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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 the 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 

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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, I 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. 

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3. Climate Change Impacts on Rainfed Maize Yields in Kansas: Statistical vs. Process-Based Models

   https://doi.org/10.3390/agronomy13102571  

   Rawat, Meenakshi ; Sharda, Vaishali ; Lin, Xiaomao ; Roozeboom, Kraig ( October 2023 , Agronomy)

   The changing climate and the projected increase in the variability and frequency of extreme events make accurate predictions of crop yield critically important for addressing emerging challenges to food security. Accurate and timely crop yield predictions offer invaluable insights to agronomists, producers, and decision-makers. Even without considering climate change, several factors including the environment, management, genetics, and their complex interactions make such predictions formidably challenging. This study introduced a statistical-based multiple linear regression (MLR) model for the forecasting of rainfed maize yields in Kansas. The model’s performance is assessed by comparing its predictions with those generated using the Decision Support System for Agrotechnology Transfer (DSSAT), a process-based model. This evaluated the impact of synthetic climate change scenarios of 1 and 2 °C temperature rises on maize yield predictions. For analysis, 40 years of historic weather, soil, and crop management data were collected and converted to model-compatible formats to simulate and compare maize yield using both models. The MLR model’s predicted yields (r = 0.93) had a stronger association with observed yields than the DSSAT’s simulated yields (r = 0.70). A climate change impact analysis showed that the DSSAT predicted an 8.7% reduction in rainfed maize yield for a 1 °C temperature rise and an 18.3% reduction for a 2 °C rise. The MLR model predicted a nearly 6% reduction in both scenarios. Due to the extreme heat effect, the predicted impacts under uniform climate change scenarios were considerably more severe for the process-based model than for the statistical-based model.

    

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4. 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 reaction 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. 

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5. Mixed‐Valence Manganese Carboxylate Clusters, {Mn III 6 Mn II 4 }, {Mn III 7 Mn II 5 Na}, and {Mn III 7 Mn II 5 }, Derived from the Combined Use of Di‐2‐pyridyl Ketone with Selected Aliphatic Diols

   https://doi.org/10.1002/ejic.202300735  

   Skordi, Katerina ; Alexandropoulos, Dimitris I. ; Fournet, Adeline D. ; Panagiotou, Nikos ; Perlepes, Spyros P. ; Christou, George ; Tasiopoulos, Anastasios J. ( February 2024 , European Journal of Inorganic Chemistry)

   Three new polynuclear clusters with the formulae [Mn₁₀O₄(OH)(OMe){(py)₂C(O)₂}₂{(py)₂C(OMe)(O)}₄(MeCO₂)₆](ClO₄)₂(1), Na[Mn₁₂O₂(OH)₃(OMe){(py)₂C(O)₂}₆{(py)₂C(OH)(O)}₂(MeCO₂)₂(H₂O)₁₀](ClO₄)₈(2) and [Mn₁₂O₄(OH)₂{(py)₂C(O)₂}₆{(py)₂C(OMe)(O)}(MeCO₂)₃(NO₃)₃(H₂O)(DMF)₂](NO₃)₂(3) were prepared from the combination of di‐2‐pyridyl ketone, (py)₂CO, with the aliphatic diols (1,3‐propanediol (pdH₂) or 1,4‐butanediol (1,4‐bdH₂)) in Mn carboxylate chemistry. The reported compounds do not include the aliphatic diols employed in this reaction scheme; however, their use is essential for the formation of1–3. The crystal structures of1–3are based on multilayer cores which, to our knowledge, are reported for the first time in Mn cluster chemistry. Direct current (dc) magnetic susceptibility studies showed the presence of dominant antiferromagnetic exchange interactions within1–3. Alternating current (ac) magnetic susceptibility studies revealed the presence of out‐of‐phase signals below 3.0 K for2and3indicating the slow relaxation of the magnetization vector, characteristic of single‐molecule magnets; theU_effvalue of2was found to be 23 K and the preexponential factorτ₀~7.6×10⁻⁹ s.

    

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