Fermin Franco-Medrano

MCCs cytoskeleton tend to align in a series of stripes, passing through several stages. Multiciliated Cells (MCCs)'s basal bodies (BBs) tend follow the alignment of the cytoskeleton. The BBs' tend to orient their basal feet (BF) towards the cytoskeleton at an angle. In order to model the alignment and orientation of BBs we first model the alignment stages of the cytoskeleton. Real cells have a changing irregular shape, approximately hexagonal. So far, simulations do not account for the cell shape, difficult to handle by the method of Finite Differences. The Finite Element Method is suitable to handle different shapes and fine emerging structures in the solutions. We propose the FreeFEM++ language for simulating the the Active Hydrodynamics Equations of the cytoskeleton. The alignment stages of the cytoskeleton are reproduced with good agreement of the timescales. The Finite Element Method allows for precise solutions and flexibility on the cell boundary shape. A moving cell boundary can be investigated using FreeFEM++.

We propose a two-phase-fluid model for a turbulent full-cone high speed atomizing liquid jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of a liquid and a gas with its phases in dynamic equilibrium. To derive the model, we impose conservation of the liquid volume and total momentum fluxes. Our model equation admits analytical solutions for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dynamic pressure and gas the entrainment rate coefficient are calculated. Assuming a far-field approximation, we theoretically derive a constant gas entrainment rate coefficient solely in terms of the cone angle. Moreover, we carry out experiments for a single-phase turbulent air jet and show that the predictions of our...

Many Industrial applications, e.g. sprays, fuel injection, water cutters, etc., also in medicine and environment. There is a long history of their study but there is no satisfactory theoretical model. We propose a simple and comprehen- sive two-phase fluid model. Basic assumptions: (i) stable high- speed jet; (ii) mixture of liquid and gas with its phases in dynamic equilibrium. We impose partial conservation of the volumetric liquid mass flux and energy. Solving the model’s Eqs. we numerically calculate the composite density, velocity, pressure and width of the jet. We obtain good comparison with experimental data.

ENGLISH: Abstract. In this work we analyze the process of kinetic energy equipartition and mass segregation within globular clusters. For this purpose, the results of four N-body numerical simulations, computed by the hybrid code EuroStar (which combines a direct force method, NBODY6, with a mean field method, SCF), are presented and discussed. We use two-mass components models: a light and a heavy component, consisting of particles of mass m1 and m2 , respectively. The mass contrast parameter, μ ≡ m2/m1, varies for each experiment and the total mass of the heavy component, M2, is fixed at 10 % of the total mass of the system, Mtot (i.e. q ≡ M2/Mtot = 0,1); only one of the experiments is made with a model of equal mass particles, as reference for the analysis of the other experiments. As a numerical integration quality criterium for the simulations, the relative error of the total energy is monitored. An analysis is made separating eight different particle subsystems from the global...

* Excellent Poster Award * Keypoints: • Industrial applications, e.g. sprays, fuel injection, water cutters, etc., medicine and environment. • Long history of their study but there is no satisfactory theoretical model. • We propose a simple and comprehensive two-phase fluid model. • Basic assumptions: (i) stable high-speed jet; (ii) mixture of liquid and gas with its phases in dynamic equilibrium. • We impose partial conservation of the volumetric mass flux and power, the latter being novel. • Solving the model’s Eqs. we calculate the composite density, velocity, impinging pressure and width of the jet. • Good comparison with experimental data.

ENGLISH: In this work we analyze the noise present in automotive-use fans produced in a local industrial plant. Samples were taken from the populations of defective (D) and non-defective (N) items, according to the current detection criteria, and also from the population of client-rejected items (and returned to the company). For each item, the sound frequency spectrum was measured under controlled conditions. Since a conventional curve correlation analysis resulted in statistically indistinguishable samples, a frequency by frequency analysis was made by two-sample one-sided hypothesis testing for the mean intensity of the sampled groups. ’Characteristic frequencies’ were found, where we obtained a confidence level higher than 99 % of there being a difference between the mean intensity of the groups (in that frequency). The characteristic frequencies between samples N and D where found to be at 3165.38, 6503.03 and 13113.72 Hz, which differ considerably from those found between samp...

Looking forward in future, the development of next multicore microprocessors may allow a computing scenario of multiple parallel reading and writing in memory. We developed a data partitioning and a scheme of multiple hash tables for that future scenario. This paper presents some results showing that, for multiple hash tables with a total number of slots less than the target data-set, our key conversion prior to the modulo operation produces a number of address collisions less than, or in the worst case, equal to the modulo operation alone.

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real $n$-th degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept of \emph{Canonical Polynomial Maps} which are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed \emph{Product Distance Function} for a given fixed point. The values of this product distance determine the stability of the fixed point in question, when it bifurcates, and even when chaos arises, as it passes through what we hav...

The dynamics of full-cone high-speed atomizing liquid jets has many applications. Despite the long history of their study, a theoretical model that can satisfactorily describe this dynamics on a sound physical ground has been yet to be established. In this study, we propose a two-phase-fluid fully analytical model that describes the dynamics of a wide class of jets in a simple but comprehensive manner. The basic assumptions are that (\textit{i}) the jet is stable and that (\textit{ii}) it can be approximated by mixture of a liquid and a gas with its phases in dynamic equilibrium. To derive the model, we impose conservation of the volumetric mass and momentum fluxes. The main result is that we get dimensionless analytical solutions of the model equations for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dimensionless dynamic pressure is calculated also analytically. Moreover, we show that the predictions of our model compare well with experimental data.

Industrial applications, e.g. sprays, fuel injection, water cutters, etc., medicine and environment. Long history of their study but there is no satisfactory theoretical model. We propose a simple and comprehensive two-phase fluid model. Basic assumptions: (i) stable high-speed jet; (ii) mixture of liquid and gas with its phases in dynamic equilibrium. We impose conservation of the volumetric mass flux and momentum flux. Solving the model’s Eqs. we calculate the composite density, velocity, impinging pressure and width of the jet. Good comparison with experimental data.

We theoretically analyze the hydrodynamic stability of an evaporating flat surface, extending previous works on the subject by including previously neglected factors in the linear stability analysis. We analyze four cases for gravity, no gravity, surface tension and no surface tension. The results improve upon previous theoretical studies and are generally consistent with them, although with some notable corrections.

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter λ and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real mth degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept of canonical polynomial maps which are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates and even when chaos arises, as it passes through what we have termed stability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.

MCCs cytoskeleton tend to align in a series of stripes, passing through several stages. Multiciliated Cells (MCCs)'s basal bodies (BBs) tend follow the alignment of the cytoskeleton. The BBs' tend to orient their basal feet (BF) towards the cytoskeleton at an angle. In order to model the alignment and orientation of BBs we first model the alignment stages of the cytoskeleton. Real cells have a changing irregular shape, approximately hexagonal. So far, simulations do not account for the cell shape, difficult to handle by the method of Finite Differences. The Finite Element Method is suitable to handle different shapes and fine emerging structures in the solutions. We propose the FreeFEM++ language for simulating the the Active Hydrodynamics Equations of the cytoskeleton. The alignment stages of the cytoskeleton are reproduced with good agreement of the timescales. The Finite Element Method allows for precise solutions and flexibility on the cell boundary shape. A moving cell boundary can be investigated using FreeFEM++.

単純だが包括的にジェットの幅広い種類のダイナミクスを記述する二相流体モデルを提案する。基本的な仮定は①ジェットは軸対称であり、②動的平衡にある液体と気体の混合状態として近似することができる。質量と運動量流束を全体的または部分的な保存のいずれかを課すことによって、4つのモデルを導出し、解析解・半解析解そして数値解を求めた。主な結果は、ノズルからの軸方向距離の関数として、二相流体の混合平均密度及び速度を予測することが出来、そこから動圧が計算出来る。また、文献に広く用いられている平衡速度係数の実験式を理論的に導出する。各モデルの結果を比較し、その予測は実験データとよく比較することを示す。
　液体ジェットは産業応用が多様で盛んに用いられている。例えば、スプレー、燃料噴射、水カッター等はもちろん、医療や環境問題でも活躍する。二相流体を構成する霧化液体ジェットの応用範囲は非常に大きい。しかしながら、噴霧プロセスの複雑さ、多数の物理現象と多くの変数を含む噴霧過程、ジェットが飛ぶ環境との相互作用とノズル内の状態（またはある他の発生源）に至るまで、数多くの物理現象の数学的モデリングの課題として残されている。いくつかの数学的モデルは、この領域でジェットのさまざまな側面を記述するためにたてられた。我々の知る限り、従来のモデルは、液体・気体混合ジェットの平均密度やスプレーの動的な圧力などの物理量を説明できない。

• The gas entrainment rate coefficient of an atomizing liquid jet has been extensively measured for broad experimental settings.
• Formulas derived from data fitting or dimensional analysis are available.
• Ricou & Spalding’s (RS) formula from dimensional analysis is widely known.
• To the authors’ knowledge, so far there is no theoretical derivation of it.
• We here present such derivation based on the ideal atomizing liquid jet model.
• Our formula generalizes and reduces to RS’s under an approximation for large distances
from the nozzle (far field).
• A novel approximation for the near field is also given.
• Acceptable comparison with experiments.

The dynamics of full-cone high-speed atomizing liquid jets has many applications. Despite the long history of their study, a theoretical model that can satisfactorily describe this dynamics on a sound physical ground has been yet to be established. In this study, we propose a two-phase-fluid fully analytical model that describes the dynamics of a wide class of jets in a simple but comprehensive manner. The basic assumptions are that (\textit{i}) the jet is stable and that (\textit{ii}) it can be approximated by mixture of a liquid and a gas with its phases in dynamic equilibrium. To derive the model, we impose conservation of the volumetric mass and momentum fluxes. The main result is that we get dimensionless analytical solutions of the model equations for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dimensionless dynamic pressure is calculated also analytically. Moreover, we show that the predictions of our model compare well with experimental data.

Many Industrial applications, e.g. sprays, fuel injection, water cutters, etc., also in medicine and environment. There is a long history of their study but there is no satisfactory theoretical model. We propose a simple and comprehen-
sive two-phase fluid model. Basic assumptions: (i) stable high-
speed jet; (ii) mixture of liquid and gas with its phases in dynamic equilibrium. We impose partial conservation of the
volumetric liquid mass flux and energy. Solving the model’s Eqs. we numerically calculate the composite density,
velocity, pressure and width of the jet. We obtain good comparison with experimental data.

Looking forward in future, the development of next multicore
microprocessors may allow a computing scenario of multiple parallel reading and writing in memory. We developed a data partitioning and a scheme of multiple hash tables for that future scenario. This paper presents some results showing that, for multiple hash tables with a total number of slots less than the target data set, our key conversion prior to the
modulo operation produces a number of address collisions less than, or in the worst case, equal to the modulo operation alone.

Poster contribution (Excellent Poster Award) presented to the Forum of Mathematics for Industry 2014 in Fukuoka, Japan, October 2014.

Key Points:

• Industrial applications, e.g. sprays, fuel injection, water cutters, etc., medicine and environment.
• Long history of their study but there is no satisfactory theoretical model.
• We propose a simple and comprehensive two-phase fluid model.
• Basic assumptions: (i) stable high-speed jet; (ii) mixture of liquid and gas with its phases in dynamic equilibrium.
• We impose partial conservation of the volumetric mass flux and power, the latter being novel.
• Solving the model’s Eqs. we calculate the composite density, velocity, impinging pressure and width of the jet.
• Good comparison with experimental data.

We theoretically analyze the hydrodynamic stability of an evaporating flat surface, extending previous works on the subject by including previously neglected factors in the linear stability analysis. We analyze four cases for gravity, no gravity, surface tension and no surface tension. The results improve upon previous theoretical studies and are generally consistent with them, although with some notable corrections.

The problem set up to solve in this work consists of extending and improving the characterization of the dynamics of general real quadratic polynomial maps, whose coefficients depend on a single parameter λ, and to generalize this characterization to
real cubic polynomial maps, in a consistent theory that allows to be further extended for real n-th grade polynomials. Basically, we can sinthetize the findings of this work as having succesfully given conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this we have defined “canonical polynomial maps” which are topologically conjugate to any polynomial map of the same degree with real fixed points. Then, the stability of the fixed points of the canonical polynomial maps has been found to depend solely on a special function called “product distance” of a given fixed point. The values of this product distance determine the stability of the fixed point and when it bifurcates, and even when chaos arises, as it passes through different “stability bands”, although the exact values and widths of these stability bands are yet to be calculated for regions of type greater than one for higher order polynomials.

In this work we analyze the process of kinetic energy equipartition and mass segregation within globular clusters. For this purpose, the results of four N-body numerical simulations, computed by the hybrid code EuroStar (which combines a direct force method, NBODY6, with a mean field method, SCF), are presented and discuted. We use two-mass components models: a light and a heavy component,
consisting of particles of mass m1 and m2 , respectively. The mass contrast parameter, μ ≡ m2 /m1 , varies for each experiment and the total mass of the heavy component,
M2 , is fixed at 10 % of the total mass of the system, Mtot (i.e. q ≡ M2 /Mtot = 0,1); only one of the experiments is made with a model of equal mass particles, as reference for the analysis of the other experiments. As a numerical integration quality
criterium for the simulations, the relative error of the total energy is monitored. An analysis is made separating eight different particle subsystems from the global system and derived from it by their mass (light or heavy) and integrator characteristics (NBODY6 or SCF). For each of the eight subsystems (where applicable) —and for the global system of course— we analyze the mean quadratic velocity (v 2 ), the
kinetic energy equipartition parameter between the mass groups (ξm), the kinetic energy equipartition parameter between the integrator groups (ξi), 19 lagrangian
radii (1, 2, ..., 9, 10, 20, ..., 80 and 90 % of the total mass), the central mass density (ρ0 ) and the near half-mass radius mass density (ρh). The general behaviour of the global system is consistent with the process of gravothermal collapse (for all
experiments, including the model of equal mass particles), contracting its internal lagrangian radii and expanding its external lagrangian radii, as a function of time, with a logarithmical nearly linear rate that varies for each experiment. Once the stage of core collapse is reached, there is an abrupt expansion of the inner lagrangian radii and a consequent reduction of ρ0 . The behaviour of the mass components of the global system is aproximately consistent with a kinetic energy equipartition process at the beginning of the simulation and a consequent mass segregation, at an initial time scale comparable with the theoretical Spitzer (1969) equipartition time, teq . Past ∼ teq , the general behaviour of the mass components is aproximately consistent with a process of gravothermal collapse in both components. Although the state of kinetic energy equipartition is not reached globally for any of the analyzed experiments, this
state does seem to be reached in the core (NBODY6 subsystem) of —at least— the M2-1 experiment. There are considerable differences in the temporal evolution
of the parameters of light and heavy particles when their analysis is divided into their own respective integrator groups (NBODY6 and SCF subgroups) for each mass component. The main reason for this is that NBODY6 is a collisional method and, therefore, it accounts for two-body interactions in an effective way —wich are necessary for the development of certain evolutionary processes, particularily the mass
segregation process—, while SCF does not take into account this interactions. The separation of particles in both integrator subsystems led to undesirable evolutionary
patterns in the study of the physical phenomena of interest, product of the underlying physical models of the respective integrators —under the parameters, models and conditions in which the hybrid integrator EuroStar was used in the present work—. Spite the latter, in general, the results are aproximately consistent with the theory and previous work about the dynamical evolution of globular clusters, particularily that of the models of two-mass components with q = 0,1.

In this work we analyze the noise present in automotive-use fans produced in a local industrial plant. Samples were taken from the populations of defective (D) and non-defective (N) items, according to the current detection criteria, and also from the population of client-rejected items (and returned to the company). For each item, the sound frequency spectrum was measured under controlled conditions. Since a conventional curve correlation analysis resulted in statistically indistinguishable samples, a frequency by frequency analysis was made by two-sample one-sided hypothesis testing for the mean intensity of the sampled groups. ’Characteristic frequencies’ were found, where we obtained a confidence level higher than 99 % of there being a difference between the mean intensity of the groups (in that frequency). The characteristic frequencies between samples N and D where found to be at 3165.38, 6503.03 and 13113.72 Hz, which differ considerably from those found between samples N and C, found at 2562.45, 9087.01, 11347.99 y 14233.45 Hz. Considering these last characteristic frequencies (related to rejection by the client), an acceptance criterion for the items was designed using automated hypothesis testing, which is now in line with the demands of the client. The designed criterion, fixed at a 0.10 significance level, rejects between 90 and 100 % of C group items, accepts between 60 and 80 % of current N population and rejects between 52 and 75 % of D group items.