In this work we develop an electromagnetic theory consistent with the Galilean relativity invariance. The formalism is based on the enlargement of the 3+1 space-time to a 4+1 space-time that permit to encode a set of linear Galilean transformation in the extended phase-space. In addition, it is well known that in odd dimensions it is possible to include in the action a Chern-Simons term. As a result, we obtain a set of electrodynamics equations which contain a non-linear interaction between the magnetic and electric fields.
Auxetic metamaterials are characterized by their unique property to stretch or compress in all directions when a force is applied.
We focus our study in finding new properties of auxetic metamaterials by building analogies between elastic systems and condensed matter problems.
In one instance we related an antiferromagnetic XY model to an auxetic material of rotating units, by comparing magnetic spins to solid rotations, as a result domain walls were found in such materials. We also modified a mechanical analogue of the SSH model such that we were able to control the position of the topologically protected mode, by extending the mechanical system.
Words in human language interact in sentences non-randomly, and allow humans to construct an astronomical variety of sentences from a limited number of discrete units. The co-occurrence of words in sentences reflects the organization of language in a subtle way that can be described in terms of a graph of word interactions. We study the topological structure of the Spanish human language, through the representation of a complex network in the novel “La Hojarasca” by Gabriel Garcia Marquez, focusing on the local properties of the network. We calculate its different statistical properties, such as the nearest neighbors and the clustering coefficient, the average distance (that is, the minimum average number of jumps that must be made from one arbitrary word to another), the degree distributions, Zipf's law, reciprocity and occurrence of binary structures in the text, that characterize the topological structure and behavior of the network. We find a composite power law behavior for both the average nearest neighbor’s degree and average clustering coefficient as a function of the vertex degree. This implies the existence of different functional classes of vertices. We developed the model of empirical results based on the procedures given by A. P. Masucci and G. J. Rodgers in the Orwell’s 1984.
We apply nonlinear dynamics tools to analyze musical works, in this particular case, the trios of the composers W. A. Mozart (1756-1791) and M. Feldman (1926-1987). Mozart is one of the most important composers of the Classical period. His work is characterized by its symmetry, formal perfection and a mathematical organization. On the other hand, Feldman is, in turn, an important composer of the XX century, which has a nonlinear discourse and great temporal extension; features that move it away from the classical discourse. From the Mozart’s trios (KV. 10, 11, 12, 13, 14, 15, 496 and 564) and Feldman’s (For Philip Guston and Three Voices), numerical series were generated representing the durations of event interventions sounds of each work. Subsequently, we constructed symbolic sequences with the aim to perform an analysis of symbolic dynamics that allowed us to find power-laws in what concerns the interventions of each of the instruments combinations. In parallel, we performed descriptive statistical analysis to obtain data distributions and frequency histograms. Through the Data Cluster, the first results were obtained: the works could be grouped by the level of similarity they have, quantitatively demonstrating the differences in the works of each composer; also, a model of the Mozart time series was obtained. Finally, it was established that the composition of these works responds to a complex phenomenon, in which the relations of the instruments with each other and with silence generate complexity in the composition.
In this work we consider the Chirikov standard mapping described by a nonlinear and two-dimensional mapping in momentum and angle variables and control parameters. Defined the model we build the phase space for the conservative system and observe a mixed structure composed by chaotic sea, periodic islands and a set of invariant spanning curves. Dissipation is introduced in the system and large chaotic attractors are observed. The maximum of the chaotic attractors as a function of the control parameters is investigated and provide a power law fitting. To characterise the chaotic behavior the Lyapunov exponents are considered.
We found a new integer sequence: 3, 5, 6, 10, 12, 20, 24, 20, 48, 80, 96, 160, … that comes from a bifurcation cascade into the parameter plane, exiting a chaotic window and going to another chaotic region in a system of two coupled logistic maps whose dynamical behavior is done in terms of their integer periodicities [1]. By this way we justify a new seed in the K. Brokhaus sequence reported in the On-line Encyclopedia of Integer Sequences (OEIS) [2]. We proposed the same recurrent relation:
a(n) = 2*a(n-2) for n > 2
with new seeds: a(1) = 3 and a(2) = 5.
[1] R. O. E. Bustos-Espinoza and G. M. Ramírez Ávila, Synchronization conditions of coupled maps using periodicities, The European Physical Journal Special Topics, 225, 2697-2705, 2016
[2] THE ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES
We implemented electronic logistic maps like those used by L'her et al. [1]. We worked with sets of three almost identical oscillators for the two possible motifs working with three mutually coupled oscillators. The aim is to verify which of the motifs enhance synchronous behavior by determining the synchronization region experimentally. The latter is obtained by computing the value of the synchronicity factor in the same line of the method used by Bustos-Espinoza & Ramírez Avila [2].
[1] L'Her A, Amil P., Rubido N., Marti A. C., and Cabeza C., 1996, Electronically-implemented coupled logistic maps, The European Physical Journal B.
[2] Bustos-Espinoza R. O. E. and Ramírez Ávila G. M, 2016, Synchronization conditions of coupled maps using periodicities, The European Physical Journal Special Topics.
How to generate knowledge, science, technology, innovation and also integral and sustainable development for Bolivia, since the job of the municipalities.
City of knowledge
We are looking for reply in Bolivia some of the small knowledge cities of other countries and getting the better conditions for the scientific investigation.
Where do we want to get with the cities of knowledge?
1.- All of then go to have a science advance, technology and innovation.
2.- What for?
3.- For whom it is?
What for?
For getting knowledge, technology and innovation, so the actions that solve the problems as the most important needs, to get the sustainable development of their countries.
FOR WHOM IT IS?
• For the focus population
• For getting better life conditions
• For a wellness and a life quality
Taking these thoughts
A city of knowledge could be implanted in anywhere that a country could select. In Bolivia, we think the best place is Cochabamba city.
WHAT WE NEED FOR THIS PROJECT?
We need to identify which are the real inputs or primary materials to help the job of the cities of knowledge.
HOW TO IDENTIFY THE PRIMARY MATERIALS FOR A CITY OF KNOWLEDGE?
It is very important to identify and get the primary materials, main need from the municipalities and communities through a real combination.
Human resources + Natural resources + economic resources
These problems and need that have been identified are the primary materials for building a city of knowledge, for the achievement of goals. If we don´t do this, the project will not be able to be supported.
The cities of knowledge couldn´t do investigations with no the primary materials and the topics of work will not be important or useful.
OBJECTIVES OF THE CITY OF KNOWLEDGE IN BOLIVIA
• Integral and sustainable development in Bolivia, that also would be environmental friendly.
• Good quality Job creation
• Eradication of poverty
• Wellness in Bolivian people
For example, in Vancouver, Canada, there is a dam which generates energy but it is completely friendly with the environment.
Also, Portland in USA, has a building which has been done with all the commodities, services and vegetation program for inside and outside of the place. It looks so natural.
HOW TO ACHIEVE THE GOALS OF THE CITY OF KNOWLEDGE IN BOLIVIA?
• The BACA suggest a strategic plan which is based in getting the best combination of human, natural and economic resources.
• This project should be done trough:
• Small planning method, participation of many groups, echo sustainable, and without a social exclusion.
• The knowledge, science, technology and innovation will be the most important parts for getting the municipals development; all of them will achieve the integral and sustainable development of Bolivia.
ACHIEVEMENT OF GOALS
We will have a country with integral and sustainable development, environmental friendly. It will be called, BOLIVIA.
The structure of the parameter plane for a family of two dimensional, nonlinear and area contracting mappings is investigated. Several dynamical features in the system such as tangent, period-doubling, pitchfork and cusp bifurcations were found and discussed together with cascades of period-adding, period-doubling, and the Feigeinbaum scenario. The presence of spring and saddle-area structures allow us to conclude that cubic homoclinic tangencies are present in the system. A set of complex sets such as streets with the same periodicity and the period-adding of spring-areas are observed in the parameter space of the mapping.
Thanks FAPESP (2018/14685-9) and CNPq (303242/2018-3, 421254/2016-5, 311105/2015-7).
[1] Juliano A. de Oliveira, Leonardo T. Montero, Diogo R. da Costa, J. A. Méndez-Bermúdez, Rene O. Medrano-T and Edson D. Leonel. Chaos, 29, 053114, 2019.
We studied synchronization as a function of coupling strength in threesome Rulkov neurons feautured by their periodicities, and considering electrically and bidirectional coupling. Firstly, we determined the dynamical behavior of a single neuron by using its periodicities into the parameter plane. we identified the typical behavior of spiking-bursting in several regions of this plane. Several basins of attraction for the Rulkov model were obtained exhibiting multistability. We worked with identical and different neurons but with the same periodicity. We found that the heterogeneous configuration enhances synchronization; aspect that was verified by analyzing the time series of the slow variable.
This work describes the population dynamics of cancerous cells when they interact with normal cells as well as with the effector cells that are related to the immunological response. The model is based on logistic equations describing the growth of the populations of cancerous and normal cells, the Lotka-Volterra model for competitive species including the radiation effects on both cells, and the Michaelis-Menten equation describing the interaction among the cancerous and effector cells. The parameters of the model are in a relationship with the interactions between the different types of cells and in particular on the effects on the inactivation of the cancerous cells due to the action of the normal ones and the transformation of the normal cells caused by the presence of tumoral ones. We also consider the radiosensitivity of each type of cells.
We performed a linear stability analysis of our model, determining volumes of stability in several projections of the parameter space. The model exhibits a great dynamical richness going from fixed points to chaotic behaviors. We took into consideration several regions of the parameter space looking for parameter values leading to the situation in which the radiation tends to eliminate the tumoral cells with no or slight modifications on the populations of normal cells. The latter could constitute an important application concerning effective radiotherapy treatment.
In condensed matter systems, solitons have become relevant due to their particle-like properties. In particular, they have turned fundamental to describe fluxons in Josephson junctions (JJ's). In this work, we investigate analytically and numerically the stability of bubble-like fluxons in the 2D sine-Gordon system under the action of a coaxial dipole current. Through a linear stability analysis, we reduce the problem to a Schrödinger-like equation with a modified Pöschl-Teller potential, solving the problem exactly. We provide a theoretical description of the response of bubble fluxons to the coaxial dipole current, finding a stabilization domain, emergence of internal modes, and bubble break up. We also explore the effect of a uniform external microwave field on the dynamics.
In this work we revised the Friedmann–Lemaître–Robertson–Walker cosmology from the approach of dynamical systems. We start by a derivation of the dynamical equations from a dimensionally reduced Lagrangian density of the full Einstein-Hilbert Action. The dynamical system can be characterized by a set of three non-linear equations plus a constraint. By a suitable manipulation of the system, it is possible to rewrite the equations as a set of two equations that resemble in some respects a Lotka-Volterra system.
Some experimental reports revealed that the cyclopropanated pentacyclic [1] and pyran derivatives [2] undergo ring opening reaction to form monocyclic compounds under the catalysis of Zeise’s salt. Present DFT study on the mechanism of the rearrangement reaction shows that this reaction prefers involvement of two metal atoms, provided by the Zeise’s dimer to generate the product. Moreover, an external water molecule or alcohol is required to generate the end product. The reduced activation barrier of the reaction pathway, catalyzed by two metal atoms, explains the occurrence of the rearrangement reaction at ambient condition.
1. Hoberg JO, Jennings PW, Organometallics, 1996, 15, 3902-3904.
2. Beyer J, Skaanderup PR, Madsen R, J. Am. Chem. Soc. 2000, 122, 9575-9583.
Chaos characterization in a dynamical system is done by specifying invariant quantities, which allow us, for example, to establish the stability of the trajectories, or to establish the geometry and information produced in strange attractors. Particularly useful invariants are the Lyapunov exponents, the entropy, and the fractal dimensions. In this work, we study experimentally the behaviour of the largest Lyapunov exponent - obtained from time series measurements and reconstructing the attractor using a Time Delay Embedding algorithm - in a system of two coupled chaotic circuits as we vary the control parameters. We estimate from these measurements the system's entropy. The experimental results are successfully compared with numerical simulations in the parameter space composed of the coupling strength and parameter mismatch. Moreover, we discuss the possible behaviours emerging from these results for a wide range of parameters, also considering the possible synchronized states.
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behavior. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC), however, the main factors favoring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis elegans neural networks as well as in networks with similar randomness and small-worldness. We analyze the effectiveness and robustness of the inference process under different observations and collective dynamics, contrasting the results obtained from using membrane potentials and inter-spike interval time-series. We find that overall, small-worldness favors network inference and degree heterogeneity hinders it. In particular, success rates in C. elegans networks -- that combine small-world properties with degree heterogeneity -- are closer to success rates in Erdös-Rényi network models rather than those in Watts-Strogatz network models. These results are relevant to understand better the relationship between topological properties and function in different neural networks.
A biological system is characterized by a set of different interdependent scales which interact non-linearly. It has been therefore proposed that the dynamics of physiological variables reflect the underlying modulation mechanisms. Among all physiological variables in humans, heart rate variability (HRV) is the most studied one and has been proved to serve as an independent predictor for some chronic degenerative diseases. Our research team proposes Caenorhabditis elegans as an animal model to explore the relationship between the dynamics of physiological variables and its underlying modulation mechanisms. Hereby we aim to test the hypothesis that the variability of the pharyngeal pumping could be a relevant index of functional decline in exposure to stressors and ageing in this organism.
In C. elegans, feeding is achieved through pharyngeal muscular contractions (pharyngeal pumping) controlled by pacemaker neurons. In view of its neurogenic nature, the C. elegans pharynx can be used as a simplified model of the human heart. Furthermore, the C. elegans lifespan is only around two weeks; hence physiological alterations can be visualized over the course of aging. Age-related changes in tissue morphology and function, and a decline in C. elegans health are strongly correlated with a reduction in pharyngeal pumping rate (number of pumps/ total recording time) and thus with a decline in survival probability. Traditionally pharyngeal pumping has been assessed by eye and therefore the underlying variability has not yet been taken into account.
Using a meteorological database of the variavbles, pressure,humidity,pressure,temperatura,solar radiation intensity and wind spead and dirección wing form the Tambo Quemado station (Lat (S) 18o 17’ 21’’ lon (W) 69o 0’ 17’’ Altitud 4681 masl) going from March 2006 to August 2007, we performed a time series analysis of each variable. Firstly, use obtain the FFT to determine the existence of some regular oscillatory behaviour. The variables related to wind resulted the more complicated to analyze; thus, we take the problema using nolinear tools for time series analysis. In particular, we use autocorrelation, embedding techniques and recurrence quantification analysis. The recostruction of the phase space queve us the posibility to caracterize the caotic behavior of some the above mentioned variables.
A sphere contained in a rotating ring is a known and simple nonlinear system that shows vast dynamic behavior. Although the theoretical treatment of the system, particularly referring to the parameter control – angular velocity – is frequent, it is not common to find an experimental arrangement that allows for bifurcation and stability analysis.
This work shows the characterization of the system with a simple experimental setup and under different established situations. The assembled experiment allows obtaining the bifurcation diagram of the parameter control predicted by the theory, when working with a single sphere. Additionally, it allows the study of the system in the situation in which there is more than one sphere, verifying the equiprobable behavior of the new equilibrium point. Some interesting results were found in particular cases when treatment with various spheres and fluids is performed.
The theory of evolution by natural selection, first formulated by Darwin in 1859, is the process by which organisms change over time as a result of changes in heritable physical or behavioral traits. In this study we aimed at observing evolutionary processes of natural selection and genetic drift using a model without artificial intervening selection. In our model, time and space are discrete and a single organism can interact with its environment as well as other organisms. The environment is comprised of a set of resources with specific decay and diffusion rates (e.g. ATP, fat, smell). Each organism possesses an internal state and the ability to perceive its immediate surrounding environment. The internal state is determined by possessed resources and a short memory of previous time steps. In each time step, an individual performs an action which influences themselves as well as their environment in the following times. Their basic actions consist of movement, reproduction and consumption. These actions are decided with an artificial neural network, which is specific to an individual. The factors that contribute to the decision consist of their internal state as well as the state of their immediate environment. When they reproduce, there are minor mutations within each generation, causing genetic drift and speciation in the long term. In our model we considered two landscape configurations: homogeneous and island-like landscapes. In the homogeneous landscape the resources are plentiful and evenly distributed, while in the island-like landscape, nutrients are concentrated in particular locations with different sizes and distances scattered across the landscape. We hypothesized a lower genetic drift and natural selection in a homogeneous compared with the island-like landscape. Within a relatively short period of time, we were able to observe and quantify genetic drift. On the final diversified populations we conducted statistical analyses on genotypic and phenotypic traits.
Chagas Disease American trypanosomiasis is caused by a flagellated parasite: Trypanosoma cruzi, transmission by an insect of the genus Triatoma, and also by blood transfusions. In Latin America, the number of people infected is approximately 6 million, with a population exposed to the risk of infection of 550000.
It is our interest to develop a non-invasive and low-cost methodology capable of detecting any early alteration of cardiac production by T. cruzi.
For this, we analyzed the 24-hour Holter ECG records in 107 patients with ECG abnormalities (CH2), 102 patients without ECG abnormalities (CH1) who had positive serological results for Chagas disease and 83 volunteers without positive serological results. Chagas disease (CONTROL).
We used the approximate entropy to quantify the regularity of the electrocardiograms (ECG) in the three groups. We analyzed 288 ECG segments per patient. Significant differences were found between the CONTROL and CH2 groups, which was used to stratify the risk in the CH1 group.
Deep Learning techniques have improved notoriously in the last decade. In particular, Neural Networks with adequate training are been widely used for image recognition and classifying objects. This poster shows how Neural Networks can analyze phase portraits through image recognition in order to classify different dynamical behaviours. Hence, chaos, homoclinic orbits or other behaviours can be classified by the Neural Network. This could give a new tool for data analysis.
In this research work we intend to establish a methodology, which in an unambiguous way, allows us to identify the correlation of movement between different sections of the structure of a protein.
For this, the different conformations given for the same protein determined by means of nuclear magnetic resonance will be analyzed. Consequently, the quaternion associated with each residue of a given protein will be determined and then the distance between the quaternions corresponding to homologous residues in different structures will be measured.
When analyzing these differences with machine learning methods, we expect to find a correlation between the dynamics of the different residues in the protein.
We carried out experiments concerning the Belousov-Zhabotinsky (BZ) reaction in a closed reactor working with a pH of 0.097. The Oregonator model and an extended Field-Köros-Noyes mechanism for the organic set of reactions provide us the explicit form of the two system parameters that depend on the relative proportion of reagents. Although some kinetic values play the role of scaling parameters, from an experimental point of view both parameters subtend a “space of concentrations.” We prepared different reagents reference concentrations (potassium bromate and malonic acid at constant bromomalonic acid) to obtain the kinetic series by means of spectroscopic measure of Ce(IV)-concentration at a wavelength of 400 nm. The classification of the dynamics that results from the reference concentrations allowed us to identify two regions of states in the space of concentrations: one containing the oscillatory regime and the other with the stationary states, both separated by a fringe that is the counterpart of the Hopf bifurcation curve in the parameter space predicted by the Oregonator. We also observed the modification of the bifurcation fringe with increasing pH value; the dependence of the Hopf bifurcation curve with respect to the parameter related to the acidity justifies the BZ reaction inhibitory tendency as pH increases. Finally, we report the numerical study of the complete synchronization of two identical oscillators modeled by the Oregonator with diffusive and bidirectional coupling; we propose a structural dependence of the synchronized system with respect to the coupling coefficient.
In the context of pattern formation studies, specifically on Faraday Waves, we have designed and assembled a new experimental setup, which, due to its versatility, can adapt to different configurations given by specific requirements and measurements. This setup consists of a quasi-one-dimensional liquid column vertically perturbed under a localized injection of energy. We vary the geometry of the bottom, initially, with triangular and rectangular reliefs to study how pattern formation is affected by them.
In the present work, the possible correlation of the movement between the residues located in the disordered and orderly areas of the protein structures will be sought. For this, protein dynamics simulations will be carried out, through classical molecular dynamics.
A series of simulations will be carried out for each protein under study, to determine the temporal evolution of the protein structure. For the structure stored along the simulation path, the set of quaternions that describe each of its residues will be determined.
Subsequently, the distance between the quaternions of homologous residues will be measured and these differences will be analyzed with deep learning methods to find possible correlations between the movements of the protein residues.
In this work, I propose a plausible strategy to analyze the stability of non-permanently polarized balls from two-dimensional colloidal system. The model is constructed by a closed chain of classical-electrical dipoles that interact with first neighborhoods electrically. It is described by a sine-Gordon equation plus another additional terms. To analyze the stability on time of this colloidal system I’ve parametrized the polarization of balls as a function of time. Finally, I also present some perspectives and discussions according to simulation studies, geometrical approaches and time-dependence in the electrical potential.
We work on the characterization of the atmosphere, considering it as a nonlinear system. Once characterized, we make the prediction of neutron flux in the Chacaltaya mountain under Monte Carlo simulations. We take into account the pressure, temperature and density of the air, together with concentrations of: vapor of H2O, CO, CO2, N2 and O3. A validation of the simulation results is also done through experimental measurements.
We investigate numerically the effects of external time-periodic potentials on time-localized perturbations to the amplitude of electromagnetic waves propagating in normal-dispersion fiber lasers which are described by the complex Ginzburg-Landau equation. Two main effects were found: The formation of domains enclosed by two maxima of the external periodic field and the generation of a chaotic behavior of these domains in the region of relatively high amplitudes and low frequencies of the external fields. Maps and bifurcation diagrams of the largest Lyapunov exponent and moments, such as energy and momentum, are also provided for different values of the amplitude and frequency of such external potentials. Published by AIP Publishing. https://doi.org/10.1063/1.5006919
[1] Urzagasti, D., Vargas, B. A., & Quispe-Flores, L. A. (2017). Chaotic one-dimensional domains induced by periodic potentials in normal-dispersion fiber lasers. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(10), 103116.
A fixed dipole with fractal symmetry was set up using a circle generation computational tool. The arrangement was composed of either 8 or 9 circles that repeated sequentially. The dielectric field generated by this arrangement was analysed. Different points of symmetry were observed and were correlated to the stability levels of the arrangement.
Two-dimensional octagonal-diamond (OD) atomic lattices have been explored in recent times to study phenomena related to topological phase transitions induced by spin-orbit interaction and gauge fields [1], and magnetic phases and metal-insulator transitions with Hubbard interaction [2,3]. It can lead to the appearance of nontrivial nearly flat band states with particular topological properties [4]. Here we study the octagonal-diamond photonic lattice formed of linearly coupled waveguides, proposed by [4] as a possible experimental realization of an artificial flat-band system.
We investigated analytically and numerically the existence and stability of linear and nonlinear localized modes in a two-dimensional OD lattice. The primitive cell consists of four sites, linearly coupled with each other with the same coupling constant, including two diagonal couplings. The eigenvalue spectrum of the linear lattice consists of two flat bands and two dispersive bands [4]. The upper dispersive band intersects the upper flat band in the middle of the Brillouin zone, as well as the second flat band at the end of the Brillouin zone. In the linear case, there are two types of localized linear solutions, which are composed of eight sites each, having either monomer (+ - + - + - + -) or dimer (+ + - - + + - -) staggered phase structure [4]. In the presence of Kerr nonlinearity, both focusing and defocusing, compacton-like solutions [5] are unstable due to intersections of the upper dispersive band and the flat bands. We are currently in the process of finding soliton solutions in the requency gaps occurring between the flat bands and the isolated dispersive bands.
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Numerical simulations of confined particles with different mass and charge against gravity were carried out. The equilibrium configurations were determined solving the dynamical equations by implementing the Verlet algorithm. The evolution of the centre of mass and the different equilibrium particle distributions were studied.
We obtained experimentally a vast gallery of attractors for Chua's and RL-Diode circuits. Using mutual coupling, we studied the possibility of synchronization in both of synchronization for two oscillators and then expand our system to several oscillators.