The Hunga Tonga Hunga Ha’apai submarine volcano has experienced repeated eruptions in the latest decades.The recent one,in January 2022,released an enormous amount of energy inducing global perturbations,as tsunamis ...The Hunga Tonga Hunga Ha’apai submarine volcano has experienced repeated eruptions in the latest decades.The recent one,in January 2022,released an enormous amount of energy inducing global perturbations,as tsunamis and atmospheric waves.The structure of the volcano is poorly understood,especially its internal structure.Deep-seated magmatic connections are difficult to define or visualize.We use a high-resolution gravity data set obtained via satellite to calculate the Bouguer anomaly over its structure,to perform a preliminary exploration of its interior.Executing 3D gravity inversions,we find a complex plumbing system with various exhaust trajectories and multiple surface pockets of low-density material within the volcanic edifice;some appear to be associated with ring fractures.This is in line with the report of the 2009 eruption,described as beginning from multiple vents.We found no signs of a magma chamber within 6 km depth,although several volcanic conduits are identified from such depth to the surface.Density variations occur within a plumbing conduit or may vary from one conduit to another in the same volcano.These models yield quantitative estimates for areas of magma-water interaction,constituting a baseline to compare with structural changes to be induced in future eruptions.展开更多
We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes ...We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes the value S at time t. We then use Samuelson’s formula with this factor which is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can systematically introduce the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamical system in the form of a set of ordinary differential equations we only have to solve a partial differential equation for the transition probability density. In this context, we verify, for the sake of consistency, that this formula coincides with the Black-Scholes model and compare several numerical implementations.展开更多
A new analysis of a previously studied traveling agent model, showed that there is a relation between the degree of homogeneity of the medium where the agents move, agent motion patterns, and the noise generated from ...A new analysis of a previously studied traveling agent model, showed that there is a relation between the degree of homogeneity of the medium where the agents move, agent motion patterns, and the noise generated from their displacements. We proved that for a particular value of homogeneity, the system self organizes in a state where the agents carry out Lévy walks and the displacement signal corresponds to 1/f noise. Using probabilistic arguments, we conjectured that 1/f noise is a fingerprint of a statistical phase transition, from randomness (disorder) to predictability (order), and that it emerges from the contextuality nature of the system which generates it.展开更多
Satellite data sets are an asset in global gravity collections;their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in g...Satellite data sets are an asset in global gravity collections;their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing;with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data;we conclude that the GGMplus data set offers higher resolution in the cases analyzed.展开更多
The remaining fault scarps of a collapsed structure at 32 ka,named Tetelzingo crater,that included Citlaltépetl(CT)volcano,and the associated gravity field,are the basis of a reconstruction of the structures invo...The remaining fault scarps of a collapsed structure at 32 ka,named Tetelzingo crater,that included Citlaltépetl(CT)volcano,and the associated gravity field,are the basis of a reconstruction of the structures involved.The gravity field is obtained from the GGMplus model,from which 3D inversions at resolutions of 1000,500,and 250 m are performed.Low-gravity anomalies are associated with Sierra Negra(4580 m)and Citlaltépetl(5521 m)volcanoes,as well as with the Chichimeco Dome Complex(~4000 m)(CDC).They are located within a SW-NE anomaly that serves as a constraint to the reconstruction.The associ-ated Bouguer anomaly appears as a continuous low-gravity surface;however,its vertical derivative Dz shows that the sources of those three structures are separated.The fault scarps are complemented with inferred trajectories that suggest the existence of two volcanoes before the collapse at 32 ka:Citlaltépetl and the Ancestral Teteltzingo.Density cross-sections identify three stratified magmatic deposits under the summit of CT.On the summit of CT,there is an anomalous concentration of high-density materials,attributed to the presence of domes and lava flows,which mask the position of the volcano’s chimney.The existence of the Ancestral Teteltzingo volcano(ATE)is inferred NE of CT from the associated density distribution;CDC is at the center of the ATE struc-ture and is interpreted as a resurgent activity at<8 ka.Sierra Negra volcano(SN)shows low-density distributions in and around its summit,contradicting the idea that this is an extinct volcano.展开更多
This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. ...This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.展开更多
In this paper, a system of fractional differential equations that model the synchronized bioluminescence behavior of a set of fireflies put on two spatial arrangements is presented; the alternative representation of t...In this paper, a system of fractional differential equations that model the synchronized bioluminescence behavior of a set of fireflies put on two spatial arrangements is presented; the alternative representation of these equations contains fractional operators of IAouvillc-Caputo type. The objective of the model is to qualitatively recover synchronization and show that it is persistent. It is shown that the effort made by each firefly glow changes with respect to the number of male competitors and the distance between them. The conditions on biological parameters are interpreted.展开更多
Los Humeros is a Pleistocene caldera in the eastern portion of the Trans Mexican Volcanic Belt,exploited for geothermal resources for over five decades,presently providing over 90 MWe.We model the gravity field,obtain...Los Humeros is a Pleistocene caldera in the eastern portion of the Trans Mexican Volcanic Belt,exploited for geothermal resources for over five decades,presently providing over 90 MWe.We model the gravity field,obtaining 3D density models from high-resolution(220 m)satellite-derived gravity data and compare these models with geological and magneto-telluric descriptions detailed elsewhere.An additional comparison with a geological E-W section indicates that the most voluminous caldera formations coincide with a low-density region extending from the surface to below 6 km bsl that is likely associated with the caldera activity.Interpretation of three additional density crosssections leads us to infer that the magmatic system feeding Los Humeros also has a component surfacing 12 km north of the center of the caldera,a result that is first disclosed here.Comparison of the density distributions with three corresponding electrical resistivity profiles obtained elsewhere from magnetotelluric soundings shows that low-resistivity regions prevail above 1 km asl where high-density pockets alternate with low-density regions.High-resistivity regions can be associated with high-or low-density regions.Vertical channels-2 km wide extending 6-8 km,of intermediate resistivity(150-300 ohmm),appear in three resistivity profiles analyzed.In one case,it coincides with a low-density region(<2.57 g/cm3)and in the others appear associated with fractured regions pertaining to the resurgent activity.We find that the magma chamber is not directly located under Los Humeros caldera;it is rather displaced -7 km to the north of the location of the caldera.Comparison with two shallow resistivity profiles shows that geothermal fluids induce propylitic alterations in high-and low-density regions.展开更多
基金support from the Consejo Nacional de Ciencia y Tecnología(CONACYT,México)supported by Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas,Universidad Nacional Autónoma de México。
文摘The Hunga Tonga Hunga Ha’apai submarine volcano has experienced repeated eruptions in the latest decades.The recent one,in January 2022,released an enormous amount of energy inducing global perturbations,as tsunamis and atmospheric waves.The structure of the volcano is poorly understood,especially its internal structure.Deep-seated magmatic connections are difficult to define or visualize.We use a high-resolution gravity data set obtained via satellite to calculate the Bouguer anomaly over its structure,to perform a preliminary exploration of its interior.Executing 3D gravity inversions,we find a complex plumbing system with various exhaust trajectories and multiple surface pockets of low-density material within the volcanic edifice;some appear to be associated with ring fractures.This is in line with the report of the 2009 eruption,described as beginning from multiple vents.We found no signs of a magma chamber within 6 km depth,although several volcanic conduits are identified from such depth to the surface.Density variations occur within a plumbing conduit or may vary from one conduit to another in the same volcano.These models yield quantitative estimates for areas of magma-water interaction,constituting a baseline to compare with structural changes to be induced in future eruptions.
文摘We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes the value S at time t. We then use Samuelson’s formula with this factor which is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can systematically introduce the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamical system in the form of a set of ordinary differential equations we only have to solve a partial differential equation for the transition probability density. In this context, we verify, for the sake of consistency, that this formula coincides with the Black-Scholes model and compare several numerical implementations.
文摘A new analysis of a previously studied traveling agent model, showed that there is a relation between the degree of homogeneity of the medium where the agents move, agent motion patterns, and the noise generated from their displacements. We proved that for a particular value of homogeneity, the system self organizes in a state where the agents carry out Lévy walks and the displacement signal corresponds to 1/f noise. Using probabilistic arguments, we conjectured that 1/f noise is a fingerprint of a statistical phase transition, from randomness (disorder) to predictability (order), and that it emerges from the contextuality nature of the system which generates it.
文摘Satellite data sets are an asset in global gravity collections;their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing;with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data;we conclude that the GGMplus data set offers higher resolution in the cases analyzed.
基金supported by IIMAS and the Geophysics Institute,both at UNAMmaterial support from both institutions.This research did not receive any specific grant from funding agencies in the public,commer-cial,or nonprofit sectors.
文摘The remaining fault scarps of a collapsed structure at 32 ka,named Tetelzingo crater,that included Citlaltépetl(CT)volcano,and the associated gravity field,are the basis of a reconstruction of the structures involved.The gravity field is obtained from the GGMplus model,from which 3D inversions at resolutions of 1000,500,and 250 m are performed.Low-gravity anomalies are associated with Sierra Negra(4580 m)and Citlaltépetl(5521 m)volcanoes,as well as with the Chichimeco Dome Complex(~4000 m)(CDC).They are located within a SW-NE anomaly that serves as a constraint to the reconstruction.The associ-ated Bouguer anomaly appears as a continuous low-gravity surface;however,its vertical derivative Dz shows that the sources of those three structures are separated.The fault scarps are complemented with inferred trajectories that suggest the existence of two volcanoes before the collapse at 32 ka:Citlaltépetl and the Ancestral Teteltzingo.Density cross-sections identify three stratified magmatic deposits under the summit of CT.On the summit of CT,there is an anomalous concentration of high-density materials,attributed to the presence of domes and lava flows,which mask the position of the volcano’s chimney.The existence of the Ancestral Teteltzingo volcano(ATE)is inferred NE of CT from the associated density distribution;CDC is at the center of the ATE struc-ture and is interpreted as a resurgent activity at<8 ka.Sierra Negra volcano(SN)shows low-density distributions in and around its summit,contradicting the idea that this is an extinct volcano.
文摘This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.
文摘In this paper, a system of fractional differential equations that model the synchronized bioluminescence behavior of a set of fireflies put on two spatial arrangements is presented; the alternative representation of these equations contains fractional operators of IAouvillc-Caputo type. The objective of the model is to qualitatively recover synchronization and show that it is persistent. It is shown that the effort made by each firefly glow changes with respect to the number of male competitors and the distance between them. The conditions on biological parameters are interpreted.
基金supported by IIMAS and Instituto de Geofísica,UNAMwe acknowledge material support from both institutions.
文摘Los Humeros is a Pleistocene caldera in the eastern portion of the Trans Mexican Volcanic Belt,exploited for geothermal resources for over five decades,presently providing over 90 MWe.We model the gravity field,obtaining 3D density models from high-resolution(220 m)satellite-derived gravity data and compare these models with geological and magneto-telluric descriptions detailed elsewhere.An additional comparison with a geological E-W section indicates that the most voluminous caldera formations coincide with a low-density region extending from the surface to below 6 km bsl that is likely associated with the caldera activity.Interpretation of three additional density crosssections leads us to infer that the magmatic system feeding Los Humeros also has a component surfacing 12 km north of the center of the caldera,a result that is first disclosed here.Comparison of the density distributions with three corresponding electrical resistivity profiles obtained elsewhere from magnetotelluric soundings shows that low-resistivity regions prevail above 1 km asl where high-density pockets alternate with low-density regions.High-resistivity regions can be associated with high-or low-density regions.Vertical channels-2 km wide extending 6-8 km,of intermediate resistivity(150-300 ohmm),appear in three resistivity profiles analyzed.In one case,it coincides with a low-density region(<2.57 g/cm3)and in the others appear associated with fractured regions pertaining to the resurgent activity.We find that the magma chamber is not directly located under Los Humeros caldera;it is rather displaced -7 km to the north of the location of the caldera.Comparison with two shallow resistivity profiles shows that geothermal fluids induce propylitic alterations in high-and low-density regions.
