One-dimensional linear analysis of the compound jet

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

Stability limits of minimum volume and breaking axisymmetric liquid bridges between unequal disks

This paper deals with the stability limits of minimum volume and the breaking of axisymmetric liquid columns held by capillary forces between two concentric,circular solid disk of different radii. The problem has been analyzed both theoreti-cally and experimentally. A theoretical analysis concerning the breaking of liquid bridges has been performed by using a one-dimensional slice model already used in liquid bridge problems. Experiments have been carried out by using milli-metric liquid bridges, and minimum volume stability limits as well as the volumes of the drops resulting after breaking have been measured for a large number of liquid bridge configurations. Experimental results being in agreement with theoretical prediction.

Dynamic stability of long axisymmetric liquid bridges

This paper deals with the non-linear forced oscillations of axisymmetric long liquid bridges between equal disks. The dynamics of the liquid bridge has been analyzed by using a self-similar, one-dimensional model already used in similar problems. The influence of the dynamics on the static stability limits, as well as the main characteristics of the non-linear behaviour of long liquid bridges, have been studied with in the range of validity of the mathematical model used here.

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Role of aromatic residues in stabilization of the [Fe4S4] cluster in high-potential iron proteins (HiPIPs): physical characterization and stability studies of Tyr-19 mutants of Chromatium vinosum HiPIP.

The functional role of residue Tyr-19 of Chromatium vinosum HiPIP has been evaluated by site-directed mutagenesis experiments. The stability of the [Fe4S4] cluster prosthetic center is sensitive to side-chain replacements. Polar residues result in significant instability, while nonpolar residues (especially with aromatic side chains) maintain cluster stability. Two-dimensional NMR data of native and mutant HiPIPs are consistent with a model where Tyr-19 serves to preserve the structural rigidity of the polypeptide backbone, thereby maintaining a hydrophobic barrier for exclusion of water from the cluster cavity. Solvent accessibility results in more facile oxidation of the cluster by atmospheric oxygen, with subsequent rapid hydrolysis of the [Fe4S4]3+ core.

Structure and stability of a second molten globule intermediate in the apomyoglobin folding pathway.

Apomyoglobin folding proceeds through a molten globule intermediate (low-salt form; I1) that has been characterized by equilibrium (pH 4) and kinetic (pH 6) folding experiments. Of the eight alpha-helices in myoglobin, three (A, G, and H) are structured in I1, while the rest appear to be unfolded. Here we report on the structure and stability of a second intermediate, the trichloroacetate form of the molten globule intermediate (I2), which is induced either from the acid-unfolded protein or from I1 by > or = 5 mM sodium trichloroacetate. Circular dichroism measurements monitoring urea- and acid-induced unfolding indicate that I2 is more highly structured and more stable than I1. Although I2 exhibits properties closer to those of the native protein, one-dimensional NMR spectra show that it maintains the lack of fixed side-chain structure that is the hallmark of a molten globule. Amide proton exchange and 1H-15N two-dimensional NMR experiments are used to identify the source of the extra helicity observed in I2. The results reveal that the existing A, G, and H helices present in I1 have become more stable in I2 and that a fourth helix--the B helix--has been incorporated into the molten globule. Available evidence is consistent with I2 being an on-pathway intermediate. The data support the view that apomyoglobin folds in a sequential fashion through a single pathway populated by intermediates of increasing structure and stability.

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks.

Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Three-Dimensional kinetic adaptations of gait throughout pregnancy and postpartum

Biomechanical adaptations that occur during pregnancy can lead to changes on gait pattern. Nevertheless, these adaptations of gait are still not fully understood. The purpose was to determine the effect of pregnancy on the biomechanical pattern of walking, regarding the kinetic parameters. A three-dimensional analysis was performed in eleven participants. The kinetic parameters in the joints of the lower limb during gait were compared at the end of the first, second, and third trimesters of pregnancy and in the postpartum period, in healthy pregnant women. The main results showed a reduction in the normalized vertical reaction forces, throughout pregnancy, particularly the third peak. Pregnant women showed, during most of the stance phase, medial reaction forces as a motor response to promote the body stability. Bilateral changes were observed in hip joint, with a decrease in the participation of the hip extensors and in the eccentric contraction of hip flexors. In ankle joint a decrease in the participation of ankle plantar flexors was found. In conclusion, the overall results point to biomechanical adjustments that showed a decrease of the mechanical load of women throughout pregnancy, with exception for few unilateral changes of hip joint moments.

Thermal, chemical, and enzymatic stability of the cyclotide kalata B1: The importance of the cyclic cystine knot

The cyclotides constitute a recently discovered family of plant-derived peptides that have the unusual features of a head-to-tail cyclized backbone and a cystine knot core. These features are thought to contribute to their exceptional stability, as qualitatively observed during experiments aimed at sequencing and characterizing early members of the family. However, to date there has been no quantitative study of the thermal, chemical, or enzymatic stability of the cyclotides. In this study, we demonstrate the stability of the prototypic cyclotide kalata B1 to the chaotropic agents 6 M guanidine hydrochloride (GdHCl) and 8 M urea, to temperatures approaching boiling, to acid, and following incubation with a range of proteases, conditions under which most proteins readily unfold. NMR spectroscopy was used to demonstrate the thermal stability, while fluorescence and circular dichroism were used to monitor the chemical stability. Several variants of kalata B1 were also examined, including kalata 132, which has five amino acid substitutions from B1, two acyclic permutants in which the backbone was broken but the cystine knot was retained, and a two-disulfide bond mutant. Together, these allowed determinations of the relative roles of the cystine knot and the circular backbone on the stability of the cyclotides. Addition of a denaturant to kalata B1 or an acyclic permutant did not cause unfolding, but the two-disulfide derivative was less stable, despite having a similar three-dimensional structure. It appears that the cystine knot is more important than the circular backbone in the chemical stability of the cyclotides. Furthermore, the cystine knot of the cyclotides is more stable than those in similar-sized molecules, judging by a comparison with the conotoxin PVIIA. There was no evidence for enzymatic digestion of native kalata B1 as monitored by LC-MS, but the reduced form was susceptible to proteolysis by trypsin, endoproteinase Glu-C, and thermolysin. Fluorescence spectra of kalata B1 in the presence of dithiothreitol, a reducing agent, showed a marked increase in intensity thought to be due to removal of the quenching effect on the Trp residue by the neighboring Cys5-Cys17 disulfide bond. In general, the reduced peptides were significantly more susceptible to chemical or enzymatic breakdown than the oxidized species.

Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

Structure of thermolysin cleaved microcin J25: Extreme stability of a two-chain antimicrobial peptide devoid of covalent links

sThe structure of a two-chain peptide formed by the treatment of the potent antimicrobial peptide microcin J25 (MccJ25) with thermolysin has been characterized by NMR spectroscopy and mass spectrometry. The native peptide is 21 amino acids in size and has the remarkable structural feature of a ring formed by linkage of the side chain of Glu8 to the N-terminus that is threaded by the C-terminal tail of the peptide. Thermolysin cleaves the peptide at the Phe10-Val11 amide bond, but the threading of the C-terminus through the N-terminal ring is so tight that the resultant two chains remain associated both in the solution and in the gas phases. The three-dimensional structure of the thermolysin-cleaved peptide derived using NMR spectroscopy and simulated annealing calculations has a well-defined core that comprises the N-terminal ring and the threading C-terminal tail. In contrast to the well-defined core, the newly formed termini at residues Phe10 and Val11 are disordered in solution. The C-terminal tail is associated to the ring both by hydrogen bonds stabilizing a short beta-sheet and by hydrophobic interactions. Moreover, unthreading of the tail through the ring is prevented by the bulky side chains of Phe19 and Tyr20, which flank the octapeptide ring. This noncovalent two-peptide complex that has a remarkable stability in solution and in highly denaturing conditions and that survives in the gas phase is the first example of such a two-chain peptide lacking disulfide or interchain covalent bonds.