Manuel Solano | Benemérita Universidad Autónoma de Puebla (BUAP) (original) (raw)
Papers by Manuel Solano
Gas Bubble Dynamics in the Human Body
Cerebral arterial gas embolism (CAGE) is a dramatic event with a very rapid onset of symptoms and... more Cerebral arterial gas embolism (CAGE) is a dramatic event with a very rapid onset of symptoms and occurs in diving and in a variety of medical procedures without the requirement for preceding supersaturation of tissues with inert gas. Decompression sickness (DCS) occurs only when there is prior accumulation of a gas-load in tissues (supersaturation) followed by subsequent depressurization, and bubbles mainly occur in the tissues and the venous side of the circulation. There is increasing evidence that microparticles, microbubbles, inflammatory mediators and ischemia-reperfusion injury all play important roles in CAGE and DCS. Gas embolism in the spinal cord is very rare, but a majority of DCS cases involve the spinal cord and this is often also accompanied by cerebral effects. The anatomy of the blood supply of the brain and spinal cord has important influences on CAGE and spinal DCS. The effects of bubbles occurring in cardiopulmonary bypass (CPB) are compared and contrasted with those seen in CAGE and DCS. Nine clinical case examples of CAGE and DCS are very briefly described and the outcomes are described in Chapter 9 .
Understanding the anatomy and physiology of the cardiovascular and pulmonary systems is essential... more Understanding the anatomy and physiology of the cardiovascular and pulmonary systems is essential to appreciate the dynamics of bubbles in the body, including the structure of arterial and venous vessels, cell membranes and the transport of gases. Bubbles may be spherical, but if larger than the diameter of an enclosing vessel will become “sausage-shaped” (cylindrical with hemispherical end-caps). Microbubbles and microparticles play important roles in decompression sickness (DCS) and arterial gas embolism (AGE). Bubbles may be stabilized by a surrounding skin of molecules and thereby persist much longer than would be expected otherwise. The pulmonary bubble filter is a crucial defense against venous bubbles entering the arterial circulation, but may be bypassed by a patent foramen ovale and other mechanisms. The uptake and elimination of inert gases may be described by “washin” and “washout” exponentials. The appendix describes fundamental concepts of gas pressures in the body.
We address the problem of the dynamics, i.e., the rate of growth and dissolution, of a gas bubble... more We address the problem of the dynamics, i.e., the rate of growth and dissolution, of a gas bubble lodged in a soft elastic solid meant to approximate soft tissues in the body, such as muscles, connective tissues and joint capsules. The basic rate equation used previously for a gas bubble suspended in a simple liquid: dR/dt=3RTDR(∂c/∂r)R,t−R2dPh/dt3PhR+4γ is rederived, with appropriate modifications made to the underlying Young-Laplace equation for gas bubble pressure, and to the diffusion equation for the contribution of elasticity to dissolved solute diffusion. We find that using the generalized Young-Laplace equation, which reduces the gas bubble pressure relative to a simple liquid medium, has a major effect on the gas bubble dynamics, while the modification of solute diffusivity due to elastic effects in the medium is relatively minor. The overall effect of taking the elasticity of the medium into account is to slow down the rate of gas bubble dissolution, increase the rate of g...
The fundamental gas bubble expansion/contraction rate equation derived in Chapter 3, for a spheri... more The fundamental gas bubble expansion/contraction rate equation derived in Chapter 3, for a spherical gas bubble suspended in a simple liquid medium, i.e., dR/dt=3RTDR(∂c/∂r)R,t−R2dPh/dt3PhR+4γ is solved in this chapter for a range of different conditions and approximations. Its solution, i.e., its integrated form—which provides the bubble radius R vs. time t explicitly—requires an explicit expression for the dissolved solute concentration gradient in the medium at the bubble’s surface (∂c/∂r)R, t. However, the form obtained for this term depends on a variety of choices that can be made. It depends on whether one solves the full diffusion equation or the simpler Laplace equation (the steady-state approximation of the diffusion equation) and on the details of the gas bubble diffusion model that is chosen. Here we provide solutions for the radius vs. time of a dissolving gas bubble for both the full diffusion equation and the Laplace equation, for fixed and variable ambient pressures, ...
Although prompt treatment of decompression sickness (DCS) and arterial gas embolism (AGE) is best... more Although prompt treatment of decompression sickness (DCS) and arterial gas embolism (AGE) is best, diffusion of gases through bubbles and streaming around bubbles likely contributes to better than expected outcomes even after prolonged delays. Quantitative analysis within the limits of the best available model (LHV3) is provided for the application of normobaric oxygen, pressure, and both combined (hyperbaric oxygen) on bubble size. This demonstrates that breathing oxygen before commencing hyperbaric treatment is very effective in shrinking “uncovered” or “bare” bubbles. The analysis further demonstrates that helium bubbles will extinguish faster than the same size nitrogen bubbles. Further, treatment with the USN Table 6 would be expected to eliminate even the largest likely sizes of uncovered bubbles. No model of bubble dynamics presently available accurately predicts the duration of persistence of any size of bubble surrounded by a skin of phospholipids or protein molecules, but ...
Decompression models that describe the distribution of excess dissolved inert gas in the body and... more Decompression models that describe the distribution of excess dissolved inert gas in the body and provide a means of estimating the risk of incurring decompression sickness (DCS) are introduced. Both older deterministic models, the first of which was developed by J.S. Haldane over a century ago, and more recent probabilistic models are described. The models are further distinguished by whether they consist of independent parallel compartments, or interconnected compartments. A compartment, in the context of the independent compartment models, is viewed as a collection of tissues with similar values of their inert gas exchange rate constants. Alternately, and particularly in the context of the interconnected compartment models, a compartment can be viewed as a physical region in the body containing dissolved inert gas, which plays a role in the development of DCS. Interconnected compartments exchange dissolved inert gas both with the circulatory system and with each other, while inde...
Gas Bubble Dynamics in the Human Body, 2018
Solubility, saturation, supersaturation, and undersaturation are all explained in the context of ... more Solubility, saturation, supersaturation, and undersaturation are all explained in the context of gas-liquid solutions. Solutions composed both of one and several different gaseous solutes are considered. The chemical potential of a specific chemical species is introduced and its basic role in solute distribution is described. Solute distribution or redistribution occurs so as to lower the value of its chemical potential, because doing so lowers the system free energy. This is made manifest within a single phase by solutes tending to spontaneously diffuse down their concentration gradients, from higher to lower concentrations. For a pair of contiguous phases, such as a gas and a liquid, the tendency to lower the system free energy causes the volatile solute to be driven from the phase in which its chemical potential is larger to the phase in which it is lower. The crucial role of surface tension on gas bubble pressure is described. It is particularly important for small gas bubbles (<50 μ), and it is expressed quantitatively by the Young-Laplace equation. Surface tension tends to increase the pressure acting on the contents of a gas bubble beyond what it would be from the effect of ambient hydrostatic pressure only.
Journal of applied physiology (Bethesda, Md. : 1985), Jan 14, 2017
Blood flow through intrapulmonary arteriovenous anastomoses (QIPAVA) occurs in healthy humans at ... more Blood flow through intrapulmonary arteriovenous anastomoses (QIPAVA) occurs in healthy humans at rest and during exercise when breathing hypoxic gas mixtures at sea level and may be a source of right-to-left shunt. However, at high altitude QIPAVA is reduced compared to sea level as detected using transthoracic saline contrast echocardiography (TTSCE). It remains unknown whether the reduction in QIPAVA (i.e., lower bubble scores) at high altitude is due to a reduction in bubble stability resulting from the lower barometric pressure (PB), or represents an actual reduction in QIPAVA. To this end, QIPAVA, pulmonary artery systolic pressure (PASP), cardiac output (QT) and the alveolar-to-arterial oxygen difference (AaDO2) were assessed at rest and during exercise (70-190W) in the field (5,260m) and in the lab (1,668m) in 4 conditions; normobaric normoxia (NN; PIO2=121 mmHg, PB=625 mmHg, n=8), normobaric hypoxia (NH; PIO2=76 mmHg, PB=625 mmHg, n=7), hypobaric normoxia (HN; PIO2=121 mmHg,...
Mathematical Biosciences, 2020
We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate t... more We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straightforward extensions of those for a one-component gas bubble. They were derived by using the Young-Laplace equation and Dalton's law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry's law for gas solubilities, and Fick's law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O 2 , N 2 , He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N 2-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N 2 partial pressure can be quite high (e.g. ∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygenrich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.
International Journal of Geometric Methods in Modern Physics, 2008
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah–Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed. A possible application of fluctons in the N = 4 Topologically Twisted Supersymmetric Yang–Mills Theory is explored and the case of gravity is discussed briefly.
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah-Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed, and the case of gravity is discussed briefly.
Fractal/non-fractal morphological transitions allow for the systematic study of the physical mech... more Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of quantities such as the two-point density radial or angular correlations. However, persistent discrepancies found during the analysis of basic models, using these two quantification methods, demand important clarifications. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial-angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential, that, under the fractal dimension inte...
Revista Mexicana De Fisica, 2007
The topological phases of Yang-Mills theory are studied. The authors propose the fluctons as the ... more The topological phases of Yang-Mills theory are studied. The authors propose the fluctons as the topological fluctuations of vacuum, which are not necessari...
Fractal/non-fractal morphological transitions allow for the systematic study of the physical mech... more Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of the twopoint radialor angular-density correlations. However, these two quantification methods lead to relevant discrepancies during the analysis of basic systems, such as in the diffusion-limited aggregation fractal. Hence, the corresponding clarification regarding the limits of the radial/angular scaling equivalence is needed. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial/angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters and growth regimes. Specifically, we show that the angular...
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah-Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed, and the case of gravity is discussed briefly.
Entropy, 2021
We propose a novel framework to describe the time-evolution of dilute classical and quantum gases... more We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell–Boltzmann, Fermi–Dirac, or Bose–Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be...
Gas Bubble Dynamics in the Human Body
Cerebral arterial gas embolism (CAGE) is a dramatic event with a very rapid onset of symptoms and... more Cerebral arterial gas embolism (CAGE) is a dramatic event with a very rapid onset of symptoms and occurs in diving and in a variety of medical procedures without the requirement for preceding supersaturation of tissues with inert gas. Decompression sickness (DCS) occurs only when there is prior accumulation of a gas-load in tissues (supersaturation) followed by subsequent depressurization, and bubbles mainly occur in the tissues and the venous side of the circulation. There is increasing evidence that microparticles, microbubbles, inflammatory mediators and ischemia-reperfusion injury all play important roles in CAGE and DCS. Gas embolism in the spinal cord is very rare, but a majority of DCS cases involve the spinal cord and this is often also accompanied by cerebral effects. The anatomy of the blood supply of the brain and spinal cord has important influences on CAGE and spinal DCS. The effects of bubbles occurring in cardiopulmonary bypass (CPB) are compared and contrasted with those seen in CAGE and DCS. Nine clinical case examples of CAGE and DCS are very briefly described and the outcomes are described in Chapter 9 .
Understanding the anatomy and physiology of the cardiovascular and pulmonary systems is essential... more Understanding the anatomy and physiology of the cardiovascular and pulmonary systems is essential to appreciate the dynamics of bubbles in the body, including the structure of arterial and venous vessels, cell membranes and the transport of gases. Bubbles may be spherical, but if larger than the diameter of an enclosing vessel will become “sausage-shaped” (cylindrical with hemispherical end-caps). Microbubbles and microparticles play important roles in decompression sickness (DCS) and arterial gas embolism (AGE). Bubbles may be stabilized by a surrounding skin of molecules and thereby persist much longer than would be expected otherwise. The pulmonary bubble filter is a crucial defense against venous bubbles entering the arterial circulation, but may be bypassed by a patent foramen ovale and other mechanisms. The uptake and elimination of inert gases may be described by “washin” and “washout” exponentials. The appendix describes fundamental concepts of gas pressures in the body.
We address the problem of the dynamics, i.e., the rate of growth and dissolution, of a gas bubble... more We address the problem of the dynamics, i.e., the rate of growth and dissolution, of a gas bubble lodged in a soft elastic solid meant to approximate soft tissues in the body, such as muscles, connective tissues and joint capsules. The basic rate equation used previously for a gas bubble suspended in a simple liquid: dR/dt=3RTDR(∂c/∂r)R,t−R2dPh/dt3PhR+4γ is rederived, with appropriate modifications made to the underlying Young-Laplace equation for gas bubble pressure, and to the diffusion equation for the contribution of elasticity to dissolved solute diffusion. We find that using the generalized Young-Laplace equation, which reduces the gas bubble pressure relative to a simple liquid medium, has a major effect on the gas bubble dynamics, while the modification of solute diffusivity due to elastic effects in the medium is relatively minor. The overall effect of taking the elasticity of the medium into account is to slow down the rate of gas bubble dissolution, increase the rate of g...
The fundamental gas bubble expansion/contraction rate equation derived in Chapter 3, for a spheri... more The fundamental gas bubble expansion/contraction rate equation derived in Chapter 3, for a spherical gas bubble suspended in a simple liquid medium, i.e., dR/dt=3RTDR(∂c/∂r)R,t−R2dPh/dt3PhR+4γ is solved in this chapter for a range of different conditions and approximations. Its solution, i.e., its integrated form—which provides the bubble radius R vs. time t explicitly—requires an explicit expression for the dissolved solute concentration gradient in the medium at the bubble’s surface (∂c/∂r)R, t. However, the form obtained for this term depends on a variety of choices that can be made. It depends on whether one solves the full diffusion equation or the simpler Laplace equation (the steady-state approximation of the diffusion equation) and on the details of the gas bubble diffusion model that is chosen. Here we provide solutions for the radius vs. time of a dissolving gas bubble for both the full diffusion equation and the Laplace equation, for fixed and variable ambient pressures, ...
Although prompt treatment of decompression sickness (DCS) and arterial gas embolism (AGE) is best... more Although prompt treatment of decompression sickness (DCS) and arterial gas embolism (AGE) is best, diffusion of gases through bubbles and streaming around bubbles likely contributes to better than expected outcomes even after prolonged delays. Quantitative analysis within the limits of the best available model (LHV3) is provided for the application of normobaric oxygen, pressure, and both combined (hyperbaric oxygen) on bubble size. This demonstrates that breathing oxygen before commencing hyperbaric treatment is very effective in shrinking “uncovered” or “bare” bubbles. The analysis further demonstrates that helium bubbles will extinguish faster than the same size nitrogen bubbles. Further, treatment with the USN Table 6 would be expected to eliminate even the largest likely sizes of uncovered bubbles. No model of bubble dynamics presently available accurately predicts the duration of persistence of any size of bubble surrounded by a skin of phospholipids or protein molecules, but ...
Decompression models that describe the distribution of excess dissolved inert gas in the body and... more Decompression models that describe the distribution of excess dissolved inert gas in the body and provide a means of estimating the risk of incurring decompression sickness (DCS) are introduced. Both older deterministic models, the first of which was developed by J.S. Haldane over a century ago, and more recent probabilistic models are described. The models are further distinguished by whether they consist of independent parallel compartments, or interconnected compartments. A compartment, in the context of the independent compartment models, is viewed as a collection of tissues with similar values of their inert gas exchange rate constants. Alternately, and particularly in the context of the interconnected compartment models, a compartment can be viewed as a physical region in the body containing dissolved inert gas, which plays a role in the development of DCS. Interconnected compartments exchange dissolved inert gas both with the circulatory system and with each other, while inde...
Gas Bubble Dynamics in the Human Body, 2018
Solubility, saturation, supersaturation, and undersaturation are all explained in the context of ... more Solubility, saturation, supersaturation, and undersaturation are all explained in the context of gas-liquid solutions. Solutions composed both of one and several different gaseous solutes are considered. The chemical potential of a specific chemical species is introduced and its basic role in solute distribution is described. Solute distribution or redistribution occurs so as to lower the value of its chemical potential, because doing so lowers the system free energy. This is made manifest within a single phase by solutes tending to spontaneously diffuse down their concentration gradients, from higher to lower concentrations. For a pair of contiguous phases, such as a gas and a liquid, the tendency to lower the system free energy causes the volatile solute to be driven from the phase in which its chemical potential is larger to the phase in which it is lower. The crucial role of surface tension on gas bubble pressure is described. It is particularly important for small gas bubbles (<50 μ), and it is expressed quantitatively by the Young-Laplace equation. Surface tension tends to increase the pressure acting on the contents of a gas bubble beyond what it would be from the effect of ambient hydrostatic pressure only.
Journal of applied physiology (Bethesda, Md. : 1985), Jan 14, 2017
Blood flow through intrapulmonary arteriovenous anastomoses (QIPAVA) occurs in healthy humans at ... more Blood flow through intrapulmonary arteriovenous anastomoses (QIPAVA) occurs in healthy humans at rest and during exercise when breathing hypoxic gas mixtures at sea level and may be a source of right-to-left shunt. However, at high altitude QIPAVA is reduced compared to sea level as detected using transthoracic saline contrast echocardiography (TTSCE). It remains unknown whether the reduction in QIPAVA (i.e., lower bubble scores) at high altitude is due to a reduction in bubble stability resulting from the lower barometric pressure (PB), or represents an actual reduction in QIPAVA. To this end, QIPAVA, pulmonary artery systolic pressure (PASP), cardiac output (QT) and the alveolar-to-arterial oxygen difference (AaDO2) were assessed at rest and during exercise (70-190W) in the field (5,260m) and in the lab (1,668m) in 4 conditions; normobaric normoxia (NN; PIO2=121 mmHg, PB=625 mmHg, n=8), normobaric hypoxia (NH; PIO2=76 mmHg, PB=625 mmHg, n=7), hypobaric normoxia (HN; PIO2=121 mmHg,...
Mathematical Biosciences, 2020
We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate t... more We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straightforward extensions of those for a one-component gas bubble. They were derived by using the Young-Laplace equation and Dalton's law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry's law for gas solubilities, and Fick's law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O 2 , N 2 , He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N 2-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N 2 partial pressure can be quite high (e.g. ∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygenrich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.
International Journal of Geometric Methods in Modern Physics, 2008
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah–Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed. A possible application of fluctons in the N = 4 Topologically Twisted Supersymmetric Yang–Mills Theory is explored and the case of gravity is discussed briefly.
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah-Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed, and the case of gravity is discussed briefly.
Fractal/non-fractal morphological transitions allow for the systematic study of the physical mech... more Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of quantities such as the two-point density radial or angular correlations. However, persistent discrepancies found during the analysis of basic models, using these two quantification methods, demand important clarifications. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial-angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters. Specifically, we show that the angular scaling behaves as a critical power-law, whereas the radial scaling as an exponential, that, under the fractal dimension inte...
Revista Mexicana De Fisica, 2007
The topological phases of Yang-Mills theory are studied. The authors propose the fluctons as the ... more The topological phases of Yang-Mills theory are studied. The authors propose the fluctons as the topological fluctuations of vacuum, which are not necessari...
Fractal/non-fractal morphological transitions allow for the systematic study of the physical mech... more Fractal/non-fractal morphological transitions allow for the systematic study of the physical mechanisms behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of the twopoint radialor angular-density correlations. However, these two quantification methods lead to relevant discrepancies during the analysis of basic systems, such as in the diffusion-limited aggregation fractal. Hence, the corresponding clarification regarding the limits of the radial/angular scaling equivalence is needed. In this work, considering three fundamental fractal/non-fractal transitions in two dimensions, we show that the unavoidable emergence of growth anisotropies is responsible for the breaking-down of the radial/angular equivalence, rendering the angular correlation scaling crucial for establishing appropriate order parameters and growth regimes. Specifically, we show that the angular...
From the perspective of topological field theory we explore the physics beyond instantons. We pro... more From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah-Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed, and the case of gravity is discussed briefly.
Entropy, 2021
We propose a novel framework to describe the time-evolution of dilute classical and quantum gases... more We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell–Boltzmann, Fermi–Dirac, or Bose–Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be...