flavour phenomenology. Our result, on the possibility of having KK gauge boson modes as light as a few TeV, constitutes one of the first theoretical motivations for experimental searches of direct signatures at the LHC collider, of this interesting version of the RS model which accommodates fermion masses.

Neutrinos in a warped extra dimension

Amongst the diverse propositions for extra dimensional scenarios, the model of Randall and Sundrum (RS), which offers a solution for the long standing puzzle of the gauge hierarchy problem, has attracted considerable attention from both the theoretical and experimental points of view. In the context of the RS model with gauge bosons and fermions living in the bulk, a novel type of mechanism has arisen for interpreting the strong mass hierarchy of the Standard Model fermions. This purely geometrical mechanism is based on a type and flavor dependent localization of fermions along a warped extra dimension. Here, we find concrete realizations of this mechanism, reproducing all the present experimental data on masses and mixings of the entire leptonic sector. We consider the case of Dirac neutrino masses (due to an additional right handed neutrino) where the various constraints on RS parameter space are taken into account. The scenarios, elaborated in this paper, generate the entire lepton mass hierarchy and mixing, essentially, via the higher-dimensional mechanism, as the Yukawa coupling dependence is chosen to be minimal. In addition, from the above mechanism, we predict the typical lepton mixing angle 10^-5 < sin(theta_13) < 10^-1, a neutrino mass spectrum with normal hierarchy and the smallest neutrino mass to lie approximately in the range: 10^-11 eV < m_nu_1 < 10^-2 eV. A large part of the sin(theta_13) interval should be testable in future neutrino experiments.

Geometrical generation of cosmic magnetic fields within standard electromagnetism

We study the evolution of cosmological magnetic fields in FRW models with curved spatial sections and outline a geometrical mechanism for their superadiabatic amplification on large scales. The mechanism operates within standard electromagnetic theory and applies to FRW universes with open spatial sections. We discuss the general relativistic nature of the effect and show how it modifies the adiabatic magnetic evolution by reducing the depletion rate of the field. Assuming a universe that is only marginally open today (i.e. for 1i Ω0 » 10 i2 ), we estimate the main features of the superadiabatically amplified residual field and find that is of astrophysical interest.

Assembly process modeling for virtual assembly process planning

Virtual assembly process planning (VAPP) provides a more efficient, intuitive and convenient method for assembly process planning. Previous efforts in this field are concentrated on how to assemble components together and how to analyze this assembly process in a virtual environment. However, how the interactive planning process can be modeled and organized, which is important for VAPP because of its significant influence on data organization and planning efficiency, are mostly not included. Based on analysis of the requirement of VAPP, a hierarchical assembly task list (HATL) model is proposed. In the model, assembly tasks are defined to express component assembling operations and are sequentially and hierarchically organized according to different subassemblies, which can perfectly model the construction process of product. For each assembly task, its major mission is to establish assembly relations, which is realized by an automatic geometrical constraint recognition mechanism. A three-layer virtual part model and a modified collision detection algorithm are firstly put forward to provide basic information for it. Then the automatic constraint recognition algorithm based on assembly intents filtering mechanism including destination intent, design intent and precedence intent, is detailed. All models and algorithms have been verified by a desktop-mode experiment VAPP system. However, it can also be suitable for immersive mode.

GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS

This paper gives a short overview of various applications of stabilization by vibration, along with the exposition of the geometrical mechanism of this phenomenon. More specifically, the following observation is described: a rapidly vibrated holonomic system can be approximated by a certain associated nonholonomic system. It turns out that effective forces in some rapidly vibrated (holonomic) systems are the constraint forces of an associated auxiliary nonholonomic constraint. In particular, we review a simple but remarkable connection between the curvature of the pursuit curve (the tractrix) on the one hand and the effective force on the pendulum with vibrating support. The latter observation is a part of a recently discovered close relationship between two standard classical problems in mechanics: (1) the pendulum whose suspension point executes fast periodic motion along a given curve, and (2) the Chaplygin skate (known also as the Prytz planimeter, or the "bicycle"). The former is holonomic, the latter is nonholonomic. The holonomy of the skate shows up in the effective motion of the pendulum. This relationship between the pendulum with a twirled pivot and the Chaplygin skate has somewhat unexpected physical manifestations, such as the drift of suspended particles in acoustic waves. Finally, a higher-dimensional example of "geodesic motion" on a vibrating surface is described.

Superadiabatic-type magnetic amplification in conventional cosmology

We consider the evolution of cosmological magnetic fields in Friedmann-Robertson-Walker models and outline a geometrical mechanism for their superadiabatic amplification on large scales. The mechanism operates within standard electromagnetic theory and applies to Friedmann-Robertson-Walker universes with open spatial sections. We discuss the general relativistic nature of the effect and show how it modifies the adiabatic magnetic evolution. Assuming a universe that is only marginally open today, we estimate the main features of the superadiabatically amplified residual field.

Realistic neutrino masses from multi-brane extensions of the Randall-Sundrum model?

Scenarios based on the existence of large or warped (Randall-Sundrum model) extra dimensions have been proposed for addressing the long standing puzzle of gauge hierarchy problem. Within the contexts of both those scenarios, a novel and original type of mechanism generating small (Dirac) neutrino masses, which relies on the presence of additional right-handed neutrinos that propagate in the bulk, has arisen. The main objective of the present study is to determine whether this geometrical mechanism can produce reasonable neutrino masses also in the interesting multi-brane extensions of the Randall-Sundrum model. We demonstrate that, in some multi-brane extensions, neutrino masses in agreement with all relevant experimental bounds can indeed be generated but at the price of a constraint (stronger than the existing ones) on the bulk geometry, and that the other multi-brane models even conflict with those experimental bounds.

Single microdroplet ejection using an ultrasonic longitudinal mode with a PZT/tapered glass capillary

We have developed an ultrasonic PZT/tapered glass capillary resonant actuator that can eject a single droplet every acoustic cycle without also generating satellite droplets. The mechanism of the actuation is resonant longitudinal motion-induced squeezing of a tapered volume. The actuator is driven at 160 kHz and requires voltages less than 2 Vpp to operate. In this paper, the droplet generation of isopropanol and water mixtures, which have different densities, viscosities, and surface tensions, is investigated. It is determined that the geometrical squeezing mechanism and the ejected jet breakup makes the droplet size independent of frequency, but more a function of the ejecting orifice diameter that is much smaller than the capillary wavelength.

Conformational Polymer Statistics from the Geometrical Scaling of Monomeric Units and the Characteristic Ratio from Circle Maps. Application to Carbohydrate Macromolecules

AbstractSummary: Basic results on conformational chain statistics were formerly derived from scaling concepts for geometry and a relativistic picture of Brownian self‐diffusion in liquids. A polymer conformation was interpreted as a geometrical scaling law of its monomer shape, where the concept of characteristic ratio identifies a mean metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules. Here, we add the former theoretical results to first numerical calculations. They are performed for three polysaccharides, provided with different chain topologies and constrained conformationally to identical square‐well energy states with increasing width. The spatial coil dilation‐contraction has been described satisfactorily by dihedral sine‐like rotations on a circle at dimeric length scales. New intrinsic quantities, like inner characteristic ratio and angular Kuhn step, both belonging to the shape of single molecules, have been finally defined. The geometrical mechanism bringing them at larger scales, to point out the chain shape size, is still unknown and under consideration.Conformational energy landscape of nigerose.imageConformational energy landscape of nigerose.

Contribution of x-ray topography and high-resolution diffraction to the study of defects in SiC

A short review is presented of the various synchrotron white beam x-ray topography (SWBXT) imaging techniques developed for characterization of silicon carbide (SiC) crystals and thin films. These techniques, including back-reflection topography, reticulography, transmission topography, and a set of section topography techniques, are demonstrated to be particularly powerful for imaging hollow-core screw dislocations (micropipes) and closed-core threading screw dislocations, as well as other defects, in SiC. The geometrical diffraction mechanism commonly underlying these imaging processes is emphasized for understanding the nature and origins of these defects. Also introduced is the application of SWBXT combined with high-resolution x-ray diffraction techniques to complete characterization of 3C/4H or 3C/6H SiC heterostructures, including polytype identification, 3C variant mapping, and accurate lattice mismatch measurements.

Cationic intermediates in trans- to cis- isomerization reactions of allylic systems. An exploratory ab initio study

Computational analyzes were undertaken to investigate the geometrical isomerization mechanism of a truncated tail-end model (C 1–C 10) of the full lycopene molecule, the products of which are the 5- cis and 7- cisforms. The global conformational minima were identified for the neutral all- trans reactant, the cationic isomerization intermediates and that of these two cis-isomeric products. Energies and stabilities were compared during different stages of the isomerization mechanism of the segments. The C 4 allylic hydride affinity values of the all- trans to the 5- cis, and the 7- cis isomers of this lycopene model, are in the range of 255–260 kcal mol −1, which are within the expected limits of such hydride affinity values (210 kcal mol −1 for weak and 360 kcal mol −1 for strong hydride affinity) at the RHF/3-21G level of theory. The bond lengths involving alternating single and double carbon–carbon bonds roughly coincide with the expected changes along each intermediate of the putative isomerization pathway. The following sequence of stability was observed in the tail-end model of neutral lycopene isomers: 5-cis> all-trans>7-cis For the cation, the order of stability was different: all-trans>5-cis>7-cis

Probabilistic aspects of the SU(2)-harmonic oscillator

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Probabilistic aspects of the SU(2)-harmonic oscillator

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha &lt;--&gt;beta phase transition in quartz

Spontaneous strains for the a ↔ b transition in quartz were determined from lattice parameter data collected by X-ray powder diffraction and neutron powder diffraction over the temperature range ;5‐1340 K. These appear to be compatible with previous determinations of the order parameter variation in a quartz only if there is a non-linear relationship between the individual strains and the square of the order parameter. An expanded form of the 2-4-6 Landau potential usually used to describe the phase transition was developed to account for these strains and to permit calculation of the elastic constant variations. Calibration of the renormalized coefficients of the basic 2-4-6 potential, using published heat capacity data, provides a quantitative description of the excess free energy, enthalpy, entropy, and heat capacity. Values of the unrenormalized coefficients in the Landau expansion that include all the strain-order parameter coupling coefficients were used to calculate variations of the elastic constants. Values of the bare elastic constants were extracted from published elasticity data for b quartz. Calculated variations of C11 and C12 match their observed variations closely, implying that the extended Landau expansion provides a good representation of macroscopic changes within the (001) plane of quartz. Agreement was not as close for C33, suggesting that other factors may influence the strain parallel to [001]. The geometrical mechanism for the transition involves both rotations and shearing of SiO4 tetrahedra, with each coupled differently to the driving order parameter. Only the shearing part of the macroscopic distortions appears to show the same temperature dependence as other properties that scale with Q 2 . Coupling between the strain and the order parameter provides the predominant stabilization energy for a quartz and is also responsible for the first-order character of the transition.

A dynamical mechanism for the selection of physical states in ‘geometric quantization schemes’

Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which provides dynamically the desired reduction.

2D into 3D Hough-space mapping for planar object pose estimation

A novel approach is proposed that relates the classical two-dimensional Hough space to a different Hough space embedding 3D information about the poses of planar objects in a single gray-level image. The Hough transform is used to detect rectilinear segments that, suitably grouped into a bounded figure, constitute a planar surface. Then, a pure geometrical mechanism is used to map the numerical Hough space representation of the image into a similar representation in a reference system that is fixed with respect to the surface. The object pose to be estimated is computed by comparing the numerical representations of the test and model images (usually in a fronto-parallel view) in the same space invariant to the object pose.

The effect of procedural variables and mechanical activation on the thermal decomposition of calcite. An approach by experimental design

Second-order orthogonal experimental design has been used to examine the effect of mechanical activation, mass sample, heating rate and molar fraction of carbon dioxide in the environmental atmosphere on the thermal decomposition of calcite. The mathematical model of the activation energy ( E a ) for various mechanisms was examined by the Coats-Redfern equation using the best-fit procedure and the method of the shape of the TG/DTG curves. The best-fit procedure gave the second-order reaction mechanism (F2) as the predominant mechanism while the shape method gave the contacting area geometrical mechanism (R2) and the two-dimensional diffusion mechanism (D2) as the predominant mechanisms. The mathematical models for the change of enthalpy ( Δ H and the temperature of the maximum rate of decomposition ( T max) were found, but unfortunately only the T max model was of significance.

A study of cation arrays in MB2, MB4 and MB6 borides. Part I. Their relation to their parent metals

Abstract The crystal structure of MB2, MB4 and MB6 borides are analyzed on the basis of their metal arrays. In all of them, the identity of the parent metal can be recognized. Some of the compounds present metal fragments which maintain the topology and shortest M-M distances of the pure metal. In other compounds, these distances are absent but distances to the second and even third nearest neighbors are recognizable. This feature does not seem to depend either on the stoichiometry or the nature of the metal involved. For all the compounds, a geometrical mechanism is proposed, based on the formation of metastable metal structures.