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1. Embedding properties of network realizations of dissipative reduced order models

   Druskin, Guddati ( July 2022 , HOUSEHOLDER SYMPOSIUM XXI)

   Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from themore »transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back« less
2. Electrocatalytic Conversion of Furanic Compounds for Production of Valuable Chemicals

   Li, Wenzhen ; Chadderdon, Xiaotong ; Chadderdon, David ; Liu, Hengzhou ( August 2021 , 72nd International Society of Electrochemistry Meeting)

   Biomass is abundant, inexpensive and renewable, therefore, it is highly expected to play a significant role in our future energy and chemical landscapes. The US DOE has identified furanic compounds (furfural and 5-(hydroxymethyl)furfural (HMF)) as the top platform building-block chemicals that can be readily derived from biomass sources [1]. Electrocatalytic conversion of these furanic compounds is an emerging route for the sustainable production of valuable chemicals [2, 3]. In my presentation, I will first present our recent mechanistic study of electrochemical reduction of furfural through a combination of voltammetry, preparative electrolysis, thiol-electrode modifications, and kinetic isotope studies [4]. It is demonstrated that two distinct mechanisms are operable on metallic Cu electrodes in acidic electrolytes: (i) electrocatalytic hydrogenation (ECH) and (ii) direct electroreduction. The contributions of each mechanism to the observed product distribution are clarified by evaluating the requirement for direct chemical interactions with the electrode surface and the role of adsorbed hydrogen. Further analysis reveals that hydrogenation and hydrogenolysis products are generated by parallel ECH pathways. Understanding the underlying mechanisms enables the manipulation of furfural reduction by rationally tuning the electrode potential, electrolyte pH, and furfural concentration to promote selective formation of important bio-based polymer precursors and fuels. Next, Imore »will present electrocatalytic conversion of HMF to two biobased monomers in an H-type electrochemical cell [5]. HMF reduction (hydrogenation) to 2,5-bis(hydroxymethyl)furan (BHMF) was achieved under mild electrolyte conditions and ambient temperature using a Ag/C cathode. Meanwhile, HMF oxidation to 2,5-furandicarboxylic acid (FDCA) with ~100% efficiency was facilitated under the same conditions by a homogeneous nitroxyl radical redox mediator, together with an inexpensive carbon felt anode. The selectivity and efficiency for Ag-catalyzed BHMF formation were sensitive to cathode potential, owing to competition from HMF hydrodimerization reactions and water reduction (hydrogen evolution). Moreover, the carbon support of Ag/C was active for HMF reduction and contributed to undesired dimer/oligomer formation at strongly cathodic potentials. As a result, high BHMF selectivity and efficiency were only achieved within a narrow potential range near –1.3 V. Fortunately, the selectivity of redox-mediated HMF oxidation was insensitive to anode potential, thus allowing HMF hydrogenation and oxidation half reactions to be performed together in a single cathode-potential-controlled cell. Electrocatalytic HMF conversion in a paired cell achieved high molar yields of BHMF and FDCA, and nearly doubled electron efficiency compared to the unpaired cell. Finally, I will briefly introduce our recent work on the development of a three-electrode flow cell with an oxide-derived Ag (OD-Ag) cathode and catbon felt anode for paring elecatalytic oxidation and reduction of HMF. The flow cell has a remarkable cell voltage reduction from ~7.5 V to ~2.0 V by transferring the electrolysis from the H-type cell to the flow cell [6]. This represents a more than fourfold increase in the energy efficiency at the 10 mA operation. A combined faradaic efficiency of 163% was obtained to BHMF and FDCA. Alternatively, the anodic hydrogen oxidation reaction on platinum further reduced the cell voltage to only ~0.85 V at 10 mA operation. These paired processes have shown potential for integrating renewable electricity and carbon for distributed chemical manufacturing in the future.« less
3. Carbonyl and ester C–O bond hydrosilylation using κ ⁴ -diimine nickel catalysts

   https://doi.org/10.1039/C8DT01857J  

   Rock, Christopher L. ; Groy, Thomas L. ; Trovitch, Ryan J. ( January 2018 , Dalton Transactions)

   The synthesis of alkylphosphine-substituted α-diimine (DI) ligands and their subsequent addition to Ni(COD) 2 allowed for the preparation of ( iPr2PPr DI)Ni and ( tBu2PPr DI)Ni . The solid state structures of both compounds were found to feature a distorted tetrahedral geometry that is largely consistent with the reported structure of the diphenylphosphine-substituted variant, ( Ph2PPr DI)Ni . To explore and optimize the synthetic utility of this catalyst class, all three compounds were screened for benzaldehyde hydrosilylation activity at 1.0 mol% loading over 3 h at 25 °C. Notably, ( Ph2PPr DI)Ni was found to be the most efficient catalyst while phenyl silane was the most effective reductant. A broad scope of aldehydes and ketones were then hydrosilylated, and the silyl ether products were hydrolyzed to afford alcohols in good yield. When attempts were made to explore ester reduction, inefficient dihydrosilylation was noted for ethyl acetate and no reaction was observed for several additional substrates. However, when an equimolar solution of allyl acetate and phenyl silane was added to 1.0 mol% ( Ph2PPr DI)Ni , complete ester C–O bond hydrosilylation was observed within 30 min at 25 °C to generate propylene and PhSi(OAc) 3 . The scope of this reactionmore »was expanded to include six additional allyl esters, and under neat conditions, turnover frequencies of up to 990 h −1 were achieved. This activity is believed to be the highest reported for transition metal-catalyzed ester C–O bond hydrosilylation. Proposed mechanisms for ( Ph2PPr DI)Ni -mediated carbonyl and allyl ester C–O bond hydrosilylation are also discussed.« less
4. The importance of the counter-cation in reductive rare-earth metal chemistry: 18-crown-6 instead of 2,2,2-cryptand allows isolation of [Y ^II (NR ₂ ) ₃ ] ¹⁻ and ynediolate and enediolate complexes from CO reactions

   https://doi.org/10.1039/C9SC05794C  

   Ryan, Austin J. ; Ziller, Joseph W. ; Evans, William J. ( February 2020 , Chemical Science)

   The use of 18-crown-6 (18-c-6) in place of 2.2.2-cryptand (crypt) in rare earth amide reduction reactions involving potassium has proven to be crucial in the synthesis of Ln( ii ) complexes and isolation of their CO reduction products. The faster speed of crystallization with 18-c-6 appears to be important. Previous studies have shown that reduction of the trivalent amide complexes Ln(NR 2 ) 3 (R = SiMe 3 ) with potassium in the presence of 2.2.2-cryptand (crypt) forms the divalent [K(crypt)][Ln II (NR 2 ) 3 ] complexes for Ln = Gd, Tb, Dy, and Tm. However, for Ho and Er, the [Ln(NR 2 ) 3 ] 1− anions were only isolable with [Rb(crypt)] 1+ counter-cations and isolation of the [Y II (NR 2 ) 3 ] 1− anion was not possible under any of these conditions. We now report that by changing the potassium chelator from crypt to 18-crown-6 (18-c-6), the [Ln(NR 2 ) 3 ] 1− anions can be isolated not only for Ln = Gd, Tb, Dy, and Tm, but also for Ho, Er, and Y. Specifically, these anions are isolated as salts of a 1 : 2 potassium : crown sandwich cation, [K(18-c-6) 2 ] 1+ , i.e. [K(18-c-6) 2more »][Ln(NR 2 ) 3 ]. The [K(18-c-6) 2 ] 1+ counter-cation was superior not only in the synthesis, but it also allowed the isolation of crystallographically-characterizable products from reactions of CO with the [Ln(NR 2 ) 3 ] 1− anions that were not obtainable from the [K(crypt)] 1+ analogs. Reaction of CO with [K(18-c-6) 2 ][Ln(NR 2 ) 3 ], generated in situ , yielded crystals of the ynediolate products, {[(R 2 N) 3 Ln] 2 (μ-OCCO)} 2− , which crystallized with counter-cations possessing 2 : 3 potassium : crown ratios, i.e. {[K 2 (18-c-6) 3 ]} 2+ , for Gd, Dy, Ho. In contrast, reaction of CO with a solution of isolated [K(18-c-6) 2 ][Gd(NR 2 ) 3 ], produced crystals of an enediolate complex isolated with a counter-cation with a 2 : 2 potassium : crown ratio namely [K(18-c-6)] 2 2+ in the complex [K(18-c-6)] 2 {[(R 2 N) 2 Gd 2 (μ-OCHCHO) 2 ]}.« less
5. Aluminium( iii ) dialkyl 2,6-bisimino-4 R -dihydropyridinates(−1): selective synthesis, structure and controlled dimerization

   https://doi.org/10.1039/C9DT00847K  

   Gallardo-Villagrán, Manuel ; Vidal, Fernando ; Palma, Pilar ; Álvarez, Eleuterio ; Chen, Eugene Y.-X. ; Cámpora, Juan ; Rodríguez-Delgado, Antonio ( June 2019 , Dalton Transactions)

   A family of stable and otherwise selectively unachievable 2,6-bisimino-4- R -1,4-dihydropyridinate aluminium (III) dialkyl complexes [AlR' 2 (4-R- i PrBIPH)] (R = Bn, Allyl; R′ = Me, Et, i Bu) have been synthesized, taking advantage of a method for the preparation of the corresponding 4- R -1,4-dihydropiridine precursors developed in our group. All the dihydropyrdinate(−1) dialkyl aluminium complexes have been fully characterized by 1 H- 13 C-NMR, elemental analysis and in the case 2′a , also by X-ray diffraction studies. Upon heating in toluene solution at 110 °C, the dimethyl derivatives 2a and 2′a dimerize selectively through a double cycloaddition. This reaction leads to the formation of two new C–C bonds that involve the both meta positions of the two 4- R -1,4-dihydropyridinate fragments, resulting the binuclear aluminium species [Me 2 Al(4-R- i PrHBIP)] 2 (R = Bn ( 3a ); allyl ( 3′a )). Experimental kinetics showed that the dimerization of 2′a obeys second order rate with negative activation entropy, which is consistent with a bimolecular rate-determining step. Controlled methanolysis of both 3a and 3′a release the metal-free dimeric bases, (4-Bn- i PrHBIPH) 2 and (4-allyl- i PrHBIPH) 2 , providing a convenient route to these potentially useful ditopicmore »ligands. When the R′ groups are bulkier than Me ( 2b , 2′b and 2′c ), the dimerization is hindered or fully disabled, favoring the formation of paramagnetic NMR-silent species, which have been identified on the basis of a controlled methanolysis of the final organometallic products. Thus, when a toluene solution of [AlEt 2 (4-Bn- i PrBIPH)] ( 2b ) was heated at 110 °C, followed by the addition of methanol in excess, it yields a mixture of the dimer (4-Bn- i PrHBIPH) 2 and the aromatized base 4-Bn- i PrBIP, in ca . 1 : 2 ratio, indicating that the dimerization of 2b competes with its spontaneous dehydrogenation, yielding a paramagnetic complex containing a AlEt 2 unit and a non-innocent (4-Bn- i PrBIP) ˙− radical-anion ligand. Similar NMR monitoring experiments on the thermal behavior of [AlEt 2 (4-allyl- i PrBIPH)] ( 2′b ) and [Al i Bu 2 (4-allyl-iPrBIPH)] ( 2′c ) showed that these complexes do not dimerize, but afford exclusively NMR silent products. When such thermally treated samples were subjected to methanolysis, they resulted in mixtures of the alkylated 4-allyl- i PrBIP and non-alkylated i PrBIP ligand, suggesting that dehydrogenation and deallylation reactions take place competitively.« less