Neural network closures for nonlinear model order reduction

Many reduced-order models are neither robust with respect to parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework for projection-based reduced-order modeling of such nonlinear and nonstationary systems. As a demonstration, we focus on a nonlinear advection-diffusion system given by the viscous Burgers equation, which is a prototypical setting of more realistic fluid dynamics applications due to its quadratic nonlinearity. In our proposed methodology the effects of truncated modes are modeled using a single layer feed-forward neural network architecture. The neural network architecture is trained by utilizing both the Bayesian regularization and extreme learning machine approaches, where the latter one is found to be more computationally efficient. A significant emphasis is laid on the selection of basis functions through the use of both Fourier bases and proper orthogonal decomposition. It is shown that the proposed model yields significant improvements in accuracy over the standard Galerkin projection methodology with a negligibly small computational overhead and provide reliable predictions with respect to parameter changes.     

A search method for optimal control of a flow shop system of traditional machines

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.     

Vertices of given degree in series‐parallel graphs

We show that the numbers of vertices of a given degree k ≥ 1 in several kinds of series‐parallel labeled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labeled planar graphs. The proof method is based on generating functions and singularity analysis. In particular, we need systems of equations for multivariate generating functions and transfer results for singular representations of analytic functions. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Classroom-based interventions in mathematics education: relevance, significance, and applicability

This special issue discusses various pedagogical innovations and myriad of significant findings. This commentary is not a synthesis of these contributions, but a summary of my own reflections on selected aspects of the nine papers comprising the special issue. Four themes subsume these reflections: (1) Gestural Communication (Alibali, Nathan, Church, Wolfgram, Kim and Knuth 2013); (2) Development of Ways of Thinking (Jahnke and Wambach 2013; Lehrer, Kobiela and Weinberg 2013; Mariotti 2013; Roberts and A. Stylianides 2013; Shilling-Traina and G. Stylianides 2013; Tabach, Hershkowitz and Dreyfus 2013); (3) Learning Mathematics through Representation (Saxe, Diakow and Gearhart 2013); and (4) Challenges in Dialogic Teaching (Ruthven and Hofmann 2013).     

Optimizing parametric oscillators with tunable boundary conditions

Parametric excitation or pumping is an effective method to create large oscillations by periodically altering a physical parameter of the governing dynamics. Precisely tuned pumping frequencies can lead to exponentially growing oscillations limited only by nonlinear effects like axial stretching of transversely vibrating string. It is demonstrated that a tuned passive dynamical system amplifies the otherwise limited transverse vibrations amplitudes of a nonlinear string considerably and thus increasing the selectivity of the system. This effect becomes more noticeable for shorter wavelengths where nonlinear stretching limits the obtainable vibration amplitudes severely. The present work analyses a passive dynamical system connected to one end of a taught string which parametrically couples its axial motion to transverse vibration. Analysis shows that a specific selection of parameters can reduce the limiting effect of nonlinear stretching thus allowing one to excite high-order modes with small external forces. The result can possibly affect other disciplines where effective parametric amplification is necessary.     

Generation of 287 W, 5.5 ps pulses at 78 MHz repetition rate from a cryogenically cooled Yb:YAG amplifier seeded by a fiber chirped-pulse amplification system

We generate linearly polarized, 287 W average-power, 5.5 ps pulses using a cryogenically cooled Yb:YAG amplifier at a repetition rate of 78 MHz. An optical-to-optical efficiency of 41% is obtained at 700 W pump power. A 6 W, 0.4 nm bandwidth picosecond seed source at 1029 nm wavelength is constructed using a chirped-pulse fiber amplification chain based on chirped volume Bragg gratings. The combination of a fiber amplifier system and a cryogenically cooled Yb:YAG amplifier results in good spatial beam quality at large average power. Low nonlinear phase accumulation as small as 5.1 x 10(-3) rad in the bulk Yb:YAG amplifier supports power scalability to a > 10 kW level without being affected by self-phase modulation. This amplification system is well suited for pumping high-power high-repetition-rate optical parametric chirped-pulse amplifiers.     

A Molecular Secret Sharing Scheme

A method for implementing a secret sharing scheme at the molecular level is presented. By creating molecular code generators that are self‐assembled from several molecular components, we established a means for distributing distinct code‐activating elements among several participants. In this way, an authorization code can only be generated when all the participants are present, which ensures that highly secured systems cannot be operated by unauthorized individuals or disloyal users. Additional layers of protection result from the ability to program the security code by replacing one or several molecular components and by subjecting the system to distinct chemical inputs.     

Influence of microwave irradiation on thermal properties of PVA and PVA/graphene nanocomposites

Journal of Thermal Analysis and Calorimetry - This article discusses the effect of microwave irradiation on the thermal properties of poly(vinyl alcohol)/graphene nanocomposites, prepared using a...     

Synthesis,characterization, crystal structure,and antimicrobial studies of novel thiourea derivative ligands and their platinum complexes

N,N-Di-R-N′-(4-chlorobenzoyl)thiourea (Di-R: diethyl, di-n-propyl, di-n-butyl and diphenyl) ligands (HL^1–4) and their Pt(II) complexes (cis-[Pt(L^1–4-S,O)₂]) have been synthesized and structurally characterized by elemental analyses, FT-IR and NMR spectroscopy. HL² ligand and cis-[Pt(L⁴-S,O)₂] metal complex have been also characterized by a single-crystal X-ray diffraction study. HL², C₁₄H₁₉ClN₂OS, crystallizes in the monoclinic space group P2₁/n (no. 14), with Z = 4, and unit cell parameters, a = 11.1405(16) Å, b = 9.7015(12) Å, c = 14.790(2) Å, β = 106.547(7)°. The cis-[Pt(L⁴-S,O)₂], C₄₀H₂₈Cl₂N₄O₂PtS₂: triclinic, space group P-1 (no. 2), a = 8.9919(3) Å, b = 14.7159(6) Å, c = 15.7954(6) Å, α = 113.9317(18)°, β = 97.4490(18)°, and γ = 105.0492(16)°. Single crystal analysis of complex, cis-[Pt(L^1–4-S,O)₂], revealed that a square planar coordination geometry is formed around the platinum atom by two sulfur and two oxygen atoms of the related ligands, which are in a cis configuration. In addition, the thiourea derivative ligands and their complexes were evaluated for both their in-vitro antibacterial and antifungal activity. The results have been reported, explained, and compared with fluconazole and ampicillin, used as reference drugs.