Drawing information from the ground state G-particle-hole matrix to study electronic excited states

Very recently, we have shown the suitability to combine the G-particle-hole Hypervirial (GHV) equation method (Alcoba et?al. in Int J Quantum Chem 109:3178, 2009) with the Hermitian Operator (HO) method (Bouten et?al. in Nucl Phys A 202:127, 1973) for computing various energy differences of an electronic system spectrum (Valdemoro et?al. in J Math Chem 50:492, 2012). The purpose of this paper is to extend our preliminary studies by applying the combined GHV-HO method to obtain the set of ground and low-lying excited states potential energy curves of several selected electronic systems. The calculations confirm the reliability of the method.     

The Homfly polynomial of double crossover links

Motivated by double crossover DNA polyhedra (He et al. in Nature 452:198, 2008; Lin et al. in Biochemistry 48:1663, 2009; Zhang et al. in J Am Chem Soc 131:1413, 2009; Zhang et al. in Proc Natl Acad Sci USA 105:10665, 2008; He et al. in Angew Chem Int Ed 49:748, )2010, in this paper, we construct a new type of link, called the double crossover link, formed by utilizing the “ $n$ -point star” to cover each vertex of a connected graph $G$ . The double crossover link can be used to characterize the topological properties of double crossover DNA polyhedra. We show that the Homfly polynomial of the double crossover link can be obtained from the chain polynomial of the truncated graph of $G$ with two distinct labels. As an application, by using computer algebra (Maple) techniques, the Homfly polynomial of a double crossover tetrahedral link is obtained. Our result may be used to characterize and analyze the topological structure of DNA polyhedra.     

On-line optimizing control of the intermittent simulated moving bed process

The I-SMB process is one of the modifications to the standard SMB process that has been demonstrated both theoretically and experimentally to exhibit rather competitive performance (Katsuo and Mazzotti in J Chromatogr A 1217:1354, 2010a, 3067, 2010b; Katsuo et al. in J Chromatogr A 1218:9345, 2011). This work aims at showing that also the I-SMB process can be controlled and optimized by using the optimizing on-line controller developed at ETH Zurich for the standard SMB process (Erdem et al. in Ind Eng Chem Res 43:405, 2004a, 3895, 2004b; Grossmann et al. in Adsorption 14:423, 2008, AIChE J 54:1942008). This is achieved by using a virtual I-SMB unit based on a detailed model of the process; past experience with the on-line controller shows that the controller’s behavior on a virtual platform is essentially the same as in laboratory experiments.     

In-situ imaging sensors for bioprocess monitoring: state of the art

Over the last two decades, more and more applications of sophisticated sensor technology have been described in the literature on upstreaming and downstreaming for biotechnological processes (Middendorf et al. J Biotechnol 31:395–403, 1993; Lausch et al. J Chromatogr A 654:190–195, 1993; Scheper et al. Ann NY Acad Sci 506:431–445, 1987), in order to improve the quality and stability of these processes. Generally, biotechnological processes consist of complex three-phase systems—the cells (solid phase) are suspended in medium (liquid phase) and will be streamed by a gas phase. The chemical analysis of such processes has to observe all three phases. Furthermore, the bioanalytical processes used must monitor physical process values (e.g. temperature, shear force), chemical process values (e.g. pH), and biological process values (metabolic state of cell, morphology). In particular, for monitoring and estimation of relevant biological process variables, image-based inline sensors are used increasingly. Of special interest are sensors which can be installed in a bioreactor as sensor probes (e.g. pH probe). The cultivation medium is directly monitored in the process without any need for withdrawal of samples or bypassing. Important variables for the control of such processes are cell count, cell-size distribution (CSD), and the morphology of cells (Höpfner et al. Bioprocess Biosyst Eng 33:247–256, 2010). A major impetus for the development of these image-based techniques is the process analytical technology (PAT) initiative of the US Food and Drug Administration (FDA) (Scheper et al. Anal Chim Acta 163:111–118, 1984; Reardon and Scheper 1995; Schügerl et al. Trends Biotechnol 4:11–15, 1986). This contribution gives an overview of non-invasive, image-based, in-situ systems and their applications. The main focus is directed at the wide application area of in-situ microscopes. These inline image analysis systems enable the determination of indirect and direct cell variables in real time without sampling, but also have application potential in crystallization, material analysis, polymer research, and the petrochemical industry.

The development of radioactive glass surrogates for fallout debris

The production of glass that emulates fallout is desired by the nuclear forensics community for training and measurement exercises. The composition of nuclear fallout is complex, with widely varying isotopic compositions (Fahey et al., Proc Natl Acad Sci USA 107(47):20207–20212, 2010; Bellucci et al., Anal Chem 85:7588–7593, 2013; Wallace et al., J Radioanal Nucl Chem, 2013; Belloni et al., J Environ Radioact 102:852–862, 2011; Freiling, Science 139:1058–1059, 1963; Science 133:1991–1999, 1961; Bunney and Sam Government Report: Naval Ordinance Laboratory, White Oak, 1971). As the gaseous cloud traverses from hotter to cooler regions of the atmosphere, the processes of condensation and nucleation entrain environmental materials, vaporized nuclear materials and fission products. The elemental and isotopic composition of the fission products is altered due to chemical fractionation (i.e. the fission product composition that would be expected from fission of the original nuclear material is altered by differences in condensation rates of the elements); the fallout may be enriched or depleted in volatile or refractory fission products. This paper describes preliminary work to synthesize, irradiate and fractionate the fission product content of irradiated particulate glass using a thermal distillation 2 h after irradiation. The glass was synthesized using a solution-based polymerization of tetraethyl orthosilicate. (Izrael, Radioactive fallout after nuclear explosions and accidents, 2002) Uranium was incorporated into the glass particulate at trace concentrations during polymerization. The particulate was subjected to a short thermal neutron irradiation then heated to 1,273 K approximately 2 h after the end of irradiation. Fission products of ^{133, 134, 135}I, ^{132, 134}Te, ¹³⁵Xe, ¹³⁸Cs and ^{91, 92}Sr were observed to be distilled from the particulate. The results of these preliminary studies are discussed.     

Highlights of non-equilibrium,non-isobaric,non-isothermal desorption of nitrogen from a LiX zeolite column by rapid pressure reduction and rapid purge by oxygen

The effects of adsorption kinetics, column pressure drop, gas phase mass and heat dispersions, gas–solid heat transfer resistance, and adsorber adiabaticity on desorption of N₂ from a LiX zeolite column by O₂ purge as well as pressurization–depressurization of the column using pure N₂ were recently studied using a numerical model of these processes [Chai et al. in Ind Eng Chem Res 50:8703, 2011, Chai et al. in Adsorption 18:87, 2012, Chai et al. in AIChE J 59:365 2013; Rama Rao et al. in Adsorption 2013]. The role of adsorbent particle size and column length to diameter ratio in determining the durations and efficiency of these processes were also investigated. These studies revealed several important limiting and optimum conditions for optimum operation of these processes which can be useful in design of a practical rapid pressure swing adsorption (RPSA) process for medical oxygen concentrator (MOC) application. The purpose of this short review article is to consolidate and re-emphasize these important results in a single article to be used as a guideline for design of a RPSA-MOC unit.     

A multiconfigurational perturbation theory study of the electronic structure and EPR g values of an oxomolybdenum enzyme model complex

We have studied the electronic structure (ground and excited states) and g matrix of a model compound for oxomolybdenum enzymes featuring the MoO–dithiolate moiety in C _s symmetry, by means of multiconfigurational second-order perturbation theory (CASPT2) for a range of fold angles (5–29°), i.e. the angle between the S–Mo–S and S–C–C–S planes of the dithiolate ligand. We found no evidence of a suggested 3-center pseudo-σ bonding interaction between the singly occupied orbital of the ground state and the symmetric in-plane dithiolate orbital (Inscore et al. in Inorg Chem 38:1401–1410, 1999). This is complemented with our alternative assignment of band 4 in the electronic spectrum as the transition out of the a″ instead of the a′ dithiolate in-plane orbital into the singly occupied ground-state orbital, believed to probe the dominant hole superexchange pathway (Inscore et al. in Inorg Chem 38:1401–1410, 1999; Burgmayer et al. in J Inorg Biochem 101:1601–1616, 2007). Principal g values of 1.9652, 1.9090, 2.0003 were obtained at a fold angle of 21°. The latter value is so close to the free electron g _e factor is due to an important positive contribution from the LMCT transition corresponding to band 4, counteracting the negative contributions from the ligand field transitions.     

A novel algorithm for solving quasi penta-diagonal linear systems

In this paper, a novel numerical algorithm for solving quasi penta-diagonal linear systems is presented. The computational costs of the algorithm is less than those of three successful algorithms given by El-Mikkawy and Rahmo (Comput Math Appl 59:1386–1396, 2010), by Lv and Le (Appl Math Comput 204:707–712, 2008), and by Jia et al. (Int J Comput Math 89:851–860, 2012). In addition, a new recursive method for inverting the quasi penta-diagonal matrices is also discussed. The implementation of the algorithm using Computer Algebra Systems (CASs) such as MATLAB and MAPLE is straightforward. Two numerical examples are given in order to demonstrate the performance and efficiency of our algorithm.     

Activation enthalpies of pericyclic reactions: the performances of some recently proposed functionals

We have assessed the performances of three recently proposed functionals, RC (Ragot and Cortona in J Chem Phys 121:7671, 2004), TCA (Tognetti et al. in J Chem Phys 128:034101, 2008), and RevTCA (Tognetti et al. in Chem Phys Lett 460:536, 2008) by calculating the activation enthalpies for ten pericyclic reactions and eighteen 1,3-dipolar cycloadditions. We have found that the local functional (RC) gives results only marginally better than the local-density approximation ones, while the two GGA functionals, TCA and RevTCA, both strongly improve the results with respect to PBE. The performances of RevTCA, in particular, are not far different from those of a hybrid functional such as B3LYP.     

On the determinant evaluation of quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices

Recently, three computational algorithms for evaluating the determinant of quasi penta-diagonal matrices have been proposed by El-Mikkawy and Rahmo (Comput Math Appl 59:1386–1396, 2010), by Neossi Nguetchue and Abelman (Appl Math Comput 203:629–634, 2008), and by Jia et al. (Int J Comput Math 89:851–860, 2013), respectively. In the current paper, two novel algorithms with less computational costs are proposed for the determinant evaluation of general quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices. Furthermore, three numerical experiments are given to show the performance of our algorithms. All of the numerical computations were performed on a computer with aid of programs written in MATLAB.     

Constraints on {\rm I}\beta cellulose twist from DFT calculations of ^{13}\hbox {C} NMR chemical shifts

We investigate theoretically the NMR response of twisted configurations of \({\rm I}\beta\) cellulose in the tg conformation. These finite helical angle structures were constructed by a mathematical deformation of zero-angle configurations obtained via the periodic density functional energy minimizations with dispersion corrections (DFT-D2). Subsequent calculations of the \({^{13}\hbox {C}}\) nuclear magnetic resonance chemical shifts \(({\delta}^{13} \hbox {C})\) were compared with experimental findings by Erata et al. (Cellul Commun 4:128–131, 1997) and Kono et al. (Macromolecules 36:5131–5138, 2003). We determine the sensitivity of the NMR chemical shifts to helical deformation of the microfibril and find that a substantial range of helical angle, ±2 degrees/nm, is consistent with current experimental observations, with a most probable angle of ～0.2 degree/nm. Through exhaustive combinatorial provisional assignments, we also demonstrate that there are different choices of the chemical shift \(({\delta}^{13} \hbox {C})\) assignments which are consistent with the experiments, including ones with lower deviations than existing identifications.     

Symmetry-adapted formulation of the G-particle-hole hypervirial equation method

Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et?al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization and matrix-matrix multiplication (Alcoba et?al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known challenging calculation of the torsional potential in ethylene.     

Numerical evaluation of second and third virial coefficients of some inert gases via classical cluster expansion

In this project we evaluate second virial coefficient of some inert gases via classical cluster expansion, assuming each atomic pair interaction is of Lennard-Jones type. We also try to numerically evaluate the third virial coefficient of Argon gas based on bipolar-coordinate integration (Mas et?al. in J Chem Phys 10:6694, 1999), assuming the same Lennard-Jones potential as before. The second virial coefficient (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) calculated from our model are compatible to the experimental data [19] The temperature at which B ₂(T) → 0 is called the Boyle’s temperature T _B (Vega et?al. in Phys Chem Chem Phys 4:3000–3007, 2002) for the Lennard-Jines (12-6) potential. For the second virial coefficient of He, we obtain the Boyle’s temperature as follow: T _B ?=?34.9312438964844 (K) B ₂(T) = 9.82958 × 10^?6 (cm³/mol).     

A variational density matrix approach with nonlocal effective potential

We show that using the Colle–Salvetti correlation-energy functional (Colle and Salvetti in Theoret Chim Acta 37:329, 1975) in the Hartree–Fock-type procedure suggested by Kohn and Sham (Phys Rev 140:A1133PR, 1965), one can calculate quite accurately electronic properties of systems in which the “dynamical” correlation energy is dominant. We compare our results with those obtained by Grabo and Gross (Chem Phys Lett 240:141, 1995) using the optimized effective potential method, and we discuss characteristics and advantages of our procedure.     

Nondestructive assay of plutonium in empty stainless steel boxes by apparent mass method

Apparent mass method (Venkataraman and Croft, Nucl Instrum Methods Phys Res A 505:527, 2003), initially standardized for the assay of Pu (Agarwal et al., J Nucl Mater 651:386, 2007) has been used to get Pu amount in empty stainless steel boxes generally used for storing and transferring plutonium oxide powders. The results have been compared with the neutron coincidence counting results and have been found to match well. The advantage of the method is that it can be used for any sample with nonstandard geometry and with uncertain source distribution.     

Further developments of a robust absolute calibration method utilizing beta/gamma coincidence techniques

Performing accurate and verifiable measurements is often the most challenging goal for any radiation detector and is especially challenging for the radio-xenon detectors deployed by the International Monitoring System (IMS) of the Preparatory Commission of the Comprehensive Test Ban Treaty Organization (CTBTO). Often the accuracy of the measurement is directly tied to how well the detector is calibrated, in both energy and efficiency. Standard methods often rely on using certified sealed sources to determine the absolute efficiency. Similarly, efforts to calibrate the absolute efficiency of radioactive gas cell detectors utilize a number of methodologies which allow adequate calibration but are time consuming and prone to a host of difficulties to determine uncertainties (McIntyre et al, J Radioanal Nucl Chem 282(3):755–759, 2009; Anderson et al, Stat Probab Lett 77(88):769–773, 2007). Utilizing methods developed in the 1960s for absolute measurements of activity with beta–gamma detector systems it has become clear that it is possible to achieve higher precision results that are consistent across a range of isotopes and activities (National Council on Radiation Protection and Measurement, A handbook of radioactivity measurements procedure NCPR report, 1985). Even more compelling is the ease with which this process can be used on routine samples to determine the total activity present in the detector. Additionally, recent advances in the generation of isotopically pure radio-xenon samples of ^131mXe, ¹³³Xe, and ¹³⁵Xe allow these measurement techniques to achieve much better results than have previously been possible when using mixed isotopic radio-xenon sources (Haas et al, J Radioanal Nucl Chem 282(3):677–680, 2009). This paper will discuss the beta/gamma absolute detection efficiency techniques of direct measurement of the efficiencies and the extrapolation method and compare the results using modeled and measured pure sources of ¹³³Xe and ¹³⁵Xe.     

Prigogine and the many voices of nature

Ilya Prigogine was not a systematic author: his ideas, covering a wide arch of areas, are dispersed in his many writings. In particular, his philosophical thought has to be reconstructed mainly on the basis of his works in collaboration with Isabelle Stengers: La Nouvelle Alliance (1979), Order out of Chaos (1984), and Entre le Temps et l’éternité (1988). In this paper I undertake that reconstruction in order to argue that Prigogine’s position, when read in the light of Putnam’s internalist realism, can be characterized as an ontological pluralism. The main aim of this work is to show the striking parallelism between the philosophical views of Prigogine and Stengers and those of Hilary Putnam in Reason, Truth and History (1981). This task will lead me to critically review Prigogine’s general scientific program: the attempt to establish the foundations of objective irreversibility.     

Quantum hydrodynamic model of density functional theory

In this paper, we extend the method in Cai et al. (J Math Phys 53:103503, 2012) to derive a class of quantum hydrodynamic models for the density-functional theory (DFT). The most popular implement of DFT is the Kohn–Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn–Sham equation is a non-linear Schrödinger equation, and the corresponding Wigner equation can be derived as an alternative implementation of DFT. We derive quantum hydrodynamic models of the Wigner equation by moment closure following Cai et al. (J Math Phys 53:103503, 2012). The derived quantum hydrodynamic models are globally hyperbolic thus locally wellposed. The contribution of the Kohn–Sham potential is turned into a nonlinear source term of the hyperbolic moment system. This work provides a new possible way to solve DFT problems.     

Comment on “A note on the principal measure and distributional (p,q)-chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction”

In García Guirao and Lampart (J Math Chem 48:159–164, 2010) presented a lattice dynamical system stated by Kaneko (Phys Rev Lett 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction. In this note, we give an example which shows that the proofs of Theorems 3.1 and 3.2 in [J Math Chem 51:1410–1417, 2013] are incorrect, and two open problems.