Dimensional Continuation Research Articles

Why Aristotle Can’t Do without Intelligible Matter

I argue that intelligible matter, for Aristotle, is what makes mathematical objects quantities and divisible in their characteristic way. On this view, the intelligible matter of a magnitude is a sensible object just insofar as it has dimensional continuity, while that of a number is a plurality just insofar as it consists of indivisibles that measure it. This interpretation takes seriously Aristotle's claim that intelligible matter is the matter of mathematicals generally – not just of geometricals. I also show that intelligible matter has the same meaning in all three places where it is explicitly invoked: Z.10, Z.11, and H.6. Since the H.6 passage involves a mathematical definition, this requires determining what the mathematician defines and how she defines it. I show that, as with natural scientific definitions, there must be a matterlike element in mathematical definitions. This element is not identical with, but rather refers to, intelligible matter.

Laminar Flow in a PEM Fuel Cell Cathode Channel

A Berman’s model for the laminar flow of incompressible fluid in a channel with permeable walls is extended for variable along the channel velocity of injection. The system of two–dimensional continuity and Navier–Stokes equations is reduced to a single ODE for the transversal velocity with coefficients depending on position along the channel. Numerical solution for the flow in the cathode channel of a PEM fuel cell is presented. The flow velocity profile across the channel is almost indistinguishable from the Poiseuille’s parabolic shape; however, the distribution of pressure gradient and longitudinal velocity differ quite significantly from the Berman’s result.

Numerical Study of Oil-water Separation in Inline Axial Hydrocyclone

The fluid mixture hydrocyclone is an excellent tool for downhole oil/water separation (DOWS) for high water cut. In the present work the flow through inline axial inlet hydrocyclone is investigated computationally using ANSYS-FLUENT-19 software. The three dimensional continuity and momentum equations with SST k-omega turbulence model are used to simulate the strongly swirling, turbulent flow. Oil/water two phase mixture treated as the working fluid, water is considered as the primary phase and oil is the secondary phase. The considered oil volume fraction this work is 0.25 and flow split is 0.3 for three different flow rates of (14, 28, 56) m3/hr corresponding to Reynold's number range of (1.6 to 6.6)*104. The pressure and velocity fields were analyzed in the whole hydrocyclone with core recirculation. The results are helpful to predict the flow motion inside the cyclone to estimate the oil/water separation process. The present work indicates that the water purity at cyclone exit was 90%, while the obtained oil purity was 38%.

Cortical and subcortical neuroanatomical signatures of schizotypy in 3004 individuals assessed in a worldwide ENIGMA study

Neuroanatomical abnormalities have been reported along a continuum from at-risk stages, including high schizotypy, to early and chronic psychosis. However, a comprehensive neuroanatomical mapping of schizotypy remains to be established. The authors conducted the first large-scale meta-analyses of cortical and subcortical morphometric patterns of schizotypy in healthy individuals, and compared these patterns with neuroanatomical abnormalities observed in major psychiatric disorders. The sample comprised 3004 unmedicated healthy individuals (12–68 years, 46.5% male) from 29 cohorts of the worldwide ENIGMA Schizotypy working group. Cortical and subcortical effect size maps with schizotypy scores were generated using standardized methods. Pattern similarities were assessed between the schizotypy-related cortical and subcortical maps and effect size maps from comparisons of schizophrenia (SZ), bipolar disorder (BD) and major depression (MDD) patients with controls. Thicker right medial orbitofrontal/ventromedial prefrontal cortex (mOFC/vmPFC) was associated with higher schizotypy scores (r = 0.067, pFDR = 0.02). The cortical thickness profile in schizotypy was positively correlated with cortical abnormalities in SZ (r = 0.285, pspin = 0.024), but not BD (r = 0.166, pspin = 0.205) or MDD (r = −0.274, pspin = 0.073). The schizotypy-related subcortical volume pattern was negatively correlated with subcortical abnormalities in SZ (rho = −0.690, pspin = 0.006), BD (rho = −0.672, pspin = 0.009), and MDD (rho = −0.692, pspin = 0.004). Comprehensive mapping of schizotypy-related brain morphometry in the general population revealed a significant relationship between higher schizotypy and thicker mOFC/vmPFC, in the absence of confounding effects due to antipsychotic medication or disease chronicity. The cortical pattern similarity between schizotypy and schizophrenia yields new insights into a dimensional neurobiological continuity across the extended psychosis phenotype.

Gravity in {varvec{d=2+epsilon }} dimensions and realizations of the diffeomorphisms group

We discuss two separate realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. We renormalize them in d=2+epsilon dimensions, developing a new procedure for dimensional continuation of metric theories and highlighting connections with the constructions that previously appeared in the literature. Our hope is to frame candidates for ultraviolet completions of quantum gravity in d>2 and give some perturbative mean to assess their existence in d=4, but also to speculate on some potential obstructions in the continuation of such candidates to finite values of epsilon . Our results suggest the presence of a conformal window in d which seems to extend to values higher than four.

Is there supersymmetric Lee–Yang fixed point in three dimensions?

The supersymmetric Lee–Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit nonunitary. A natural question is if there is an analogue of supersymmetric Lee–Yang fixed point in higher dimensions. The absence of any [Formula: see text] symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative [Formula: see text] expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee–Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first-order transition.

Keller-Box Scheme to Mixed Convection Flow Over a Solid Sphere with the Effect of MHD

Mixed convection is the combination of a free convection caused by the buoyancy forces due to the different density and a forced convection due to external forces that increase the heat exchange rate. This means that, in free convection, the effect of external forces is significant besides buoyancy forces. In this study the fluid type with viscoelastic effect is non-Newtonian. The viscoelastic fluids that pass over a surface of a sphere form a thin layer, which due to their dominant viscosity is called by the border layer. The obtained limiting layer is analyzed with the thickness of the boundary layer- near the lower stagnating point, then obtained dimensional boundary layer equations, continuity, momentum, and energy equations. These dimensional boundary layer equations are then transformed into non-dimensional boundary layer equations by using non-dimensional variables. Further, the non-dimensional boundary layer equations are transformed into ordinary differential equations by using stream function, so that obtained the non-similar boundary layer equations. These non-similar boundary layer equations are solved numerically by using finite difference method of Keller-Box. The discretization results are non-linear and it should be linearized using newton linearization technique. The numerical solutions are analyzed the effect of Prandtl number, viscoelastic, mixed convection, and MHD parameters towards velocity profile, temperature profile, and wall temperature.

Finite Element Analysis of Mixing Flow in a Circular Vessel with Concentric Three Blade Agitator

This study is to investigate the optimisation of the mixing process in two folds, such as, homogenisation of material and to predict the power consumption. This research work is extension of other studies conducted by different researchers. In all other research investigations, no one had employed agitator. The geometry features a cylindrical vessel fixed with a mechanically revolving stirrer along with fixed agitator. The flow is modelled for incompressible constant viscosity Newtonian fluid with isothermal condition. Simulated numerical predictions are achieved through so called a finite element algorithm. The governing equations considered here are two–dimensional equation continuity and time–dependent Navier–Stokes equation in cylindrical polar coordinates. Employed numerical scheme is constructed in multiple–stages. Where, time derivative is discretised in two step quadratic approximation of Taylor series expansion. Whereas, Galerkin approximation is employed for spatial discretisation. Whilst, at second step pressure correction is adopted through projection method. Whilst, implicitness is applied on only diffusion term to make algorithm in semi– implicit form of TGPC. The influences of inertia will be analysed through fluid inertia using dimensionless Reynolds number. The effects of rotational speed of stirrer with agitator will be explored. The computed results will be illustrated for pressure by isobars and flow structure through streamline contours plots. The keyaim of the numerical study is to estimate the improved possible design of the blenders, that enhance the mixing process

Extensions of the space of continuous functions and embedding theorems

The machinery of -dimensionally continuous functions is developed for the purpose of applying it to the Dirichlet problem for elliptic equations. With this extension of the space of continuous functions, new generalized definitions of classical and generalized solutions of the Dirichlet problem are given. Relations of these spaces of -dimensionally continuous functions to other known function spaces are studied. This has led to a new construction (seemingly more successful and closer to the classical one) of -dimensionally continuous functions, using which new properties of such spaces have been identified. The embeddings of the space in for and , and, in particular, in are proved. Previously, was shown to embed in , which secures the -dimensional continuity of generalized solutions. In the present paper, the more general embedding of in is verified and the corresponding exponents are shown to be sharp. Bibliography: 33 titles.

Scaling behavior of crystalline membranes: An ε-expansion approach

We study the scaling behavior of two-dimensional (2D) crystalline membranes in the flat phase by a renormalization group (RG) method and an ε-expansion. Generalization of the problem to non-integer dimensions, necessary to control the ε-expansion, is achieved by dimensional continuation of a well-known effective theory describing out-of-plane fluctuations coupled to phonon-mediated interactions via a scalar composite field, equivalent for small deformations to the local Gaussian curvature. The effective theory, which will be referred to as Gaussian curvature interaction (GCI) model, is equivalent to theories of elastic D-dimensional manifolds fluctuating in a (D+dc)-dimensional embedding space in the physical case D=2 for arbitrary dc. For D≠2, instead, the GCI model is not equivalent to a direct dimensional continuation of elastic membrane theory and it defines an alternative generalization to generic internal dimension D. After decoupling interactions through a Hubbard-Stratonovich transformation, we study the GCI model by perturbative field-theoretic RG within the framework of an expansion in ε=(4−D). We calculate explicitly RG functions at two-loop order and determine the exponent η characterizing the long-wavelength scaling of correlation functions to order ε2. The value of η at this order is shown to be insensitive to Feynman diagrams involving vertex corrections. As a consequence, the self-consistent screening approximation for the GCI model is shown to be exact to O(ε2). In the physical case of a single out-of-plane displacement field, dc=1, the O(ε2) correction is suppressed by a small numerical prefactor. As a result, despite the large value of ε=2, extrapolation of the first and second order results to D=2 leads to very close numbers, η=0.8 and η≃0.795. The calculated exponent values are close to earlier reference results obtained by non-perturbative renormalization group, the self-consistent screening approximation and numerical simulations. These indications suggest that a perturbative analysis of the GCI model could provide an useful framework for accurate quantitative predictions of the scaling exponent even at D=2.

Fermion traces without evanescence

We outline the evaluation of $n$-dimensional fermion traces ($n\in\mathbb{N}$) built by products of Dirac-$\gamma$ matrices suitable for a uniform dimensional continuation. Such a continuation is needed for calculations employing a dimensional regulator whenever intrinsically integer dimensional tensors yield non-vanishing contributions. A prime example for such a tensor is given by $\gamma_5$ for $n=4$. The main difference between Dimensional Regularization (DREG) and a Dimensionally Continued Regularization (DCREG) is that DCREG does not attempt to lift the algebra to continuous $d$ dimensions ($d\in\mathbb{R}$). As a consequence one has to properly deal with evanescent structures in order to ensure the uniform application of the regulator. In basic steps we identify evanescent structures in fermion traces and show that their proper treatment is crucial for example when calculating the $VVA$ anomaly in four dimensions. We checked that the performed considerations enable the evaluation of Standard Model (SM) $Z$-factors within DCREG up to including three loops.

F COMPUTATIONAL ASSESSMENT OF FOUR CYLINDERS SI ENGINEWORKING ON PETROL OR DUAL FUEL MODE(LPG-PETROL)

Liquefied petroleum gas LPG is a good alternative to gasoline fuel. It has emerged as a solution to the deteriorating urban air quality problem especially in an oil country like Iraq. Computational model is used for parametric study of spark ignition engine works on Iraqi fuel (gasoline or LPG). Transient one dimensional continuity, momentum and energy equations are solved by two – step Lax wender off (Ritchmyer) approach to evaluate brake specific fuel consumption BSFC, brake power, brake thermal efficiency, volumetric efficiency, air fuel ratio, in cylinder pressure and exhaust gas temperature. Results revealed that LPG fuel improves BSFC by 3.11% as a maximum compare to gasoline for 10 kW brake power and 9.9:1 compression ratio. The maximum cylinder pressures predicted for LPG are lower than that for gasoline fuel. The volumetric efficiency was 76.8 % for engine works with, LPG at compression ratio 9.9:1. While that for gasoline was 85.9%. The equivalence ratio is higher for gasoline than that for LPG, since the first required higher air-fuel ratio for combustion. The reported maximum exhaust gas temperature for LPG is 706oC, while that for gasoline is 741.4oC.

Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry

AbstractThere is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous.

Renormalization of gravitational Wilson lines

We continue the study of the Wilson line representation of conformal blocks in two-dimensional conformal field theory; these have an alternative interpretation as gravitational Wilson lines in the context of the AdS3/CFT2 correspondence. The gravitational Wilson line involves a path-ordered exponential of the stress tensor, and its expectation value can be computed perturbatively in an expansion in inverse powers of the central charge c. The short-distance singularities which occur in the associated stress tensor correlators require systematic regularization and renormalization prescriptions, whose consistency with conformal Ward identities presents a subtle problem. The regularization used here combines dimensional regularization and analytic continuation. Representation theoretic arguments, based on SL(2, ℝ) current algebra, predict an exact result for the Wilson line anomalous dimension and, by building on previous work, we verify that the perturbative calculations using our regularization and renormalization prescriptions reproduce the exact result to order 1/c3 included. We also discuss a related, but somewhat simpler, Wilson line in Wess-Zumino-Witten models that yields current algebra conformal blocks, and we emphasize the distinction between Wilson lines constructed out of non-holomorphic and purely holomorphic currents.

An ICME Modeling Application for the Optimization of a Tie-Down Weld Sequence in Ship Production

Aircraft tie-downs have been widely used to secure airplanes, helicopters, and other transportation vehicles to a ship's deck. A multi-pass welding process is typically used for integrating tie-downs to the deck plate to develop the required strength at the joint. During and after welding, the surrounding deck material around the tie-downs must deform elastically to preserve dimensional continuity, creating residual stresses. Weld-induced residual stress is a major concern because the tie-downs are subject to cyclic, dynamic loading which could induce cracking and directly impact the fatigue life of the deck plate structures during services. To select an optimized welding sequence that minimizes weld-induced residual stress in the welded joint, an integrated computational materials engineering approach was used to evaluate the effect of welding sequences on residual stress distributions. Various deck materials (including ABS Grade DH36 and HSLA-100 steel alloys) and welding sequences were investigated to identify the optimized welding sequence which reduced radial residual stress distribution, resulting in lower final deck plate distortion. 1. Introduction Like many heavy industries, shipbuilding has a need for developing lightweight, high-strength, durable structures to improve payload capacity and mission performance, and reduce total ownership costs. The engineering design criteria and the thin-steel alloy material advancement developed to meet these requirements has outpaced the improvement of many manufacturing processes, necessitating a greater understanding of the influence of material properties on producibility issues during construction that could impact the performance of ship structures at sea. Residual stresses are "locked-in" stresses that develop in materials and structures because of welding or material handling processes during manufacturing that are independent of the presence of any external loads. Typical residual stress-induced buckling distortions in ship structures are developed as an elastic response to any incompatible local plastic strains that exist in the material after welding (Huang et al. 2003, 2004).

On using photoconductivity decay to determine Si free carrier recombination lifetime: possibilities and challenges

Free carrier recombination lifetime (τ) in Si single crystals is a parameter, that characterizes the quality of the material. The primary procedure for τ measurement in ingots is photoconductivity decay (PCD) analyses, including contactless μ-PCD and eddy current methods. One of the main problem in this methods is a surface recombination influence on the PCD curve. It is usually assumed that in ingots the influence of surface recombination can be neglected. Well-known dependence of effective lifetime (τeff) on τ, surface recombination velocity (S) and sample thickness (d) describes the maximum value of a lifetime. Based on the numerical calculations of the one dimensional continuity equation we have shown that if the sample thickness exceed 5LD, the maximum lifetime cannot be achieved before PCD signal decline to 5% of maximum, so the question arises what is the interval of the decay curve where the experimental value of the τeff has to be determined. We used the range from 45-5% of the maximum PCD signal following the recommended SEMI MF 1575 standard (τSEMI). The dependencies of τSEMI on τ, d and S were calculated for different versions of PCD measurements and measurement equipment. The recommended thickness for lifetime measurements of non-passivated samples is in the range (1-5)LD. The hardware capabilities of contactless methods are compared.

Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions

In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid, manifold whose geometry we construct explicitely. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions $D=2,4$, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-posed Dirichlet variational principle.

Nanoparticles shape effects on peristaltic transport of nanofluids in presence of magnetohydrodynamics

Magnetohydrodynamics plays important role to manipulate the physiological fluids due to magnetic nature of physiological fluids. Magnetohydrodynamics pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. To study the effects of suspension of the nanoparticles (drugs) in physiological fluids (blood) flow are important in biomedical science and engineering. Motivated by such applications, an analytical approach is presented to study the nanoparticle shape effects on peristaltic transport of nanofluids in presence of magnetohydrodynamics in the present article. A two dimensional continuity, momentum and energy equations are considered to govern the present biophysical model. The governing equations are also linearized using lubrication theory where we consider the low Reynolds number and long wavelength approximations. Closed form solutions are obtained for axial velocity, axial pressure gradient, temperature, pressure rise, wall shear stress and stream function. The effects of three different type of shapes (bricks, cylinders, and platelets) of nanoparticles on peristaltic pumping characteristics and thermal characteristics are computed with the help of graphical illustrations. The interesting outcomes of this study are relevant to more realistic designs for ocular peristaltic pumps in drug delivery systems.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The construction allows to deal with a general background and includes the Gibbons-Hawking-Myers boundary term as a special case, when the background is taken to be a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients or regularization, the expected mass of the Boulware-Deser black hole.

O6.2. NEUROBIOLOGY OF PSYCHOMETRIC SCHIZOTYPY: INSIGHTS FROM MULTIMODAL IMAGING RESEARCH

BackgroundThe continuum approach to psychosis proposes a dimensional continuity between the neurobiology of subclinical psychotic-like experiences in healthy individuals (or schizotypy) and psychotic symptoms in clinically relevant psychosis (Linscott and van Os, 2013, Nelson et al., 2013). Preclinical models propose that cortical glutamate dysfunction related to cortico-limbic-striatal hyper-responsivity to stress may underlie both hippocampal and striatal overdrive as well as gray matter loss associated with schizophrenia-like behaviors (Berretta et al., 2001, Lodge and Grace, 2011). Our recent studies investigated whether changes in brain glutamate are present in healthy individuals with high psychometric schizotypy, and whether these are related to changes in (1) corticolimbic response to emotion and (2) gray matter volume (GMV).MethodsForty-eight healthy participants were recruited based on their score on the O-LIFE questionnaire (Mason et al., 2005), after pre-screening 250 respondents to online advertisement. Participants with high levels of unusual experiences (HS group; that is, scored >7 on the Unusual Experiences (UE) subscale of the O-LIFE), and participants with low UE (LS group; that is, <2 on O-LIFE UE subscale), were invited to participate. Groups were matched by age, gender and IQ. A structural MRI scan, glutamate proton magnetic resonance spectroscopy in the anterior cingulate cortex (ACC), and functional magnetic resonance imaging (fMRI) measuring corticolimbic response during emotional processing were acquired at 3T in a single session. Glutamate levels were analyzed using LCModel 6.3-1L. Voxel-based morphometry was applied to quantify GMV and both GMV and fMRI group level analyses were run using SPM12. Standalone imaging results as well as fMRI/sMRI × glutamate interactions were considered significant after voxel-wise P<0.05 family-wise error correction.ResultsWhile viewing emotional pictures, HS individuals showed greater activation than did subjects with LS in the caudate, and marginally in the ACC, hippocampus, medial prefrontal cortex (MPFC) and putamen. Although no between-group differences were found in glutamate concentrations, within the HS group ACC glutamate was negatively correlated with striatal activation (bilaterally in caudate and in left putamen at P < 0.05) and marginally with MPFC (P = 0.052) and amygdala (left: P = 0.062; right: P = 0.079), correlations that were not present in LS subjects. Structurally, subjects with HS showed GMV decreases in the rolandic operculum/superior temporal gyrus (P < 0.05) at the whole-brain level, and significant increases in GMV were also detected using ROI in the precuneus and ACC (both P < 0.05). Furthermore, in HS subjects ACC glutamate levels were negatively correlated with GMV in the ACC (P < 0.05). Such association was absent in LS. These findings provide, to our knowledge, the first evidence that brain glutamate levels are associated with emotional hyper-responsivity and volumetric changes in HS in brain regions thought to be critical in the pathophysiology of psychotic symptoms.DiscussionCollectively, these results are in line with a dimensional view of psychosis by suggesting that interactions between brain structure, neurochemistry, and functional response to emotion within a corticolimbic circuit are involved in the expression of psychotic-like experiences at non-clinical and clinical levels. These findings may also serve as evidence of potentially protective mechanisms, as our studies involved high-functioning individuals with HS and some of the observed effects are opposite to what would have been predicted from studies in clinical groups.