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Singular Perturbations represent an advantageous theory to deal with systems characterized by a two-time scale separation, such as the longitudinal dynamics of aircraft which are called phugoid and short period. In this work, the combination of the NonLinear Geometric Approach and the Singular Perturbations leads to an innovative Fault Detection and Isolation system dedicated to the isolation of faults affecting the air data system of a general aviation aircraft. The isolation capabilities, obtained by means of the approach proposed in this work, allow for the solution of a fault isolation problem otherwise not solvable by means of standard geometric techniques. Extensive Monte-Carlo simulations, exploiting a high fidelity aircraft simulator, show the effectiveness of the proposed Fault Detection and Isolation system.

In this work, synergism and antagonism among active ingredients of traditional Chinese medicine (TCM) were studied at system-level by using molecular imprinting technology. Reduning Injection (RDNI), a TCM injection, was widely used to relieve fever caused by viral infection diseases in China. Molecularly imprinted polymers (MIPs) synthesized by sol-gel method were used to separate caffeic acid (CA) and analogues from RDNI without affecting other compounds. It can realize the preparative scale separation. The inhibitory effects of separated samples of RDNI and sample combinations in prostaglandin E2 biosynthesis in lipopolysaccharide-induced RAW264.7 cells were studied. The combination index was calculated to evaluate the synergism and antagonism. We found that components which had different scaffolds can produce synergistic anti-inflammatory effect inside and outside the RDNI. Components which had similar scaffolds exhibited the antagonistic effect, and the antagonistic effects among components could be reduced to some extent in RDNI system. The results indicated MIPs with the characteristics of specific adsorption ability and large scale preparation can be an effective approach to study the interaction mechanism among active ingredients of complex system such as TCM at system-level. And this work would provide a new idea to study the interactions among active ingredients of TCM.

Problem of PI and PID multivariable controller design based on time-scale separation technique for linear time-invariant systems is discussed. Properties of tracking and stabilizing multivariable controllers are treated. Generalized multivariable controllers are proposed for MIMO systems when the conditions of invertibility and internal stability hold. The internal stability analysis of the system is based on consideration of the normal canonical form. Simulation results and comparison of tracking and stabilizing multivariable controllers are presented

Controller design problem for testbed of strength test for aviation builds is discussed. The description of the stand equipped by electrohydraulic drive is presented. Results of experimental researches of dynamical characteristics for the stand are shown and, as the result, the mathematical model of the given stand has been received by results of experimental tests. Proportional-integral (PI) controller is designed for force interaction via singular perturbation technique such that multi-time-scale motions are artificially induced in the closed-loop system. Multi-time-scale motions analysis allows getting analytical expressions for selection of controller parameters. Experimental results are presented.

The paper is devoted to comparison of the properties of tracking and stabilizing PI controllers which are designed via time-scale separation technique. It has been shown that the proposed tracking PI controller allows to provide robust output control and almost perfect tracking under model uncertainties and external disturbances as well as the stabilizing PI controller allows providing desired output transients performances under step change of set point. Robust control is provided due to two-time-scale motions that are artificially forced in the closed-loop system.

Summary We first show the scale separation property of envelope inversion. The nonlinear envelope extraction provides a nonlinear scale separation of the information contained in the waveform data, which can reduce the local minima in the misfit function and can be used to recover the largescale component of the model. The misfit configuration tests show that the misfit for envelope data has no local minima. Also, we further show the noise resistant property of this method. Numerical examples show that envelope inversion is to some extent resistant to seismic interference

Inexact hardware design, which advocates trading the accuracy of computations in exchange for significant savings in area, power and/or performance of computing hardware, has received increasing prominence in several error-tolerant application domains, particularly those involving perceptual or statistical end-users. In this paper, we evaluate inexact hardware for its applicability in weather and climate modelling. We expand previous studies on inexact techniques, in particular probabilistic pruning , to floating point arithmetic units and derive several simulated set-ups of pruned hardware with reasonable levels of error for applications in atmospheric modelling. The set-up is tested on the Lorenz ‘96 model, a toy model for atmospheric dynamics, using software emulation for the proposed hardware. The results show that large parts of the computation tolerate the use of pruned hardware blocks without major changes in the quality of short- and long-time diagnostics, such as forecast errors and probability density functions. This could open the door to significant savings in computational cost and to higher resolution simulations with weather and climate models.

International audience; Our aim is to demonstrate the effectiveness of the matched asymptotic expansion method in obtaining a simpli ed model for the influence of small identical heterogeneities periodically distributed on an internal surface on the overall response of a linearly elastic body. The results of some numerical experiments corroborate the precise identi cation of the di fferent steps, in particular of the outer/inner regions with their normalized coordinate systems and the scale separation, leading to the model.

A nonlinear aircraft model is presented and used to develop an overall unified approach to online trim and maneuverability envelope estimation with uncertainty quantification without any requirement for active input excitation. The concept of time scale separation makes this method suitable for the adaptive characterization of altered safe maneuvering limitations based on aircraft performance after impairment. The results can be used to provide pilot feedback and/or be combined with flight planning, trajectory generation, and guidance algorithms to help maintain safe aircraft operations in both nominal and off-nominal scenarios.

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu. Next generation uid ow systems are likely to depend on micro or nano scale dynamics that make the system behaviour multiscale in both space and time. There may be strong or weak separation between the length scales and between the time scales in di erent parts of the ow, and these scale-separations may also vary in space and time. In this paper we discuss a practical approach to improving the e ciency of hybrid particle/continuum models of such multiscale ows. Our focus is on adapting the solution method to the local scale-separation conditions, in order to balance compu- tational e ciency with accuracy. We compare results from our new hybridisation in space and time with full molecular simulations of benchmark nanoscale ows.

Model reduction techniques often prove indispensable in the analysis of physical and biological phenomena. A succesful reduction technique can substantially simplify a model while retaining all of its pertinent features. In metabolic networks, metabolites evolve on much shorter time scales than the catalytic enzymes. In this chapter, we exploit this discrepancy to justify the reduction via time scale separation of a class of models of metabolic networks under genetic regulation . We formalise the concept of a metabolic network and employ Tikhonov’s Theorem for singularly perturbed systems. We demonstrate the applicability of our result by using it to address a problem in metabolic engineering: the genetic control of branched metabolic pathways. We conclude by providing guidelines on how to generalise our result to larger classes of networks.

We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Our approach has been successfully applied to an increasing number of applications from different fields of science and technology.

Cone serotiny refers to canopy seed storage in cones that remain alive, though closed, for several years. There are some Cupressus species which have only serotinous cones, or both serotinous and non-serotinous cones on the same tree. Scale separation and seed release occurs immediately after the cone ripens in non-serotinous cones, or else the cones remain closed and alive longer, generally up to 15-20 years. Germination tests were done with serotinous cone seeds from C. arizonica Greene, C. benthamii Endl., C. lusitanica Mill., and C. macrocarpa Hartw. Germination was below 50% for all species. The highest levels of germination were obtained from 2- to 7-year-old cones, depending on the species. Cupressus arizonica showed a regular decline in germination values, from 43.5% for seeds from 3-year-old cones to 7.5% for seeds from 7-year-old cones. Cupressus benthamii had a maximum germination value of seeds from 5-year-old cones. Cupressus macrocarpa had a maximum germination capacity of 20.5% for seeds from 6-year-old cones, and it showed 7.5% germination for 12-year-old seeds. Cupressus lusitanica reached 33.5% germination of seeds from 5-year-old cones. Serotinous cones from Cupressus species, usually not collected because it is assumed that their seeds are not viable, can be utilized in cone harvesting, increasing the yield of the cone-bearing trees.

Flat magnetic separator was used to separate magnetic bioaffinity adsorbents from litre volumes of suspensions. Both magnetic cross-linked erythrocytes and magnetic chitosan were efficiently separated; at least 95% adsorbent recovery was achieved at maximum flow rate (1680 ml min−1). Using this system low amounts of trypsin were concentrated from large sample volumes using magnetic erythrocytes as affinity adsorbent.

Polyphenols are sometimes difficult to separate in classical liquid chromatography. Countercurrent chromatography uses a biphas ic liquid sys- tem to separate the components of a mixture. A centrifugal field allows to use a liquid stationary phase in an open tube. The ph ase density difference and the centrifugal field are the only parameters allowing the equilibrium between the two liquid phases. The big advantage of the technique in preparative separation is the dual-mode capability of CCC. The role of the phases can be switched during a run. The mobile phase becomes st ationary and vice versa. Then no injected material can be left in the machine. The large scale separations of a flavonoid mixture and two tannin samples are described: choice of the biphasic liquid system, analytical study, scaling-up, injection protocol, two step separation in case of dual-mode use. It was possible to inject 26 g of a tannin sample in one run.

Arakawa and Schubert’s cumulus parameterization is formulated under the two asymptotic limits: σ → 0 and τc/τL → 0, where σ is the fractional area occupied by cumulus convection, and τc and τL are the characteristic timescales for convection and large scales, respectively. The present note shows that the two asymptotic limits tend to contradict each other, so that the smallness of these two quantities is established only under a compromise. This contradiction is formally established by referring to the heat engine theories by Renno and Ingersoll, and by Emanuel and Bister. The climatological estimate for σ indicates that the timescale separation is only marginally satisfied with respect to the tropical planetary-scale circulation.

Averages used in mean-field magnetohydrodynamics must satisfy the Reynolds conditions. It is shown that for space periodic conditions the only ones correspond to filtering modulo a subgroup of Z p , whereas for functions vanishing at infinity all possible averages are trivial. In general additional hypotheses, such as scale separation, must be assumed within the plasma.

We study analytically and numerically the statics and the off-equilibrium dynamics of spin models over finitely connected random graphs. We identify a threshold value for the connectivity beyond which the loop structure of the graph becomes thermodynamically relevant. Glauber dynamics simulations show that this loop structure is responsible for the onset of dynamical features of a local character (dynamical heterogeneities and spontaneous time scale separation), consistently with previous (experimental and numerical) studies of glasses and spin glasses in their approach to the low temperature phase., Comment: 5 pages, latex, 2 postscript figures

The dissipative nature of the particle interactions is responsible for an {ital inherent} lack of scale separation in granular systems which is not related to the typical grain/container size ratios. It is demonstrated that rapid granular flows are typically supersonic, shear rates in these systems are nearly always {open_quotes}large,{close_quotes} the mean free times are comparable with the macroscopic time scale(s), and the {ital mean free paths can be of macroscopic dimensions}, the latter indicating {ital nonlocality}. Additional physical and computational implications are discussed. {copyright} {ital 1998} {ital The American Physical Society}

Mafic impact-melt breccias (IMB) from the Apollo landing sites—particularly Apollo 14, Apollo 15, Apollo 16, and Apollo 17—are abundant and form compositionally distinct groups. These groups exhibit a range of major-element compositions and incompatible-element enrichments. Although concentrations of incompatible elements span a significant range, inter-element ratios vary little and have been used in the past to infer a common KREEP component (KREEP = rich in potassium, rare-earth elements, phosphorus, and other alkali and high-field-strength elements). On the basis of an extensive, high-precision data set for melt-breccia groups from different Apollo landing sites, variations in trace-element signatures of the mafic impact-melt breccias reflect significant differences in KREEP components of source regions. These differences are consistent with variable enrichment or depletion of source regions in those trace elements that fractionated during the latest stages of residual-melt evolution and are more or l...

Clinical development of antisense drugs is rapidly increasing requirements for large quantities of oligonucleotides. As part of the manufacturing process appropriately large scale separation techniques must be developed. This article reviews applications of sample self displacement techniques to the purification of oligonucleotides and nucleic acids, wherein sample components act as displacers and enhance purities. Applications for other solutes are also reviewed where similar methods may be of use in oligonucleotide purification. Experimental data is presented for sample self displacement anion-exchange chromatography of the clinically important phosphorothioate oligonucleotides. The technique can enhance full-length purity of the product and offers maximal utilization of the chromatographic media. Full-length purities of 95% and higher are achieved by this approach and recovery yields are up to 70% depending upon starting feed purity. Recycling and real time process monitoring can further improve recovery. Techniques for column saturation with multiple linked columns are presented and their applications to oligonucleotide purification are discussed.

The one-dimensional (1-D) spatially periodic system of N classical particles, interacting via a Coulomb-like repulsive long-range force, is studied using classical mechanics. The usual Bohm–Gross dispersion relation for the collective modes is obtained in the absence of quasiresonant particles. In the presence of R quasiresonant particles, the evolution equations for M long-wavelength modes are coupled to the particles’ motion through a self-consistent wave–particle Hamiltonian. The wave–particle Lagrangian is derived from the full N-body Lagrangian. The derivation relies on an explicit scale separation argument and avoids the use of kinetic theory and continuous medium formalism.

We summarize the group's progress in applying, analyzing, and improving ODT and ODT-based stochastic turbulence models like ODTLES. Compared to DNS these models span a wider range of scales while compared to RANS/LES (i) the molecular effects are retained and (ii) no assumption of scale separation is made. In this regard ODTLES has more properties of DNS than of standard LES. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Exponential-tailed scalar probability density functions (PDF's) are obtained by high-pass filtering scalar concentration time series measured in turbulent pipe flow. This behavior reflects the scale separation of scalar and velocity fluctuations that develops in this flow, such that the low-wave-number scalar fluctuations act as an imposed scalar gradient stirred by finer-scale wall-generated shear. This observation broadens the class of flows in which long-tailed scalar PDF's are anticipated to occur.

Split-flow thin-cell fractionation (SF) was one of Cal Gidding's later inventions in the field of separation science. In the mid 1980's, he began work on this technique, which is in many ways similar to field-flow fractionation (FFF), but which ultimately offers yet another dimension to his list of credits: preparative separations. SF is applicable to particles and macromolecules and offers advantages similar to FFF techniques in separation speed, resolution, breadth in applicable size range, gentleness, and flexibility of separation conditions. However, SF singularly offers the possibility for continuous operation and thus preparative scale throughputs. After more than 10 years of developmental work by the Giddings research group, SF has now become a reliable high-resolution technique for separation of particles in the micron size range. In this article, the factors influencing resolution, throughput, and scale-up of SF are considered and discussed. Preparative scale separation using gravitational SF is shown by the separation of silica and synthetic diamond particles. © 1997 John Wiley & Sons, Inc. J Micro Sep9: 261–273, 1997

A new recycling technique named “Sandwiching recycle” is investigated, and its effectiveness in obtaining high recovery yields of the desired component from a multicomponent mixture by means of chromatographic separation is examined. This technique hinders the product from diffusion in such a way that the feed period is sandwiched in between the recycle periods. It is found that sandwiching recycle chromatography is highly effective to increase the yield of the component whose mean retention time is equivalent to its switching time, but that this recycling does not increase the yield of the impure component in the product. Because of the simpleness of its apparatus, this technique can be used for preparative scale separation of mixtures. Detailed features of the recycling method are examined by simulation to recognize what conditions should be taken into consideration to separate the target component from a mixture and to obtain high yield.

溶解・再析出を経験した三酢酸セルロースを粉末化あいはシリカゲルにコーティングした固定相でも光学分割能を示す.その光学分割能は微結晶三酢酸セルロースで重要視された天然セルロースが持つ結晶構造には依存しない.酢酸セルロース分子鎖の立体構造の規則性が重要であり,シリカゲルに担持させる際に三酢酸セルロースを溶解させるために用いる溶媒に左右される.セルロース,アミロース誘導体を用いた固定相では多数の化合物が分割されるが,それぞれ分割される化合物には違いがある.多糖に導入する置換基の構造よりも,多糖主鎖の構造の違いのほうが光学分割能に大きな差異を示す.カラム法による光学活性体の生産規模での分離には,シングルカラムを用いるバッチ式よりも試料の注入と分離成分の抜き取りを連続的に行うSMB法が高い分離効率を示し,工業規模での生産プロセスへの応用研究が急ピッチで進められている.

Only two kinds of compactification are known that lead to four-dimensional supersymmetric AdS vacua with moduli stabilisation and separation of scales at tree-level. The most studied ones are compactifications of massive IIA supergravity on SU(3) structures with smeared O6 planes, for which a general ten-dimensional expression for the solution in terms of the SU(3) structure was found. Less studied are compactifications of IIB supergravity with smeared O5/O7 planes. In this paper we derive a general ten-dimensional expression for the smeared O5/O7 solutions in terms of SU(2) structures. For a specific choice of orientifold projections, we recover the known examples and we also provide new explicit solutions., Comment: 27 + 16 pages; v2 references added and typos in few equations corrected

Enforcement of constraints on the maximum deliverable power is essential to protect lithium-ion batteries from over-charge/discharge and overheating. This paper develops an algorithm to address the often overlooked temperature constraint in determining the power capability of battery systems. A prior knowledge of power capability provides dynamic constraints on currents and affords an additional control authority on the temperature of batteries. Power capability is estimated using a lumped electro-thermal model for cylindrical cells that has been validated over a wide range of operating conditions. The time scale separation between electrical and thermal systems is exploited in addressing the temperature constraint independent of voltage and state-of-charge (SOC) limits. Limiting currents and hence power capability are determined by a model-inversion technique, termed Algebraic Propagation (AP). Simulations are performed using realistic depleting currents to demonstrate the effectiveness of the proposed method.Copyright © 2013 by ASME

We present a hybrid molecular-continuum simulation method for modelling nano- and micro-flows in network-type systems. In these types of problem, a full molecular dynamics (MD) description of the macroscopic flow behaviour would be computationally intractable, or at least too expensive to be practical for engineering design purposes. Systems that exhibit multiscale traits, such as this, can instead be solved using a hybrid approach that distinguishes the problem into macroscopic and microscopic dynamics, modelled by their respective solvers. The technique presented in this study is an extension and addition to a hybrid method developed by Borg et al. (J Comput Phys 233:400-413, 2013) for high-aspect-ratio channel geometries, known as the internal-flow multiscale method (IMM). Computational savings are obtained by replacing long channels in the network, which are highly scale-separated, by much smaller, but representative, MD simulations, without a substantial loss of accuracy. On the other hand, junction components do not exhibit this length-scale separation, and so must be simulated in their entirety using MD. The current technique combines all network elements (junctions and channels) together in a coupled simulation using continuum conservation laws. For the case of steady, isothermal, incompressible, low-speed flows, we use the conservation of mass and momentum flux equations to derive a set of molecular-continuum constraints. An algorithm is presented here that computes at each iteration the new constraints on the pressure differences to be applied over individual MD micro-elements (channels and junctions), successively moving closer to macroscopic mass and momentum conservation. We show that hybrid simulations of some example network cases converge quickly, in only a few iterations, and compare very well to the corresponding full MD results, which are taken as the most accurate solutions. Major computational savings can be afforded by the IMM-type approximation in the channel components, but for steady-state solutions, even greater savings are possible. This is because the micro-elements are coupled to a steady-state continuum conservation expression, which greatly speeds up the relaxation of individual micro-components to steady conditions as compared to that of a full MD simulation. Unsteady problems with high temporal scale separation can also be simulated, but general transient problems are beyond the capabilities of the current technique.

Michaelis and Menten introduced to biochemistry the idea of time-scale separation, in which part of a system is assumed to be operating sufficiently fast compared to the rest so that it may be taken to have reached a steady state. This allows, in principle, the fast components to be eliminated, resulting in a simplified description of the system's behaviour. Similar ideas have been widely used in different areas of biology, including enzyme kinetics, protein allostery, receptor pharmacology, gene regulation and post-translational modification. However, the methods used have been independent and ad hoc. In the present study, we review the use of time-scale separation as a means to simplify the description of molecular complexity and discuss recent work setting out a single framework that unifies these separate calculations. The framework offers new capabilities for mathematical analysis and helps to do justice to Michaelis and Menten's insights about individual enzymes in the context of multi-enzyme biological systems.

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation., 7 pages. Minor revisions are made in ver.2; In ver.3, the presentation has been revised substantially, and this version will be published in Phys. Rev. Lett

A new method is presented for the exploitation of time-scale separation in hybrid continuum-molecular models of multiscale flows. Our method is a generalisation of existing approaches, and is evaluated in terms of computational efficiency and physical/numerical error. Comparison with existing schemes demonstrates comparable, or much improved, physical accuracy, at comparable, or far greater, efficiency (in terms of the number of time-step operations required to cover the same physical time). A leapfrog coupling is proposed between the 'macro' and 'micro' components of the hybrid model and demonstrates potential for improved numerical accuracy over a standard simultaneous approach. A general algorithm for a coupled time step is presented. Three test cases are considered where the degree of time-scale separation naturally varies during the course of the simulation. First, the step response of a second-order system composed of two linearly-coupled ODEs. Second, a micro-jet actuator combining a kinetic treatment in a small flow region where rarefaction is important with a simple ODE enforcing mass conservation in a much larger spatial region. Finally, the transient start-up flow of a journal bearing with a cylindrical rarefied gas layer. Our new time-stepping method consistently demonstrates as good as or better performance than existing schemes. This superior overall performance is due to an adaptability inherent in the method, which allows the most-desirable aspects of existing schemes to be applied only in the appropriate conditions.

The common practice for obtaining a regulated output voltage from a dc-dc boost converter has the disadvantage of insufficient robustness against additive noise uncertainties. The present study is devoted to search for a technique to improve the robustness of the boost converters with input noise uncertainties. The nonlinear Current-Mode Control (CMC) is used to regulate the output voltage of the dc-dc boost converter. The new approach uses the Two-Time-Scale Separation based robust redesign technique to increase the robustness of the converters against input noise uncertainties. A uniform additive noise having amplitude of −0.3 to 0.3 V imposed to the system's input source and the performance of the output regulation was evaluated and compared to the system without any noise. The load uncertainty was also added and output was evaluated. In the last stage load uncertainty was replaced by line voltage uncertainty. The results show that in spite of imparting noise and other uncertainties, the proposed system can recover the nominal trajectories in a satisfactory manner. The study also indicated that by increasing the filter gain, redesigned system performance improved. System output with time scale design for e=0.001 is superior to other systems tested.

Type IIB toroidal orientifolds are among the earliest examples of flux vacua. By applying T-duality, we construct the first examples of massive IIA flux vacua with Minkowski space-times, along with new examples of type IIA flux vacua. The backgrounds are surprisingly simple with no four-form flux at all. They serve as illustrations of the ingredients needed to build type IIA and massive IIA solutions with scale separation. To check that these backgrounds are actually solutions, we formulate the complete set of type II supergravity equations of motion in a very useful form that treats the R-R fields democratically., Comment: 38 pages, LaTeX; references updated; additional minor comments added; published version

Stationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial/boundary value problem of the evolution equations is then formulated and a semi-analytical solution is constructed. The solution for the mixture pressure, the mixture density and the void fraction are then explicitly related to the solution of the evolution equations. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented. Publisher's Version

This chapter summarizes the major developments in the field of liquid chromatographic separation of enantiomers. After short historical overview, the materials and technologies used for analytical and preparative scale separation of enantiomers in high-performance liquid chromatography, nanoliquid chromatography, simulated moving-bed chromatography, and supercritical fluid chromatography are shortly discussed. In the final part, some current trends and future needs in liquid chromatographic separation of enantiomers are overviewed.

This article has been republished to address equation and symbol formatting errors and errors in figure citations. This republication addresses the errors referenced in the previous formal correction. The publisher apologizes for the errors.

In this chapter, we will review some analytical methods that make it possible to determine approximate solutions of the Boltzmann equation. In particular, we will discuss the structure of the Hilbert and Chapman–Enskog perturbation techniques and will also outline the essential features of the invariant manifold method, which stems from the assumption of time scale separation and, unlike the former methods, is also applicable beyond the strict hydrodynamic limit. Before reviewing the wealth of different techniques, it is worth investigating in greater depth the role of the different time scales in a particle system, which is one of the main ingredients underlying the onset of collective behavior.

The production of highly monodisperse polymer particles is very important in different fields, such as research and industry. This interest is due to their wide potential applications, ranging from drug/gene delivery to large scale separation, sensor fabrication and diagnostic applications, due to their special characteristics of uniformity in size, shape and structure. Different methods for the synthesis of monodisperse particles have been reported, but there is a necessity to find new approaches for the synthesis of functionalized monodisperse particles, in order to satisfy growing needs of industry in products with specific characteristics.

Tomographic Full waveform inversion (TFWI) provides a framework to invert the seismic data that is immune to cycle-skipping problems by extending the velocity model. However, this extension makes the propagation considerably more expensive because each multiplication by velocity becomes a convolution. We provide an alternative formulation which computes the backscattering and the forward scattering components of the gradient separately. The inversion setup includes two steps that maintain the high resolution results of TFWI. First, the linearized residual are updated in a nested inversion scheme. Second, the two components of the gradient are first mixed and then separated based on a Fourier domain scale separation to allow for a fully simultaneous inversion of model scales.

Understanding how ecosystems evolve and how they respond to external perturbations is critical if we are to predict the effects of human intervention. A particular class of ecosystems whose dynamics are poorly understood are those in which the species are related via cross-feeding. In these ecosystems the metabolic output of one species is being used as a nutrient or energy source by another species. In this paper we derive a mathematical description of cross-feeding dynamics based on the replicator equation. We show that under certain assumptions about the system (e.g., high flow of nutrients and time scale separation), the governing equations reduce to a second-order series expansion of the replicator equation. By analysing the case of two and three species we derive conditions for co-existence and show under which parameter conditions one can expect an increase in mean fitness. Finally, we discuss how the model can be parameterised from experimental data.

In this paper Monte Carlo Finite Element (MC FE) approximations for elliptic homogenization problems with random coefficients which oscillate on $n \in \mathbb{N}$ a-priori known, separated length scales are considered. The convergence of multilevel MC FE (MLMC FE) discretizations is analyzed. In particular, it is considered that the multilevel FE discretization resolves the nest physical length scale, but the coarsest FE mesh does not, so that the so-called "resonance" case occurs at intermediate MLMC sampling levels. It is proved that switching to an Hierarchic Multiscale Finite Element method such as the Finite Element Heterogeneous Multiscale method (FE{HMM) to compute all MLMC FE samples on meshes which under-resolve the physical length scales implies once more optimal efficiency (in terms of accuracy versus computational work) for the numerical estimates of statistical moments with first and second order FE-HMMs. Specifi cally, the method proposed here allows to obtain estimates of the expectation of the random solution, with accuracy versus work that is identical to the solution of a single deterministic problem obtained by a FE-HMM, and which is, moreover, robust with respect to the physical length scales. Numerical experiments corroborate our analytical findings., SAM Research Report, 2012-29

Nonlinear dynamic inversion by time scale separation (NDI) offers a quick and sim- ple design route for (full three axis) nonlinear ight control law design that yields a low complexity control law. The resulting closed loop system can be made semiglobally stable but the stability is critically dependent on the fulfillment of the time scale separation as- sumption which in general forces the inner loop (angular rates) to be considerably faster than the outer loop (velocity components). Block backstepping (BBS) is an alternative design method that does not rely on a time scale separation requirement and directly yields semiglobal stability but that involves a somewhat more complicated design procedure and resulting control law. The two methods are closely related, however, and in this paper we make a comparison of them. In particular, we show conditions under which the extra terms in the BBS control law offer (or do not offer) significant advantages over the simple NDI control law. We show this in terms of stability region, sensitivity, and robustness.

Colonies of flagellated bacteria on agar plates are known to take on diverse morphologies. A diffusion-reaction model is proposed for bacterial-colony pattern formation on a surface due to time scale separation between the slow mass migration of bacteria from the point of inoculation, and the fast, but localized, dynamics of bacterial phenotypic plasticity stimulated by public-goods cooperation and phenotypic switching. By considering two switchable phenotypes in the population, the model generates pattern diversity typifying those reported by experimental studies.

A multiscale numerical scheme is presented for modelling nano flow systems in which length-scale separation exists, but only in one direction; for example, in long nanochannel geometries. The scheme is a hybrid atomistic/continuum method, coupling a conventional fluid model with more-costly, but accurate, molecular dynamics (MD). The hybrid approach presented here is different to the common domain-decomposition style of approach, and is more akin to distributed methods, such as the Heterogeneous Multiscale Method (HMM). In our method, the molecular dynamics solver is applied only at a few physical slices of the full macro-scale domain. The greater the scale separation, the greater the computational speed-up (when compared to a full MD simulation of the same geometry). The new method is successfully tested on a converging/diverging nanochannel case containing flow of a simple Lennard-Jones liquid. Very good agreement is found when comparing the multiscale simulation results to those of a full MD simulation.Copyright © 2012 by ASME