Criteria for Integration of Flows on Levels of Aggregation

The article describes the processes and connections that occur on the road from of cellular integration to the integration of the supply chain. How to make the transition to higher levels? What is the first step and which approach is essential to ensure continuous improvement? With the changing in the organizational environment nowadays it is not satisfactory only a leveled increase. Global optimum of improvements always overcome the amount of local optimums. This idea and approach must be used when talking about flows and aggregation.production flow, cellular production, value stream mapping, continuous improvement, biological system.

Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

Global Dynamics of Advection-Dominated Accretion Revisited

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAF) around black holes, using a method similar to that of Chakrabarti (1996a). We choose the sonic radius of the flow $R_s$ and the integration constant in angular momentum equation $j$ as free parameters, and integrate the equations from the sonic point inwards to see if the solution can extend supersonically to the black hole horizon, and outwards to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed in Narayan, Kato, & Honma (1997, NKH97), an representative paper of the previous works on global ADAF solutions, although in that paper an apparently very different procedure was adopted. We obtain a complete picture in the form of $R_s-j$ parameter space which sums up the situation of ADAF solution at a glance. For comparison we also present the distribution of global solutions for inviscid flows in the $R_s-j$ space, which supports the view that there should be some similarities between the dynamical behavior of ADAF and that of adiabatic flows, and that there should be a continuous change from the properties of viscous flows to those of inviscid ones.Comment: 24 pages with 15 figures, to appear in ApJ Vol. 52

Moment-based formulation of Navier–Maxwell slip boundary conditions for lattice Boltzmann simulations of rarefied flows in microchannels

We present an implementation of first-order Navier–Maxwell slip boundary conditions for simulating near-continuum rarefied flows in microchannels with the lattice Boltzmann method. Rather than imposing boundary conditions directly on the particle velocity distribution functions, following the existing discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory, we use a moment-based method to impose the Navier–Maxwell slip boundary conditions that relate the velocity and the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the\ud domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. The results are in excellent agreement with asymptotic solutions of the compressible Navier-Stokes equations for microchannel flows in the slip regime. Our moment formalism is also valuable for analysing the existing boundary conditions, and explains the origin of numerical slip in the bounce-back and other common boundary conditions that impose explicit conditions on the higher moments instead of on the local tangential velocity

State implementation mechanisms association agreement between the EU and Ukraine

Foreign Ukraine's integration into the global economy plays an important role in the development of the national economy, which is why Ukraine is interested in supportive environments that simplifies access to foreign markets and ensure stable trade flows through continuous improvement of competitiveness of domestic production. Association Agreement between Ukraine and the European Union is a new format of relations aimed at establishing a deep and comprehensive free trade agreement Ukraine - the EU and the gradual integration of Ukraine into the EU internal market

Structure and restructuring in the Spanish economy

Accompanying report for submission in partial fulfllment of the requirements for the award of the Degree of Doctor of Philosophy based on published works to the Faculty of Science and Technology, University of Luton.The changing character of the economic environment in the last quarter of the twentieth century has resulted in a continuous process of restructuring in the economy of Spain, mediated through the structure and regulatory framework of the economy. Three specific themes contributing to restructuring are addressed: globalisation of the economy, European integration, and the role of the public sector. Globalisation ofthe economy is demonstrated through increased international flows of goods, capital, people and information, and by the incorporation of businesses in Spain within the corporate networks of foreign multinational companies. Spanish businesses too have been extending their global reach, especially into Latin America. European integration has been part of the globalisation process. A substantial proportion of international flows are now concentrated within the European Union and business networks have been adapting to the 'Single European Market'. European integration has dominated economic policy, first in measures to secure membership of the European Economic Community, then in measures to adjust to the regulatory environment of the European Community and finally in the race to achieve the Maastricht criteria. The role of the public sector in restructuring has been to 'manage' the market forces unleashed by the liberalisation ofthe economy. Market forces, embracing increased competition and technological change, have driven the restructuring process demanding responses from the government. These responses have increasingly been constrained by the shedding of responsibilities upwards to international organisations and downwards to lower tiers of administration. Isolation, protection and goverrunent intervention in the economy have given way to a more liberal, open and international environment. Transformation in the mode of regulation from state corporatism to neo-liberalism has been accompanied by globalisation of the economy, particularly integration into the European economy and the corporate space of multinational companies. Nevertheless, despite the growing emphasis on globalisation, public policy continues to play a crucial role influencing the pace, if not the direction, of restructuring

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at $Re_{\tau}=180$ as well as $590$.Comment: 28 pages, in preparation for submission to Journal of Computational Physic

Areas, nodes and networks: Some analytical considerations

In spatial interaction modelling, trips between origins and destinations within the same areal zone have a predominant influence on both the value of the gravity parameter and on the associated pattern of flows. Despite this, the relevant highly sensitive intrazonal impedance values are usually based on approximate average intrazonal distances or times. This situation has been identified in the literature as the ?self potential? problem. In this paper, integration over continuous space within the origin destination zones is applied to not only compute the intrazonal flows more accurately, but also to determine their influence on calibration of the value of the gravity parameter itself. In addition, whereas all trips are assumed to have destinations corresponding to nodes of the transport network, interzonal trips, starting from dispersed origins, are assigned shortest path routes to join the interzonal links at efficient intermediate points. In the analysis, further approximations incurred in evaluation of the sets of origin/destination flows between contiguous zones are also identified. The eventual aim is to develop practical ?rules of thumb? for correcting the conventional analysis. Flows between areal zones and facility nodes may occur along several plausible alternative paths, rather than via one abstract ?interzonal? path, as usually considered in conventional spatial interaction models. Such destination/route choice is easy to handle in the relatively uncongested conditions characterizing off-peak discretionary travel. This paper examines facility choice via alternative routes, as well as attempting to discern the influence of ?intervening opportunities?. It is indicated how intervening opportunities may influence discretionary travel positively, in contrast to their identified negative influence on the probability of choosing the final destination in journey to work travel. Such intervening opportunities can only be considered meaningfully along the alternative paths of the actual network, as specified above.