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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Membrane-Confined Iron Oxychloride Nanocatalysts for Highly Efficient Heterogeneous Fenton Water Treatment

Heterogeneous advanced oxidation processes (AOPs) allow for the destruction of aqueous organic pollutants via oxidation by hydroxyl radicals ( • OH). However, practical treatment scenarios suffer from the low availability of short-lived • OH in aqueous bulk, due to both mass transfer limitations and quenching by water constituents, such as natural organic matter (NOM). In this work, we overcome these challenges by loading iron oxychloride catalysts within the pores of a ceramic ultrafiltration membrane, resulting in an internal heterogeneous Fenton reaction that can degrade organics in complex water matrices with pH up to 6.2. With • OH confined inside the nanopores (~ 20 nm), this membrane reactor completely removed various organic pollutants with water fluxes of up to 100 L m –2 h –1 (equivalent to a retention time of 10 s). This membrane, with a pore size that excludes NOM (>300 kDa), selectively exposed smaller organics to •OH within the pores under confinement and showed excellent resiliency to representative water matrices (simulated surface water and sand filtration effluent samples). Moreover, the membrane exhibited sustained AOPs (>24 h) and could be regenerated for multiple cycles. Our results suggest the feasibility of exploiting ultrafiltration membrane-based AOP platforms for organic pollutant degradation in complex water scenarios.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Jordan–Wigner Transformation for the Description of Strong Correlation in Fermionic Systems

Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many strongly correlated electronic systems but has a combinatorial computational cost. In many cases, pair coupled cluster doubles provide a polynomial-cost approximation that closely reproduces the energies of DOCI, but it breaks down in some cases and, as shown herein, it does not provide particularly good density matrices. In this article, we demonstrate that by using the Jordan–Wigner transformation to turn the seniority zero problem back into a Fermionic one, we can provide mean-field variational results of DOCI quality for the Hubbard model and a few small molecular dissociation examples, with polynomial cost, both for the energies and for density matrices, all while being protected from collapse. This success is rooted in the proof we provide, showing that the Hartree–Fock wave function on the Jordan–Wigner-transformed Hamiltonian transforms back to variational coupled cluster doubles in the seniority zero representation, but restricted to have determinant rather than permanent amplitude coefficients, without compromising its overall accuracy.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Distinguishing Mesoscale Polar Order (Unidirectional vs Bidirectional) of Cellulose Microfibrils in Plant Cell Walls Using Sum Frequency Generation Spectroscopy

Cellulose in plant cell walls are synthesized as crystalline microfibrils with diameters of 3–4 nm and lengths of around 1–10 μm. These microfibrils are known to be the backbone of cell walls, and their multiscale three-dimensional organization plays a critical role in cell wall functions including plant growth and recalcitrance to degradation. The mesoscale organization of microfibrils over a 1–100 nm range in cell walls is challenging to resolve because most characterization techniques investigating this length scale suffer from low spatial resolution, sample preparation artifacts, or inaccessibility of specific cell types. Here, we report a sum frequency generation (SFG) study determining the mesoscale polarity of cellulose microfibrils in intact plant cell walls. SFG is a nonlinear optical spectroscopy technique sensitive to the molecular-to-mesoscale order of noncentrosymmetric domains in amorphous matrices. However, the quantitative theoretical model to unravel the effect of polarity in packing of noncentrosymmetric domains on SFG spectral features has remained unresolved. In this work, we show how the phase synchronization principle of the SFG process is used to predict the relative intensities of vibrational modes with different polar angles from the noncentrosymmetric domain axis. Applying this model calculation for the first time and employing SFG microscopy, we found that cellulose microfibrils in certain xylem cell walls are deposited unidirectionally (or biased in one direction) instead of the bidirectional polarity which was believed to be dominant in plant cell walls from volume-averaged characterizations of macroscopic samples. Here, with this advancement in SFG analysis, one can now determine the relative polarity of noncentrosymmetric domains such as crystalline biopolymers interspersed in amorphous polymer matrices, which will open opportunities to study new questions that have not been conceived in the past.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Spectroscopic Studies of Charge-Transfer Character and Photoresponses of F 4 TCNQ-Based Donor–Acceptor Complexes

F 4 TCNQ (2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane) is used widely as a hole-doping agent in photoresponsive organic semiconducting materials, yet relatively little is known about the photoresponses of the F 4 TCNQ· - anion generated via doping. Furthermore, there is still relatively little systematic exploration of how the properties of the local material or chemical environment impacts the driving force for generating these charge-transfer complexes. Here we present spectroscopic and photophysical studies of F 4 TCNQ in charge-transfer complexes (CTCs) with the electron donor N,N’-Diphenyl-N-N’-di-p-tolylbenzene-1,4-diamine (MPDA) both in dichloroethane solution and polystyrene matrices. Integer charge transfer (ICT) between donor and acceptor occurs readily in dichloroethane solvent to form F 4 TCNQ· - :MPDA + CTCs, due to a ~150 mV difference in MPDA + /MPDA and F 4 TCNQ/F 4 TCNQ· - reduction potentials. Ultrafast spectroscopic studies of the CTC as well as electrochemically generated F 4 TCNQ· - and MDPA + reveal that the photoresponses of these CTCs are dominated by that of the dopant anion, including rapid deactivation (800 fs) after excitation to the anion D 1 excited state, followed by slower (~10 ps) vibrational cooling in the anion D 0 state. Excitation to the higher-lying D 2 state results in a rapid relaxation to the D 1 state, in contrast to direct D 2 -D 0 relaxation previously observed for F 4 TCNQ· - in gas phase. CTCs embedded in polystyrene (PS) matrices are observed to lose their integer charge-transfer character upon evaporation of solvent, as evidenced by changes to electronic and vibrational absorption features associated with F 4 TCNQ· - . This change is attributed to the loss of solvent stabilization of the ion pair formed through the charge-transfer reaction. Ultrafast spectral measurements reveal that the photoresponses of the partial charge-transfer (PCT) species embedded in PS are still highly similar to those of the ICT species and unlike that of neutral F 4 TCNQ, implying the electronic properties of the PCT state are likewise dominated by properties of the reduced acceptor molecule. We conclude that excitation of ICT or PCT states introduces optical losses for photoresponses of doped organic semiconductor materials due to the large anion absorption cross section and its rapid, dissipative deactivation dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Reverse Polarizability of Rare Earth Ions (La 3+ , Gd 3+ , Lu 3+ , Y 3+ ) in Tellurite Glasses and Glass Ceramics for Optical Limiting

All-optical modulation using inherent third-order optical nonlinearity of a medium has garnered considerable interest in photonics and optoelectronics. Herein, nonlinear optical (NLO) properties of tellurite glasses and glass ceramics (GCs) containing four different rare earths (RE = La, Gd, Lu, and Y) have been deliberated in near-infrared regions under an ultrafast regime. The La-based glass exhibits ~10 times higher nonlinear refraction (n 2 ) and absorption (α 2 ) than reported NLO materials. The NLO susceptibility [χ (3) ] trend in the studied glasses is La > Gd > Lu > Y, matching with RE 3+ polarizability. Furthermore, Ln 2 Te 6 O 15 nanocrystallite-embedded transparent GCs exhibit a larger NLO coefficient due to the enhanced local field from oxygen vacancies in crystallites. Interestingly, the trend of χ (3) in GCs follows the sequence of Y > Lu > Gd > La, precisely opposite to the glasses. This observation challenges the general polarizability approach of RE 3+ ions, emphasizing that quadratic hyperpolarizability of RE 3+ is pivotal for NLO properties of GCs. Among the studied matrices, Y-containing GCs showed the lowest optical limiting (OL) threshold (5.4 mJ/cm 2 at 800 nm), much lower than those of the reported NLO materials, suggesting its potential as a femtosecond NIR-laser safety material. A combination of large α 2 and n 2 from the studied matrices indicates their advantage for harmonic generation, potentially aiding in the design of ultrafast signal processing devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Polymer-Grafted Cellulose Nanofibrils with Enhanced Interfacial Compatibility for Stronger Poly(lactic acid) Composites

Cellulose nanofibrils (CNFs) are a promising reinforcement for biodegradable composite matrices such as poly(lactic acid) (PLA), but they require commercially scalable drying methods that preserve their fibrillar morphology along with improved interfacial interactions with polymer matrices. In this work, a water-based grafting-through polymerization scheme to modify CNFs improved spray drying behavior and reinforcement capacity in PLA composites. All polymer modifications yielded CNFs with a more fibrillar morphology after spray drying, increasing specific surface area by up to 490% compared to unmodified CNFs, values similar to conventional freeze drying. Polymer-grafted CNFs in PLA composites improved the tensile strength by 16% at 20 wt % loading and stiffness by 22% at a 10 wt % loading with two different graft-polymer chemistries compared to unmodified CNF composites. Surface energy heterogeneity measurements of the reinforcements and PLA matrix were employed to understand the improvements in composite properties. Polymer modifications lowered the total surface energy of the CNFs, and calculated ratios of work of adhesion to work of cohesion suggested improved interfacial compatibility for four of the modified CNFs with PLA. Rheological oscillatory shear studies of the composites correlated solid-like melt behavior, as demonstrated by storage moduli dominance, with higher tensile strength. Thermal analysis of the composites revealed that excessive plasticization by the poly(oligoethylene glycol methyl ether methacrylate)-grafted sample potentially offset mechanical property improvements imparted by the more fibrillar morphology. This work provides an opportunity for large-scale manufacturing of CNF/PLA composites via an entirely aqueous modification scheme and industrially relevant spray drying process.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Design and Integration of Flexible Sensor Matrix for in Situ Monitoring of Polymer Composites

Sensory polymer composites are highly desirable for applications such as in situ and real-time production processes and structural health monitoring, and for technologies that include human–machine interfaces for the next generation of Internet of Things. However, the development of these materials is still in its infancy: these materials have been reported, but large-scale fabrication of polymer composites with versatile and customizable sensing capabilities has yet to be demonstrated. Here, we report on a scalable fabrication strategy that enables such materials by designing and integrating PCB technology-inspired large-area flexible sensor matrices into polymer composites. The integrated sensor matrices successfully monitored in situ the production processes and structural health of an industrial polymer composite: from the application of vacuum, resin flow and polymerization, production defects, and temperature distribution. Our results demonstrate that the proposed strategy is a simple and effective solution as a distributed monitoring platform for polymer composites and shows the potential towards next generation of sensory polymer composites.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Characterization of Hydrogen in Basaltic Materials With Laser-Induced Breakdown Spectroscopy (LIBS) for Application to MSL ChemCam Data

Here, the Mars Science Laboratory rover, Curiosity , is equipped with ChemCam, a laser–induced breakdown spectroscopy (LIBS) instrument, to determine the elemental composition of nearby targets quickly and remotely. We use a laboratory sample set including prepared mixtures of basalt with systematic variation in hydrated mineral content and compositionally well–characterized, altered basaltic volcanic rocks to measure hydrogen by characterizing the H–alpha emission line in LIBS spectra under Martian environmental conditions. The H contents of all samples were independently measured using thermogravimetric analysis. We found that H peak area increases with weight percent H for our laboratory mixtures with basaltic matrices. The increase is linear with weight percent H in the mixtures with structurally bound H up to about 1.25 wt.% H and then steepens for higher H–content samples, a nonlinear trend not previously reported but potentially important for characterizing high water content materials. To compensate for instrument, environmental, and target matrix–related effects on quantification of H content from the LIBS signal, we examined multiple normalization methods. The best performing methods utilize O 778– and C 248–nm emission lines. The methods return comparable results when applied to ChemCam data of H–bearing materials on Mars. The calibration and normalization methods tested here will aid in investigations of H by LIBS on Mars with ChemCam and SuperCam. Further laboratory work will aid quantification across different physical matrices and heterogeneous textures because of differences we observed in H in pelletized and natural rock samples of the same composition.

58 GEOSCIENCES↗
DOE OSTI2018

Dynamic air/liquid pockets for guiding microscale flow

Microscale flows of fluids are mainly guided either by solid matrices or by liquid–liquid interfaces. Yet, the solid matrices are plagued with persistent fouling problems, while liquid–liquid interfaces are limited to low-pressure applications. Here we report a dynamic liquid/solid/gas material containing both air and liquid pockets, which are formed by partially infiltrating a porous matrix with a functional liquid. Using detailed theoretical and experimental data, we show that the distribution of the air- and liquid-filled pores is responsive to pressure and enables the formation and instantaneous recovery of stable liquid–liquid interfaces that sustain a wide range of pressures and prevent channel contamination. This adaptive design is demonstrated for polymeric materials and extended to metal-based systems that can achieve unmatched mechanical and thermal stability. Our platform with its unique adaptive pressure and antifouling capabilities may offer potential solutions to flow control in microfluidics, medical devices, microscale synthesis, and biological assays.

42 ENGINEERING↗
DOE OSTI2015

Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

Here, the elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn-3m with combining macron]m polymorph of δ-ZrH 1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P 4 2 / mcm polymorph. Elastic moduli predicted with the Voigt–Reuss–Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH 1.5 and ε-ZrH 2 are θ D = 299.7, 415.6 and 356.9 K, respectively, while θ D = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Relationship between microporous structure and light gas transport through glassy polymeric membranes revealed by molecular simulations

Microporous glassy polymers are attractive materials for gas separation membranes, due to their high permeability and tailorable selectivity, provided physical aging can be delayed. The archetypal microporous glassy polymer, PTMSP, can be blended with a hyper-crosslinked isatin–triptycene porous polymer network (PPN) to delay physical aging. However, while PPN is effective at reducing physical aging, it also affects the permeability of light gases through PTMSP. Molecular dynamics simulations were used here to shed fundamental light on the mechanisms responsible for these effects. Atomistic models are developed that satisfactorily reproduce experimental observations such as matrix density and cavity size distributions for neat PTMSP as well as for PTMSP–PPN blends. Analysis of the simulation results suggests that physical aging is delayed because the PPN inclusions slow down PTMSP relaxation while reducing the connectivity between free volume pockets. To understand how PPN inclusions affect light gas permeability, the atomistic models developed are used to probe CO 2 and CH 4 diffusion and sorption. These simulations are conducted for PTMSP matrices exhibiting varying density, towards reproducing experimental permeability data. Interrogating the simulation trajectories, it is discovered that while CH 4 travels preferentially through the free volume cavities, CO 2 preferentially interacts with the available surfaces, especially in the presence of PPN. These differences help interpret experimental observations. The transport of C 2 H 6 and H 2 S through PTMSP matrices was also investigated. These gases, and in particular H 2 S, were found to absorb within PTMSP, yielding very low diffusion coefficients. The ability to predict differences in diffusion pathways for various natural gas components unveils the possibility of engineering membranes to control permeability and selectivity towards large-scale applications.

Bao Le, Tran Thi [Univ. of Oklahoma, Norman, OK (U↗
DOE OSTI2010

HY{center_dot}{center_dot}{center_dot}N{sub 2} and HXeY{center_dot}{center_dot}{center_dot}N{sub 2} complexes in solid xenon (Y=Cl and Br): Unexpected suppression of the complex formation for deposition at higher temperature

The 1:1 complexes of HY and HXeY (Y=Cl and Br) with nitrogen are characterized by FTIR spectroscopy in a Xe matrix. These complexes show small blue shifts of the HY and H-Xe stretching frequencies with respect to the monomers (ca. +10 cm{sup -1}). In the HXeY{center_dot}{center_dot}{center_dot}N{sub 2} synthesis procedure, a HY/N{sub 2}/Xe matrix with HY{center_dot}{center_dot}{center_dot}N{sub 2} complexes is first photolyzed at 193 nm to yield isolated H and Y{center_dot}{center_dot}{center_dot}N{sub 2} fragments. At the second step, annealing at ca. 40 K activates mobility of H atoms and promotes the H+Xe+Y{center_dot}{center_dot}{center_dot}N{sub 2} reaction. It is quite remarkable that the HY{center_dot}{center_dot}{center_dot}N{sub 2} and consequently HXeY{center_dot}{center_dot}{center_dot}N{sub 2} complexes are observed in Xe matrices deposited at relatively low temperature (below ca. 35 K). For Xe matrices deposited above ca. 40 K, HY molecules do not form a complex with nitrogen and the HXeY{center_dot}{center_dot}{center_dot}N{sub 2} complex does not appear after photolysis and annealing; however, this observation is not explained in this article.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Distributed non-equilibrium Green’s function algorithms for the simulation of nanoelectronic devices with scattering

Through the non-equilibrium Green’s function (NEGF) formalism, quantum-scale device simulation can be performed with the inclusion of electron-phonon scattering. Yet, the simulation of realistically sized devices under the NEGF formalism typically requires prohibitive amounts of memory and computation time. Two of the most demanding computational problems for NEGF simulation involve mathematical operations with structured matrices called semiseparable matrices. In this work, we present parallel approaches for these computational problems which allow for efficient distribution of both memory and computation based upon the underlying device structure. This is vital when simulating realistically sized devices due to the aforementioned computational burdens. First, we consider determining a distributed compact representation for the retarded Green’s function matrix G R . This compact representation is exact and allows for any entry in the matrix to be generated through the inherent semiseparable structure. The second parallel operation allows for the computation of electron density and current characteristics for the device. Specifically, matrix products between the distributed representation for the semiseparable matrix G R and the self-energy scattering terms in Σ < produce the less-than Green’s function G < . As an illustration of the computational efficiency of our approach, we stably generate the mobility for nanowires with cross-sectional sizes as large as 4.5 nm, assuming an atomistic model with scattering.

47 OTHER INSTRUMENTATION↗
DOE OSTI2012

Using heavy atom rare gas matrix to control the reactivity of 4-methoxybenzaldehyde: A comparison with benzaldehyde

Different patterns of photochemical behavior were observed for 4-methoxybenzaldehyde (p-anisaldehyde) isolated in xenon and in argon matrices. Monomers of the compound isolated in solid Xe decarbonylate upon middle ultraviolet irradiation, yielding methoxybenzene (anisole), and CO. On the other hand, p-anisaldehyde isolated in an Ar matrix and subjected to identical irradiation, predominantly isomerizes to the closed-ring isomeric ketene (4-methoxycyclohexa-2,4-dien-1-ylidene) methanone. Experimental detection of a closed-ring ketene photoproduct, generated from an aromatic aldehyde, constitutes a rare observation. The difference between the patterns of photochemical transformations of p-anisaldehyde isolated in argon and xenon environments can be attributed to the external heavy-atom effect, where xenon enhances the rate of intersystem crossing from the singlet to the triplet manifold in which decarbonylation (via p-methoxybenzoyl radical) takes place. The parent compound, benzaldehyde, decarbonylates (to benzene + CO) when subjected to middle ultraviolet irradiation in both argon and xenon matrices. This demonstrates the role of the methoxy p-anisaldehyde substituent in activation of the reaction channel leading to the formation of the ketene photoproduct.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Generalization of Lieb's variational principle to Bogoliubov–Hartree–Fock theory

In its original formulation, Lieb's variational principle holds for fermion systems with purely repulsive pair interactions. As a generalization we prove for both fermion and boson systems with semi-bounded Hamiltonian that the infimum of the energy over quasifree states coincides with the infimum over pure quasifree states. In particular, the Hamiltonian is not assumed to preserve the number of particles. To shed light on the relation between our result and the usual formulation of Lieb's variational principle in terms of one-particle density matrices, we also include a characterization of pure quasifree states by means of their generalized one-particle density matrices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Synthesis and spectroscopy of cyanotriacetylene (HC{sub 7}N) in solid argon

UV laser irradiations of cryogenic solid argon matrices doped with a mixture of acetylene and cyanodiacetylene (HC{sub 5}N) resulted in the formation of a longer carbon–nitrogen chain, cyanotriacetylene (HC{sub 7}N). The identification of this species was accomplished based on IR vibrational spectroscopy (including the study of isotopically labeled compounds), on electronic luminescence spectroscopy, and on theoretical predictions. Additionally, IR absorption bands recognized as due to HC{sub 7}N were detected in photolysed Ar matrices doped with a cyanoacetylene/diacetylene mixture; this assignment was confirmed with the mass spectrometry of gases released upon the warm-up of the sample.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Criteria for stochastic pinning control of networks of chaotic maps

This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗