Coarse Graining Research Articles

Effect of different filtration materials on oil and water separation efficiency

The key to remove oily wastewater by coarse graining is the selection of filtration materials. In this paper, the four kinds of filtration materials were tested the efficiency of oil and water separation, which are walnut shell, ceramsite, oil sand and polyethylene. The results of laboratory experiments showed that walnut shell and oil sands as oil-soluble media had higher separation efficiency. With the increase of sewage flow velocity, the separation efficiency of porous media decreases. With the increase of the thickness of the porous medium, the separation efficiency increases, and the separation efficiency can reach 100% when the thickness reaches a certain value.

Quantum gravity kinematics from extended TQFTs

In this paper, we show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a representation of the observable algebra including operators of quantum geometry. In particular, we consider the holonomy-flux algebra of (2 + 1)-dimensional Euclidean loop quantum gravity, and construct a new representation of this algebra that incorporates a positive cosmological constant. The vacuum state underlying our representation is defined by the Turaev–Viro TQFT. This vacuum state can be thought of as being peaked on connections with homogeneous curvature. We therefore construct here a generalization, or more precisely a quantum deformation at root of unity, of the previously introduced SU(2) BF representation. The extended Turaev–Viro TQFT provides a description of the excitations on top of the vacuum. These curvature and torsion excitations are classified by the Drinfeld center category of the quantum deformation of SU(2), and are essential in order to allow for a representation of the holonomies and fluxes. The holonomies and fluxes are generalized to ribbon operators which create and interact with the excitations. These excitations agree with the ones induced by massive and spinning particles, and therefore the framework presented here allows automatically for a description of the coupling of such matter to -dimensional gravity with a cosmological constant. The new representation constructed here presents a number of advantages over the representations which exist so far. In particular, it possesses a very useful finiteness property which guarantees the discreteness of spectra for a wide class of quantum (intrinsic and extrinsic) geometrical operators. Also, the notion of basic excitations leads to a so-called fusion basis which offers exciting possibilities for the construction of states with interesting global properties, as well as states with certain stability properties under coarse graining. In addition, the work presented here showcases how the framework of extended TQFTs, as well as techniques from condensed matter, can help design new representations, and construct and understand the associated notion of basic excitations. This is essential in order to find the best starting point for the construction of the dynamics of quantum gravity, and will enable the study of possible phases of spin foam models and group field theories from a new perspective.

Evaluation of mapping schemes for systematic coarse graining of higher alkanes.

A model is introduced to explore the influence of different coarse-grained (CG) resolutions on the structural and thermodynamic properties of higher alkanes. Four different mapping schemes are considered, for which the potentials are derived using the conditional reversible work (CRW) method. The CRW method is a bottom-up coarse-graining procedure, which derives effective pair potentials between nonbonded chemical groups defined by the mapping scheme from the underlying molecular interactions in a quick, inexpensive way. We consider the applicability of CRW for mapping sites including up to four heavy atoms and study the properties of n-dodecane and n-tetracosane in the liquid state. Both chemical and thermodynamic transferability are achieved for high resolution representations. However, the ability of the coarse-grained model to effectively describe the system deteriorates as the size of the mapping is increased and sampling issues arise. By looking at the configuration distributions of the dihedrals in the atomistic sampling runs (gas phase), it is shown that the gauche population is underrepresented. Here we address the problem and propose a viable solution to recover the agreement between atomistic and low resolution coarse-grained representation. All the CRW potentials presented in the paper are reported in tabulated and analytical form.

Coarse graining flow of spin foam intertwiners

Simplicity constraints play a crucial role in the construction of spin foam models, yet their effective behaviour on larger scales is scarcely explored. In this article we introduce intertwiner and spin net models for the quantum group $\text{SU}(2)_k \times \text{SU}(2)_k$, which implement the simplicity constraints analogous to 4D Euclidean spin foam models, namely the Barrett-Crane (BC) and the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK) model. These models are numerically coarse grained via tensor network renormalization, allowing us to trace the flow of simplicity constraints to larger scales. In order to perform these simulations we have substantially adapted tensor network algorithms, which we discuss in detail. The BC and the EPRL/FK model behave very differently under coarse graining: While the unique BC intertwiner model is a fixed point and therefore constitutes a 2D topological phase, BC spin net models flow away from the initial simplicity constraints and converge to several different topological phases. Most of these phases correspond to decoupling spin foam vertices, however we find also a new phase in which this is not the case, and in which a non-trivial version of the simplicity constraints holds. The coarse graining flow of the BC spin net models indicates furthermore that the phase transitions are not of second order. The EPRL/FK model by contrast reveals a far more intricate and complex dynamics. We observe an immediate flow away from the original simplicity constraints, however, with the truncation employed here, the models generically do not converge to a fixed point. The results show that the imposition of simplicity constraints can indeed lead to interesting and complex dynamics. Thus we will need to further develop coarse graining tools to efficiently study the large scale behaviour of spin foam models, in particular for the EPRL/FK model.

Financial contagion behavior analysis based on complex network approach

Recently, financial crisis occurred frequently, such as Asian crisis, sub-prime loan crisis and so on. And, financial contagion behavior analysis is an important subject in the field of international finance. This paper analyzes the financial contagion behavior of US subprime crisis and describes the co-movement behavior between US stock index return and the stock index returns of tested countries by complex network approach. The co-movement modes are defined by a coarse graining procedure, and then by weighted complex network models and evolutionary models transformation characteristics between the modes are analyzed. In order to analyze the sub-prime loan crisis contagion from US to other countries, we selected three main stock market indexes (China, Japan and Germany), S&P 500 index to present an empirical analysis, and the stock market index data is from 2006.1.1 to 2009.3.31. To analyze the contagion effect of the sub-prime crisis, the data is divided into three segments to be analyzed based on complex network approach. The empirical result shows that the co-movement modes of the S&P 500 index and the stock indexes of other countries are clustered around a few critical modes during the evolution. The co-movement modes have the characteristic of grouping, and the conversion of the co-movement modes requires an average of 3–5 days. This paper confirms the sub-prime crisis contagion behavior by comparing the parameters including degree, clustering coefficient and betweenness centrality in three stages. This research may provide further information between S&P 500 index and other stock indexes for the co-movement. More importantly, a new approach is provided for testing the financial contagion effect in this paper.

Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements

For multilevel spin systems, robustness of the quantum mechanical (QM) violation of macrorealism (MR) with respect to coarse grained measurements is investigated using three different necessary conditions of MR, namely, the Leggett-Garg inequality (LGI), Wigner's form of the Leggett-Garg inequality (WLGI) and the condition of no-signalling in time (NSIT). It is shown that for dichotomic sharp measurements, in the asymptotic limit of spin, the algebraic maxima of the QM violations of all these three necessary conditions of MR are attained. Importantly, the QM violations of all these persist in that limit even for \textit{arbitrary} unsharp measurements, i.e. for any non zero value of the sharpness parameter characterizing the degree of fuzziness of the relevant measurements. We also find that when different measurement outcomes are clubbed into two groups for the sake of dichotomising the outcomes, the asymmetry/symmetry in the number of outcomes in the two groups, signifying the degree of coarse graining of measurements, has a crucial role in discerning quantum violation of MR. The results clearly demonstrate that classicality does not emerges in the asymptotic limit of spin, whatever be the unsharpness and degree of coarse graining of the measurements.

Gaussian streaming with the truncated Zel’dovich approximation

We calculate the dark matter halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale dependent functions entering the streaming model we use local Lagrangian bias together with Convolution Lagrangian perturbation theory (CLPT) which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of proto-halos. Based on this observation we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimised if the coarse graining scale is chosen to be 1 Mpc/h at z=0, while the pairwise velocity dispersion is optimised if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon Run 2 N-body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM+CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos.

Emergent space-time via a geometric renormalization method

We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group. Furthermore we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which e.g. for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e. quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is non-integer. At the end of the paper we briefly mention the possibility that our network carries a translocal far-order which leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.

Influence of grain size and exchange interaction on the LLB modeling procedure

Reliably predicting bit-error rates in realistic heat-assisted magnetic recording simulations is a challenging task. Integrating the Landau-Lifshitz-Bloch (LLB) equation, within a coarse graining approach, can reduce the computational effort to determine the magnetization dynamics in the vicinity of the Curie temperature, compared to solving the atomistic Landau-Lifshitz-Gilbert equation. If the aim is that the dynamics of both approaches coincide, temperature dependent material functions, such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities, must be modeled carefully in order to use them as input in the LLB equation. We present an extensive study on how these functions depend on grain size and exchange interactions. We show that, if the size or the exchange constant of a reference grain is modified, the material functions can be scaled, according to the changed Curie temperature, yielding negligible errors. This is shown to be valid for volume changes of up to ±40% and variations of the exchange constant of up to ±10%. Besides the temperature dependent material curves, computed switching probabilities also agree well with probabilities separately determined for each system. Our study suggests that there is no need to recalculate the required LLB input functions for each particle. Within the presented limits, it is sufficient to scale them to the Curie temperature of the altered system.

Complexity measurement of regional groundwater resources system using improved Lempel-Ziv complexity algorithm

In this paper, the self-adaptive artificial fish swarm algorithm (SAAFSA) is used to optimize the coarse graining of segment numbers, which are used in the Lempel-Ziv complexity algorithm. This approach improves the Lempel-Ziv complexity (LZC) algorithm of equal probability coarse graining. As a case study, the complexities of monthly series of groundwater depth were analyzed at seven farms in the Hongxinglong Administration. GIS technology was used to create spatial distributions of monthly groundwater depths. A projection pursuit model based on the SAAFSA was established and used for complexity attribution analysis at selected farms with different degrees of complexity. The three selected farms, Hongqiling, 852, and Youyi, each represent a certain degree of complexity. Further analysis shows that precipitation, evaporation, temperature, and human activities are the primary factors that cause complexity variations in local groundwater depth. The results reveal the evolution of the complexity characteristics of local groundwater depth and provide scientific evidence for the need to effectively allocate regional water resources. Additionally, the proposed method can be applied in complexity analyses of other hydrologic features, as well as in research regarding nonlinear time series in economic, engineering, medical, and signal analyses.

Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases.

The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.

A Field Guide to Recent Work on the Foundations of Statistical Mechanics

This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past hypothesis, reductionism, phase average, thermodynamic limit, interventionism, entropy.

Fragmenting networks by targeting collective influencers at a mesoscopic level.

A practical approach to protecting networks against epidemic processes such as spreading of infectious diseases, malware, and harmful viral information is to remove some influential nodes beforehand to fragment the network into small components. Because determining the optimal order to remove nodes is a computationally hard problem, various approximate algorithms have been proposed to efficiently fragment networks by sequential node removal. Morone and Makse proposed an algorithm employing the non-backtracking matrix of given networks, which outperforms various existing algorithms. In fact, many empirical networks have community structure, compromising the assumption of local tree-like structure on which the original algorithm is based. We develop an immunization algorithm by synergistically combining the Morone-Makse algorithm and coarse graining of the network in which we regard a community as a supernode. In this way, we aim to identify nodes that connect different communities at a reasonable computational cost. The proposed algorithm works more efficiently than the Morone-Makse and other algorithms on networks with community structure.

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function $f_{\rm H}(A, E, t)$ for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\rm HW}(t)=-{\rm Tr}f_H \log f_H$ defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.

Incorporating Noise Quantitatively in the Phase Field Crystal Model via Capillary Fluctuation Theory.

A tacit assumption underlying most phase field models of nonequilibrium phase transformations is that of scale separation. Stochastic order parameter field theories utilize noise to separate atomic-scale fluctuations from the slowly varying fields that describe microstructure patterns. The mesoscale distribution of such stochastic variables is generally assumed to follow Gaussian statistics, with their magnitude following fluctuation-dissipation relations. However, there is still much debate about how atomic-scale fluctuations map onto the mesoscale upon coarse graining of microscopic theories. This Letter studies interface fluctuations in the phase field crystal (PFC) model and proposes a self-consistent method for relating how the effective noise strength and spectral filtering of the noise in the PFC model, and similar types of microscopic models, should be defined so as to attain the spectrum of mesoscale capillary fluctuations quantitatively.

MARTINI Coarse-Grained Model of Solid–Liquid Interface

Capillary driven motion of fluids is responsible for many natural phenomena and effective on several industrial applications. By way of illustration, consider water remediation and oil recovery, as well as the operation of some laboratory equipment such as trolling mode atomic force microscopy. Experimental study of formation of meniscus layer as a capillary driven motion in scales smaller than micro is extremely difficult and exceedingly costly. Consequently, computational models seem to be appropriate to study the capillary driven motion in nanoscale. In the present work, we have utilized the MARTINI coarse graining method to investigate the establishment of meniscus layer around a cylindrical nanoneedle. We have demonstrated that growth of meniscus layer height is a function of square root of time, which shows agreement with Lucas–Washburn relation for capillary penetration pace. Accordingly, consistency of the utilized model with the physics of the phenomenon can be concluded. Also the effect of varia...

Quantum and classical behavior in interacting bosonic systems

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

Multiblob coarse-graining for mixtures of long polymers and soft colloids.

Soft nanocomposites represent both a theoretical and an experimental challenge due to the high number of the microscopic constituents that strongly influence the behaviour of the systems. An effective theoretical description of such systems invokes a reduction of the degrees of freedom to be analysed, hence requiring the introduction of an efficient, quantitative, coarse-grained description. We here report on a novel coarse graining approach based on a set of transferable potentials that quantitatively reproduces properties of mixtures of linear and star-shaped homopolymeric nanocomposites. By renormalizing groups of monomers into a single effective potential between a f-functional star polymer and an homopolymer of length N0, and through a scaling argument, it will be shown how a substantial reduction of the to degrees of freedom allows for a full quantitative description of the system. Our methodology is tested upon full monomer simulations for systems of different molecular weight, proving its full predictive potential.

Representing environment-induced helix-coil transitions in a coarse grained peptide model

Coarse grained (CG) models are widely used in studying peptide self-assembly and nanostructure formation. One of the recurrent challenges in CG modeling is the problem of limited transferability, for example to different thermodynamic state points and system compositions. Understanding transferability is generally a prerequisite to knowing for which problems a model can be reliably used and predictive. For peptides, one crucial transferability question is whether a model reproduces the molecule's conformational response to a change in its molecular environment. This is of particular importance since CG peptide models often have to resort to auxiliary interactions that aid secondary structure formation. Such interactions take care of properties of the real system that are per se lost in the coarse graining process such as dihedral-angle correlations along the backbone or backbone hydrogen bonding. These auxiliary interactions may then easily overstabilize certain conformational propensities and therefore destroy the ability of the model to respond to stimuli and environment changes, i.e. they impede transferability. In the present paper we have investigated a short peptide with amphiphilic EALA repeats which undergoes conformational transitions between a disordered and a helical state upon a change in pH value or due to the presence of a soft apolar/polar interface. We designed a base CG peptide model that does not carry a specific (backbone) bias towards a secondary structure. This base model was combined with two typical approaches of ensuring secondary structure formation, namely a C α -C α -C α -C α pseudodihedral angle potential or a virtual site interaction that mimics hydrogen bonding. We have investigated the ability of the two resulting CG models to represent the environment-induced conformational changes in the helix-coil equilibrium of EALA. We show that with both approaches a CG peptide model can be obtained that is environment-transferable and that correctly represents the peptide's conformational response to different stimuli compared to atomistic reference simulations. The two types of auxiliary interactions lead to different kinetic behavior as well as to different structural properties for fully formed helices and folding intermediates, and we discuss the advantages and disadvantages of these approaches.

Parametrizing coarse grained models for molecular systems at equilibrium

Hierarchical coarse graining of atomistic molecular systems at equilibrium has been an intensive research topic over the last few decades. In this work we (a) review theoretical and numerical aspects of different parametrization methods (structural-based, force matching and relative entropy) to derive the effective interaction potential between coarse-grained particles. All methods approximate the many body potential of mean force; resulting, however, in different optimization problems. (b) We also use a reformulation of the force matching method by introducing a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (E. Kalligiannaki, et al., J. Chem. Phys. 2015). We apply and compare these methods to: (a) a benchmark system of two isolated methane molecules; (b) methane liquid; (c) water; and (d) an alkane fluid. Differences between the effective interactions, derived from the various methods, are found that depend on the actual system under study. The results further reveal the relation of the various methods and the sensitivities that may arise in the implementation of numerical methods used in each case.