Marek Gutowski - Academia.edu (original) (raw)
Papers by Marek Gutowski
Revealing numerical values of various important and less important physical parameters, not acces... more Revealing numerical values of various important and less important physical parameters, not accessible in direct measurements, is every day activity of experimenters. Students are taught appropriate methods already during their first year of studying. Still later they usually make use of proper software which „knows” how to fit theoretical curves to acquired data. For majority of practitioners the Least Squares Method seems uncontested, no matter that other approaches – usually based on the notion of distance – are also in sporadic use, not excluding ordinary guessing. My aim is to present the power and reliability of completely different approach, based on interval computations. The method is more than obvious once you know it, the only mystery lies in fact of its creation only this year. Leaving aside its reliability, its other important feature is exceptional robustness to outliers, even if they are numerous. Moreover, uncertainties acquired in both coordinates are no problem.
Journal of Magnetic Resonance, 2016
The electric component of microwave radiation acting on the electrons causes an alternating curre... more The electric component of microwave radiation acting on the electrons causes an alternating current which induces electron spin resonance. The oscillating part of kinetic energy of electrons is converted into Zeeman energy via Rashba magnetic field, according to oscillating electron current. Description of this energy conversion is presented and its negative contribution to the resonance signal is explained.
Physical Review B, 1992
It is shown that rapidly quenched Fe«Cr8CuNb3Sil3B9 metallic glass, when annealed in a controlled... more It is shown that rapidly quenched Fe«Cr8CuNb3Sil3B9 metallic glass, when annealed in a controlled way, shows superparamagnetic behavior at elevated temperatures. This property, as has been demonstrated, is due to the fine crystallites of the bcc-Fe(Si) solid solution created within the amorphous matrix by this annealing. Calculations performed show that the volumetric fraction of these particles is equal to 18%%uo, and that their average dimension is as small as 10 nm. It is also shown that the single particle consists of approximately 10 atoms of iron. An analysis performed allows the conclusion that the particles are chemically stable (they do not increase their volumes at the time of measurements at elevated temperatures), and that there are no interactions between them.
Nanoscale objects often behave differently than their 'normal-sized' counterparts. Someti... more Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it is enough to be small in just one direction to exhibit unusual features. One example of such a phenomenon is a very specific in-plane magnetic anisotropy observed sometimes in very thin layers of various materials. Here we recall a peculiar form of the free energy functional nicely describing the experimental findings but completely irrelevant and thus never observed in larger objects.
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of too... more Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are usefull whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perform similar tasks, yet only the interval methods are able to (dis)prove, with mathematical rigor, the (non)existence of desired solution(s). Known are several problems, not presented here, which cannot be effectively solved by any other means. This paper presents basic notions and main ideas of interval calculus and two examples of useful algorithms.
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all the hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and - perhaps - the other non-magnetic hysteretic phenomena.
In this work we report results of ferromagnetic resonance studies of a 6 nm (Ga,Mn)As layer, depo... more In this work we report results of ferromagnetic resonance studies of a 6 nm (Ga,Mn)As layer, deposited on (001)-oriented GaAs. The measurements were performed with in-plane oriented magnetic field, in the temperature range between 5K and 120K. We observe a temperature induced reorientation of the effective in-plane easy axis from [-110] to [110] direction close to the Curie temperature. The behavior of magnetization is described by anisotropy fields, H_eff (= 4 -H_2), H_2∥, and H_4∥. In order to precisely investigate this reorientation, numerical values of anisotropy fields have been determined using powerful - but still largely unknown - interval calculations. In simulation mode this approach makes possible to find all the resonance fields for arbitrarily oriented sample, which is generally intractable analytically. In 'fitting' mode we effectively utilize full experimental information, not only those measurements performed in special, distinguished directions, to reliably ...
The desired result of magnetic anisotropy investigations is the determination of value(s) of vari... more The desired result of magnetic anisotropy investigations is the determination of value(s) of various anisotropy constant(s). This is sometimes difficult, especially when the precise knowledge of saturation magnetization is required, as it happens in ferromagnetic resonance (FMR) studies. In such cases we usually resort to 'trick' and fit our experimental data to the quantity called anisotropy field, which is strictly proportional to the ratio of the searched anisotropy constant and saturation magnetization. Yet, this quantity is scalar, simply a number, and is therefore of little value for modeling or simulations of the magnetostatic or micromagnetic structures. Here we show how to 'translate' the values of magnetic anisotropy constants into the complete vector of magnetic anisotropy field. Our derivation is rigorous and covers the most often encountered cases, from uniaxial to cubic anisotropy.
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of too... more Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are useful whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perform similar tasks, yet only the interval methods are able to (dis)prove, with mathematical rigor, the (non)existence of desired solution(s). Known are several problems, not presented here, which cannot be effectively solved by any other means. This paper presents basic notions and main ideas of interval calculus and two examples of useful algorithms. Keywords reliable computations; guaranteed results; global optimization; algebraic systems; automatic result verification I. What is an interval anyway? Definition: The interval is a bounded subset of real numbers. Formally: (X = [a, b] is an inte...
There is no proof yet of convergence of Genetic Algorithms. We do not supply it too. Instead, we ... more There is no proof yet of convergence of Genetic Algorithms. We do not supply it too. Instead, we present some thoughts and arguments to convince the Reader, that Genetic Algorithms are essentially bound for success. For this purpose, we consider only the crossover operators, singleor multiple-point, together with selection procedure. We also give a proof that the soft selection is superior to other selection schemes.
Over a quarter of century after the invention of genetic algorithms and miriads of their modifica... more Over a quarter of century after the invention of genetic algorithms and miriads of their modifications, as well as successful implementations, we are still lacking many essential details of thorough analysis of it’s inner working. One of such fundamental questions is how many generations do we need to solve the optimization problem? This paper tries to answer this question, albeit in a fuzzy way, making use of the double helix concept. As a byproduct we gain better understanding of the ways, in which the genetic algorithm may be fine tuned.
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and – perhaps – the other non-magnetic hysteretic phenomena. Introduction The major hysteresis loop, observed in the sizable samples of homogeneous ferromagnetic materials, exhibits well...
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and – perhaps – the other non-magnetic hysteretic phenomena. Introduction The major hysteresis loop, observed in the sizable samples of homogeneous ferromagnetic materials, exhibits well...
— Interval analysis, when applied to the so called problem of experimental data fitting, appears ... more — Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all. Worse yet, if this happens, then we are left in the state of complete ignorance concerning the unknown parameters of interest. This is in sharp contrast with widespread statistical methods of data analysis. In this paper I show the connections between those two approaches: how to process experimental data rigorously, using interval methods, and present the final results either as intervals (guaranteed, rigorous results) or in a more familiar probabilistic form: as a mean value and its standard deviation. This article is a companion paper to [1] and is meant to be its extension, but otherwise it is self-contained. This is why we don’t repeat everything here, except for the most important thing: a correct way to bound the distances between uncertain e...
— This is the first of two papers describing the process of fitting experimental data under inter... more — This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Probably the most often encountered use of global optimization methods is finding the so called best fitted values of various parameters, as well as their uncertainties, based on experimental data. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. T...
Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic sy... more Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic systems, in particular magnetic systems. The main idea is to replace a two-dimensional Preisach density with just two real functions, describing in a unique way the reversible and irreversible processes. As a byproduct of our model we prove, that the major hysteresis loop alone is insufficient to produce the unique Preisach map.
Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it i... more Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it is enough to be small in just one direction to exhibit unusual features. One example of such a phenomenon is a very specific in-plane magnetic anisotropy observed sometimes in very thin layers of various materials. Here we recall a peculiar form of the free energy functional nicely describing the experimental findings but completely irrelevant and thus never observed in larger objects.
arXiv: Mathematical Physics, 2002
The aim of this presentation is to promote the use of interval methods in the so called 'hard... more The aim of this presentation is to promote the use of interval methods in the so called 'hard science', like physics or materials science. The example problem, simulation of ferromagnetic resonance spectra in amorphous wire, serves as an evidence of their power, even in their simplest, easy to understand, forms. The spectra, simulated for realistic values of anisotropy constants, show amazingly rich variety of their forms, probably never suspected by experimentalists. The method delivers guaranteed values of resonance fields for any orientation of the sample in the external magnetic field, not just for specific, 'highly symmetric', analytical cases; no resonance field is ever missed. The experimental data, to be published elsewhere, are in excellent concordance with numerical findings.
Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract... more Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract. The term global optimization is used in several contexts. Most oftenwe are interested in finding such a point (or points) in many-dimensional searchspace at which the objective function’s value is optimal, i.e. maximal or minimal.Sometimes, however, we are also interested in stability of the solution, that is inits robustness against small perturbations. Here I present the original, interval-analysis-based family of methods designed for exhaustive exploration of the searchspace. The power of intervalmethods makes it possible toreach all mentioned goalswithin a single, unified framework.
arXiv: Data Analysis, Statistics and Probability, 2017
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach ... more In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such an area in searched parameters' space that generates simulated curve crossing as many acquired experimental points as possible, but at least half of them. Such a task is pretty easy to attack with interval calculations. The problem is, however, that interval calculations operate on guaranteed intervals, that is on pairs of numbers determining minimal and maximal values of measured quantity while in vast majority of cases our measured quantities are expressed rather as a pair of two other numbers: the average value and its standard deviation. Here we propose the combination of interval calculus with basic notions from probability and statistics. This approach makes possible to obtain the results in familiar form as reliable values of searched pa...
Revealing numerical values of various important and less important physical parameters, not acces... more Revealing numerical values of various important and less important physical parameters, not accessible in direct measurements, is every day activity of experimenters. Students are taught appropriate methods already during their first year of studying. Still later they usually make use of proper software which „knows” how to fit theoretical curves to acquired data. For majority of practitioners the Least Squares Method seems uncontested, no matter that other approaches – usually based on the notion of distance – are also in sporadic use, not excluding ordinary guessing. My aim is to present the power and reliability of completely different approach, based on interval computations. The method is more than obvious once you know it, the only mystery lies in fact of its creation only this year. Leaving aside its reliability, its other important feature is exceptional robustness to outliers, even if they are numerous. Moreover, uncertainties acquired in both coordinates are no problem.
Journal of Magnetic Resonance, 2016
The electric component of microwave radiation acting on the electrons causes an alternating curre... more The electric component of microwave radiation acting on the electrons causes an alternating current which induces electron spin resonance. The oscillating part of kinetic energy of electrons is converted into Zeeman energy via Rashba magnetic field, according to oscillating electron current. Description of this energy conversion is presented and its negative contribution to the resonance signal is explained.
Physical Review B, 1992
It is shown that rapidly quenched Fe«Cr8CuNb3Sil3B9 metallic glass, when annealed in a controlled... more It is shown that rapidly quenched Fe«Cr8CuNb3Sil3B9 metallic glass, when annealed in a controlled way, shows superparamagnetic behavior at elevated temperatures. This property, as has been demonstrated, is due to the fine crystallites of the bcc-Fe(Si) solid solution created within the amorphous matrix by this annealing. Calculations performed show that the volumetric fraction of these particles is equal to 18%%uo, and that their average dimension is as small as 10 nm. It is also shown that the single particle consists of approximately 10 atoms of iron. An analysis performed allows the conclusion that the particles are chemically stable (they do not increase their volumes at the time of measurements at elevated temperatures), and that there are no interactions between them.
Nanoscale objects often behave differently than their 'normal-sized' counterparts. Someti... more Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it is enough to be small in just one direction to exhibit unusual features. One example of such a phenomenon is a very specific in-plane magnetic anisotropy observed sometimes in very thin layers of various materials. Here we recall a peculiar form of the free energy functional nicely describing the experimental findings but completely irrelevant and thus never observed in larger objects.
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of too... more Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are usefull whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perform similar tasks, yet only the interval methods are able to (dis)prove, with mathematical rigor, the (non)existence of desired solution(s). Known are several problems, not presented here, which cannot be effectively solved by any other means. This paper presents basic notions and main ideas of interval calculus and two examples of useful algorithms.
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all the hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and - perhaps - the other non-magnetic hysteretic phenomena.
In this work we report results of ferromagnetic resonance studies of a 6 nm (Ga,Mn)As layer, depo... more In this work we report results of ferromagnetic resonance studies of a 6 nm (Ga,Mn)As layer, deposited on (001)-oriented GaAs. The measurements were performed with in-plane oriented magnetic field, in the temperature range between 5K and 120K. We observe a temperature induced reorientation of the effective in-plane easy axis from [-110] to [110] direction close to the Curie temperature. The behavior of magnetization is described by anisotropy fields, H_eff (= 4 -H_2), H_2∥, and H_4∥. In order to precisely investigate this reorientation, numerical values of anisotropy fields have been determined using powerful - but still largely unknown - interval calculations. In simulation mode this approach makes possible to find all the resonance fields for arbitrarily oriented sample, which is generally intractable analytically. In 'fitting' mode we effectively utilize full experimental information, not only those measurements performed in special, distinguished directions, to reliably ...
The desired result of magnetic anisotropy investigations is the determination of value(s) of vari... more The desired result of magnetic anisotropy investigations is the determination of value(s) of various anisotropy constant(s). This is sometimes difficult, especially when the precise knowledge of saturation magnetization is required, as it happens in ferromagnetic resonance (FMR) studies. In such cases we usually resort to 'trick' and fit our experimental data to the quantity called anisotropy field, which is strictly proportional to the ratio of the searched anisotropy constant and saturation magnetization. Yet, this quantity is scalar, simply a number, and is therefore of little value for modeling or simulations of the magnetostatic or micromagnetic structures. Here we show how to 'translate' the values of magnetic anisotropy constants into the complete vector of magnetic anisotropy field. Our derivation is rigorous and covers the most often encountered cases, from uniaxial to cubic anisotropy.
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of too... more Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today. Interval methods are useful whenever we have to deal with uncertainties, which can be rigorously bounded. Fuzzy sets, rough sets and probability calculus can perform similar tasks, yet only the interval methods are able to (dis)prove, with mathematical rigor, the (non)existence of desired solution(s). Known are several problems, not presented here, which cannot be effectively solved by any other means. This paper presents basic notions and main ideas of interval calculus and two examples of useful algorithms. Keywords reliable computations; guaranteed results; global optimization; algebraic systems; automatic result verification I. What is an interval anyway? Definition: The interval is a bounded subset of real numbers. Formally: (X = [a, b] is an inte...
There is no proof yet of convergence of Genetic Algorithms. We do not supply it too. Instead, we ... more There is no proof yet of convergence of Genetic Algorithms. We do not supply it too. Instead, we present some thoughts and arguments to convince the Reader, that Genetic Algorithms are essentially bound for success. For this purpose, we consider only the crossover operators, singleor multiple-point, together with selection procedure. We also give a proof that the soft selection is superior to other selection schemes.
Over a quarter of century after the invention of genetic algorithms and miriads of their modifica... more Over a quarter of century after the invention of genetic algorithms and miriads of their modifications, as well as successful implementations, we are still lacking many essential details of thorough analysis of it’s inner working. One of such fundamental questions is how many generations do we need to solve the optimization problem? This paper tries to answer this question, albeit in a fuzzy way, making use of the double helix concept. As a byproduct we gain better understanding of the ways, in which the genetic algorithm may be fine tuned.
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and – perhaps – the other non-magnetic hysteretic phenomena. Introduction The major hysteresis loop, observed in the sizable samples of homogeneous ferromagnetic materials, exhibits well...
At the very heart of the successful phenomenological model of magnetic hysteresis there is the so... more At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and – perhaps – the other non-magnetic hysteretic phenomena. Introduction The major hysteresis loop, observed in the sizable samples of homogeneous ferromagnetic materials, exhibits well...
— Interval analysis, when applied to the so called problem of experimental data fitting, appears ... more — Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all. Worse yet, if this happens, then we are left in the state of complete ignorance concerning the unknown parameters of interest. This is in sharp contrast with widespread statistical methods of data analysis. In this paper I show the connections between those two approaches: how to process experimental data rigorously, using interval methods, and present the final results either as intervals (guaranteed, rigorous results) or in a more familiar probabilistic form: as a mean value and its standard deviation. This article is a companion paper to [1] and is meant to be its extension, but otherwise it is self-contained. This is why we don’t repeat everything here, except for the most important thing: a correct way to bound the distances between uncertain e...
— This is the first of two papers describing the process of fitting experimental data under inter... more — This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Probably the most often encountered use of global optimization methods is finding the so called best fitted values of various parameters, as well as their uncertainties, based on experimental data. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. T...
Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic sy... more Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic systems, in particular magnetic systems. The main idea is to replace a two-dimensional Preisach density with just two real functions, describing in a unique way the reversible and irreversible processes. As a byproduct of our model we prove, that the major hysteresis loop alone is insufficient to produce the unique Preisach map.
Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it i... more Nanoscale objects often behave differently than their 'normal-sized' counterparts. Sometimes it is enough to be small in just one direction to exhibit unusual features. One example of such a phenomenon is a very specific in-plane magnetic anisotropy observed sometimes in very thin layers of various materials. Here we recall a peculiar form of the free energy functional nicely describing the experimental findings but completely irrelevant and thus never observed in larger objects.
arXiv: Mathematical Physics, 2002
The aim of this presentation is to promote the use of interval methods in the so called 'hard... more The aim of this presentation is to promote the use of interval methods in the so called 'hard science', like physics or materials science. The example problem, simulation of ferromagnetic resonance spectra in amorphous wire, serves as an evidence of their power, even in their simplest, easy to understand, forms. The spectra, simulated for realistic values of anisotropy constants, show amazingly rich variety of their forms, probably never suspected by experimentalists. The method delivers guaranteed values of resonance fields for any orientation of the sample in the external magnetic field, not just for specific, 'highly symmetric', analytical cases; no resonance field is ever missed. The experimental data, to be published elsewhere, are in excellent concordance with numerical findings.
Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract... more Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract. The term global optimization is used in several contexts. Most oftenwe are interested in finding such a point (or points) in many-dimensional searchspace at which the objective function’s value is optimal, i.e. maximal or minimal.Sometimes, however, we are also interested in stability of the solution, that is inits robustness against small perturbations. Here I present the original, interval-analysis-based family of methods designed for exhaustive exploration of the searchspace. The power of intervalmethods makes it possible toreach all mentioned goalswithin a single, unified framework.
arXiv: Data Analysis, Statistics and Probability, 2017
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach ... more In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such an area in searched parameters' space that generates simulated curve crossing as many acquired experimental points as possible, but at least half of them. Such a task is pretty easy to attack with interval calculations. The problem is, however, that interval calculations operate on guaranteed intervals, that is on pairs of numbers determining minimal and maximal values of measured quantity while in vast majority of cases our measured quantities are expressed rather as a pair of two other numbers: the average value and its standard deviation. Here we propose the combination of interval calculus with basic notions from probability and statistics. This approach makes possible to obtain the results in familiar form as reliable values of searched pa...