On a stabilizing feedback attitude control

The attitude control of a rotating satellite with two control jets leads to a system of four controlled ordinary differential equations of the form (S) $$dx/dt = X(x) + u_1 Y^1 (x) + u_2 Y^2 (x),x(0) = 0.$$ Our goal is to derive feedback controlsu ₁,u ₂ which automatically stabilize the system (S), i.e., drive the solution to the (uncontrolled) rest solution zero. Let $$(ad^0 X,Y) = Y,(adX,Y) = [X,Y],$$ the Lie product of the vector fieldsX, Y, and inductively $$(ad^{k + 1} X,Y) = [X,(ad^k X,Y)].$$ It is known that, if $$dim span\left\{ {\left( {ad^j X,Y^1 } \right)\left( 0 \right),j = 0,1,...} \right\} = 4,$$ then all points in some neighborhood of zero can be controlled to zero with just the controlu ₁, i.e.,u ₂≡0. In this problem,Y ¹(0), ..., (ad ³ X, Y ¹)(0) are linearly independent. We give a formula for generating the directions (ad ⁱ X, Y ⁱ )(0) as endpoints of admissible trajectories. Our modified feedback control is then formed as follows. Given an ε>0, if the state of system (S) is measured to beq ¹ ∈ ?⁴, we write $$q^1 = \sum\limits_{i = 1}^4 {\alpha _1 } (ad^{i - 1} X,Y^1 )(0),$$ and choose a controlu(t,q ¹) on the interval 0≤t≤ε to drive the solution in the direction $$ - \sum\limits_{i = 1}^4 {\alpha _1 } (ad^{i - 1} X,Y^1 )(0).$$ Thus, we assume that the state is measured (say) at time intervals 0, ε, 2ε, ..., while the control depends on the measured state, but then is open loop during a time interval ε until a new state is measured; hence, the terminologymodified feedback control. Numerical results are included for both the case of one control component and the case of two control components.     

Trivalent‐Intermediate Valent Cerium Ordering in Ce2RuZn4

The new intermetallic cerium compound Ce₂RuZn₄ was synthesized from the elements in a sealed tantalum tube in a water‐cooled sample chamber of an induction furnace. Ce₂RuZn₄ crystallizes with a new structure type: P4/nmm, Z = 2, a = 719.6(1), c = 520.2(1) pm, wR2 = 0.0816, 273 F² values and 15 variables. The structure contains two crystallographically independent cerium atoms: Ce1 with CN 16 (12 Zn + 4 Ce) and Ce2 with CN 14 (2 Ru + 8 Zn + 4 Ce). Based on the interatomic distances the two sites can be assigned to trivalent Ce1 and intermediate valent Ce2. The trivalent‐intermediate valent cerium ordering is underlined by magnetic susceptibility measurements. Ce₂RuZn₄ shows modified Curie‐Weiss behaviour in the temperature range 10–290 K with an experimental magnetic moment of 2.57(1) μ_B per formula unit. Thus only half of the cerium atoms are trivalent in Ce₂RuZn₄. A remarkable feature of the Ce₂RuZn₄ structure are short Ce2–Ru distances of 260 pm. The crystal chemistry of Ce₂RuZn₄ is discussed.     

Modeling Particle Size Distribution (PSD) in Emulsion Copolymerization Reactions in a Continuous Loop Reactor

A detailed dynamic mathematical model that describes the evolution of particle size distributions (PSDs) during emulsion copolymerization reactions in a continuous loop reactor was developed and compared with experimental data. The model is based on the assumption that two distinct particle populations exist: precursor particles and stable latex particles. Precursor particles are colloidally unstable and therefore may undergo coagulation with other precursors and be absorbed by stable latex particles. It is shown that the kinetic model is able to reproduce the rather complex dynamic behavior of the vinyl acetate/Veova10 emulsion copolymerization in a continuous loop reactor, including the development of oscillatory responses of PSDs during reaction start‐up. It is also shown that, for the studied polymerization system, oscillatory responses are obtained only when both particle populations are assumed to exist and when both coagulative and micellar particle nucleations are simultaneously considered.     

Structure and properties of Ce<Subscript>3</Subscript>Pd<Subscript>3</Subscript>Bi<Subscript>4</Subscript>, CePdBi,and CePd<Subscript>2</Subscript>Zn<Subscript>3</Subscript>

The intermetallic cerium compounds Ce₃-Pd₃Bi₄, CePdBi, and CePd₂Zn₃ were synthesized from the elements in sealed tantalum ampoules in an induction furnace. The compounds were characterized by X-ray powder and single crystal diffraction: CeCo₃B₂ type (ordered version of CaCu₅), P6/mmm, a = 538.4(4), c = 427.7(4) pm, wR2 = 0.0540, 115 F ² values, 9 variables for CePd₂Zn₃ and Y₃Au₃Sb₄ type, I \({\bar 4}\)3d, a = 1005.2(2) pm, w R2 = 0.0402, 264 F ² values, 9 variables for Ce₃Pd₃Bi₄, and MgAgAs type, a = 681.8(1) pm for CePdBi. The bismuthide structures are build up from three-dimensional networks of corner-sharing PdBi₄ tetrahedra with Pd–Bi distances of 281 (Ce₃Pd₃Bi₄) and 296?pm (CePdBi), respectively. The cerium atoms are located in larger voids of coordination number 12 (Ce₃Pd₃Bi₄) and 10 (CePdBi). In CePd₂Zn₃ the cerium atoms fill larger channels within the three-dimensional [Pd₂Zn₃] network with 18 (6 Pd + 12 Zn) nearest neighbors. The three compounds contain stable trivalent cerium with experimental magnetic moments of μ_eff = 2.70(2), 2.48(1), and 2.49(1) μ_B/Ce atom for CePd₂Zn₃, Ce₃Pd₃Bi₄, and CePdBi, respectively. Susceptibility and specific heat data gave no hint for magnetic ordering down to 2.1?K.     

Polypeptide hybrid copolymers as selective micellar nanocarriers in nonaqueous media

The self-assembly of polystyrene-block-poly(l-lysine) (PS-PLLys·HCl) copolymers with different block lengths has been studied in toluene. The obtained spherical micelles exhibit size variations upon addition of acids or bases, as indicated by light and neutron scattering studies. It is shown that pyridine induces a shrinking of the polystyrene chains in the corona region of the micelles, decreasing the aggregate solvent interface. The addition of benzoic acid, on the other hand, leads to a swelling of the copolymer micelles proportional to the molar fraction of polypeptide. This behavior suggests a selective permeability of the PS-PLLys micelles and the possibility to encapsulate organic compounds in toluene depending on their chemical nature.     

New fast synthesis route for symmetric and asymmetric phenyl-substituted photochromic dithienylethenes bearing functional groups such as alcohols, carboxylic acids, or amines

This Letter describes an efficient three-step synthesis route of symmetric and asymmetric phenyl-substituted photochromic 1,2-dithienylethenes bearing unprotected functional groups (i.e., alcohols, carboxylic acids or amines). These products can be easily obtained by typical Suzuki cross-coupling between photochromic dichlorides and commercial available boronic acids or pinacol esters.     

The overall adhesion-spreading process of liposomes on a mercury electrode is controlled by a mixed diffusion and reaction kinetics mechanism

Using high-resolution chronoamperometric measurements, with sampling each 1.333 μs, the initial step of the adhesion-spreading of liposomes on a mercury electrode was studied. These measurements allow getting a deeper insight into the first interaction of the liposomes with the mercury electrode, and they show that the overall adhesion-spreading process at different potentials is partially controlled by a fast but weak interaction equilibrium resulting in a mixed diffusion- and reaction-kinetics-controlled mechanism of the overall reaction. The authors dedicate this contribution to Keith Oldham on the occasion of his 80th birthday. Since my (FS) first meeting with Keith Oldham in Alan Bond’s laboratory in Australia in 1987, I had the privilege to get Keith’s unerring advice and have stimulating discussions with him for which I like to cordially thank him.     

The entropic and enthalpic contributions to force-dependent dissociation kinetics of the pyrophosphate bond

We report quantum-chemical calculations of the activation free energy of solvolysis of the pyrophosphate bond in a conformationally flexible reactant coupled to a constraining potential. The results reveal a significant contribution of conformational entropy to the force-dependent kinetics of even a fairly small reactant, suggesting that accurate predictions or molecular interpretation of localized reaction kinetics in stretched polymers may require explicit consideration of their force-dependent conformational heterogeneity. We further show that modeling the conformational space of the reactant and the transition state as collections of overlapping harmonic wells accurately predicts the force-dependent activation free energy up to 2 nN without detailed quantum-chemical computations. An estimate of the activation energies is obtained from the minimal (Eyring-Bell-Evans) model using the local coordinate common to all nucleophilic displacement reactions.     

Size-extensive vibrational self-consistent field methods with anharmonic geometry corrections

In the size-extensive vibrational self-consistent field (XVSCF) method introduced earlier [M. Ke?eli and S. Hirata, J. Chem. Phys. 135, 134108 (2011)], only a small subset of even-order force constants that can form connected diagrams were used to compute extensive total energies and intensive transition frequencies. The mean-field potentials of XVSCF formed with these force constants have been shown to be effectively harmonic, making basis functions, quadrature, or matrix diagonalization in the conventional VSCF method unnecessary. We introduce two size-consistent VSCF methods, XVSCF(n) and XVSCF[n], for vibrationally averaged geometries in addition to energies and frequencies including anharmonic effects caused by up to the nth-order force constants. The methods are based on our observations that a small number of odd-order force constants of certain types can form open, connected diagrams isomorphic to the diagram of the mean-field potential gradients and that these nonzero gradients shift the potential minima by intensive amounts, which are interpreted as anharmonic geometry corrections. XVSCF(n) evaluates these mean-field gradients and force constants at the equilibrium geometry and estimates this shift accurately, but approximately, neglecting the coupling between these two quantities. XVSCF[n] solves the coupled equations for geometry corrections and frequencies with an iterative algorithm, giving results that should be identical to those of VSCF when applied to an infinite system. We present the diagrammatic and algebraic definitions, algorithms, and initial implementations as well as numerical results of these two methods. The results show that XVSCF(n) and XVSCF[n] reproduce the vibrationally averaged geometries of VSCF for naphthalene and anthracene in their ground and excited vibrational states accurately at fractions of the computational cost.