TY - GEN
T1 - Eco-friendly flexible wireless platforms by 3D printing pen
AU - Mehmood, Adnan
AU - Chen, Xiaochen
AU - He, Han
AU - Ukkonen, Leena
AU - Virkki, Johanna
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We present a new type of 3D printing pen fabrication of flexible passive UHF (ultra-high frequency) RFID (radio frequency identification) platforms. The used 3D printing material is cost-effective and fully biodegradable. The tag antenna is fabricated from conductive thread. This antenna and antenna-IC interconnections are fixed inside the 3D-printed platforms with 3D-printed fasteners. Thus, our solution requires no additional process steps or chemicals. For wireless evaluation, the platforms are firstly bended around different size cylinders, with and without a 3D-printed top layer. Further, the reliability of the platforms in high moisture is also tested, by keeping the platforms in water for 1 minute. Based on these preliminary tests, our manufacturing method enables establishment of highly reliable eco-friendly platforms with excellent wireless performance. The developed solutions have versatile future applications, especially in the field of wearable electronics, where lightweight, cost-effective, flexible, and waterproof platforms are needed.
AB - We present a new type of 3D printing pen fabrication of flexible passive UHF (ultra-high frequency) RFID (radio frequency identification) platforms. The used 3D printing material is cost-effective and fully biodegradable. The tag antenna is fabricated from conductive thread. This antenna and antenna-IC interconnections are fixed inside the 3D-printed platforms with 3D-printed fasteners. Thus, our solution requires no additional process steps or chemicals. For wireless evaluation, the platforms are firstly bended around different size cylinders, with and without a 3D-printed top layer. Further, the reliability of the platforms in high moisture is also tested, by keeping the platforms in water for 1 minute. Based on these preliminary tests, our manufacturing method enables establishment of highly reliable eco-friendly platforms with excellent wireless performance. The developed solutions have versatile future applications, especially in the field of wearable electronics, where lightweight, cost-effective, flexible, and waterproof platforms are needed.
U2 - 10.1109/PIERS-Fall48861.2019.9021887
DO - 10.1109/PIERS-Fall48861.2019.9021887
M3 - Conference contribution
T3 - 2019 Photonics and Electromagnetics Research Symposium - Fall, PIERS - Fall 2019 - Proceedings
SP - 2422
EP - 2425
BT - 2019 Photonics and Electromagnetics Research Symposium - Fall, PIERS - Fall 2019 - Proceedings
PB - IEEE
ER -
TY - GEN
T1 - Embroidered and e-textile conductors embedded inside 3D-printed structures
AU - Khan, Zahangir
AU - He, Han
AU - Chen, Xiaochen
AU - Ukkonen, Leena
AU - Virkki, Johanna
PY - 2019/12/1
Y1 - 2019/12/1
N2 - This paper discusses the fabrication and wireless performance evaluation of textile-integrated passive ultra-high frequency (UHF) radiofrequency identification (RFID) tags, which are embedded inside flexible additively manufactured wireless platforms. Two different methods are utilized to fabricate the tag antenna, including embroidery with conductive thread and conductive e-textiles. After antenna fabrication, RFID ICs (integrated circuits) are attached to the antenna patterns, to achieve fully functional RFID tags. These two types of tags are embedded inside flexible 3D-printed platforms, which can protect the tags from mechanical stresses and moisture. Our preliminary results show that the peak read ranges of both types of platforms are higher than 6 meters, which are suitable for versatile wireless applications.
AB - This paper discusses the fabrication and wireless performance evaluation of textile-integrated passive ultra-high frequency (UHF) radiofrequency identification (RFID) tags, which are embedded inside flexible additively manufactured wireless platforms. Two different methods are utilized to fabricate the tag antenna, including embroidery with conductive thread and conductive e-textiles. After antenna fabrication, RFID ICs (integrated circuits) are attached to the antenna patterns, to achieve fully functional RFID tags. These two types of tags are embedded inside flexible 3D-printed platforms, which can protect the tags from mechanical stresses and moisture. Our preliminary results show that the peak read ranges of both types of platforms are higher than 6 meters, which are suitable for versatile wireless applications.
U2 - 10.1109/PIERS-Fall48861.2019.9021681
DO - 10.1109/PIERS-Fall48861.2019.9021681
M3 - Conference contribution
SP - 1675
EP - 1680
BT - 2019 Photonics and Electromagnetics Research Symposium - Fall, PIERS - Fall 2019 - Proceedings
PB - IEEE
ER -
TY - GEN
T1 - Maintenance-free moisture sensor on dishcloth substrate
AU - Chen, Xiaochen
AU - He, Han
AU - Yang, Yunshan
AU - Gou, Meinan
AU - Sydanheimo, Lauri
AU - Ukkonen, Leena
AU - Virkki, Johanna
PY - 2019/12/1
Y1 - 2019/12/1
N2 - In this study, a passive UHF RFID-based moisture sensor is fabricated and evaluated. The sensor tag can sense the high humidity of the environment and indicate it with a permanent change in its backscattered signal. The sensor tag antenna and antenna-IC interconnections are fabricated on a biodegradable dishcloth material using conductive thread. The sensors are tested in an anechoic chamber and in normal office conditions, when initially dry, after dipped into water for 1 minute, and again after 24 hours of drying in air. These sensor tags initially show read ranges of 6-9 meters throughout the global UHF RFID frequency band. When wet, the read range decreases to 5 meters, while after 24 hours of drying, the read ranges of the tags permanently decrease to around 2-4 meters. The dishcloth material comes thicker when wet, also causing a change to the embroidered antenna structure, finally causing the permanent change in the backscattered signal. In normal office conditions, moisture causes the average backscattered signal an obvious change from around -66 dBm to -69 dBm.
AB - In this study, a passive UHF RFID-based moisture sensor is fabricated and evaluated. The sensor tag can sense the high humidity of the environment and indicate it with a permanent change in its backscattered signal. The sensor tag antenna and antenna-IC interconnections are fabricated on a biodegradable dishcloth material using conductive thread. The sensors are tested in an anechoic chamber and in normal office conditions, when initially dry, after dipped into water for 1 minute, and again after 24 hours of drying in air. These sensor tags initially show read ranges of 6-9 meters throughout the global UHF RFID frequency band. When wet, the read range decreases to 5 meters, while after 24 hours of drying, the read ranges of the tags permanently decrease to around 2-4 meters. The dishcloth material comes thicker when wet, also causing a change to the embroidered antenna structure, finally causing the permanent change in the backscattered signal. In normal office conditions, moisture causes the average backscattered signal an obvious change from around -66 dBm to -69 dBm.
U2 - 10.1109/PIERS-Fall48861.2019.9021487
DO - 10.1109/PIERS-Fall48861.2019.9021487
M3 - Conference contribution
SP - 2418
EP - 2421
BT - 2019 Photonics and Electromagnetics Research Symposium - Fall, PIERS - Fall 2019 - Proceedings
PB - IEEE
ER -
TY - GEN
T1 - Passive UHF RFID-based user interface on a wooden surface
AU - Mehmood, Adnan
AU - Vianto, Ville
AU - He, Han
AU - Chen, Xiaochen
AU - Buruk, Oguz Oz
AU - Ukkonen, Leena
AU - Virkki, Johanna
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We present a passive ultra-high frequency (UHF) radio frequency identification (RFID)-based human-technology interface platform. The platform comprises of two dipole antennas and three integrated circuits (IC), each with a unique ID. The platform, which is fixed on a wooden table by cutting the antennas and antenna-IC interconnections from copper tape, can be used for push button and swipe controlling. Each IC can be activated, i.e., connected to the antennas, by touching with finger. As the RFID reader can be connected to any application through WIFI, these ICs can act as wireless input points integrated into furniture, items, and textiles, where they can be used as inputs to desired digital actions. The platform allows all connected devices to be controlled accurately and effortlessly, which will take the convenience of implementation and utilization of these systems to a new level. As a preliminary trial, the platform was tested by two people giving 200 random inputs and 98% and 99% success rates were achieved. Based on these results, this type of passive RFID-based solutions could be used for administrating interfaces that would administer wide variety of interaction modalities, such as touch or tangible interaction on flat surfaces (e.g., tabletop surfaces, walls, doors).
AB - We present a passive ultra-high frequency (UHF) radio frequency identification (RFID)-based human-technology interface platform. The platform comprises of two dipole antennas and three integrated circuits (IC), each with a unique ID. The platform, which is fixed on a wooden table by cutting the antennas and antenna-IC interconnections from copper tape, can be used for push button and swipe controlling. Each IC can be activated, i.e., connected to the antennas, by touching with finger. As the RFID reader can be connected to any application through WIFI, these ICs can act as wireless input points integrated into furniture, items, and textiles, where they can be used as inputs to desired digital actions. The platform allows all connected devices to be controlled accurately and effortlessly, which will take the convenience of implementation and utilization of these systems to a new level. As a preliminary trial, the platform was tested by two people giving 200 random inputs and 98% and 99% success rates were achieved. Based on these results, this type of passive RFID-based solutions could be used for administrating interfaces that would administer wide variety of interaction modalities, such as touch or tangible interaction on flat surfaces (e.g., tabletop surfaces, walls, doors).
U2 - 10.1109/PIERS-Fall48861.2019.9021441
DO - 10.1109/PIERS-Fall48861.2019.9021441
M3 - Conference contribution
SP - 1760
EP - 1763
BT - 2019 Photonics and Electromagnetics Research Symposium - Fall, PIERS - Fall 2019 - Proceedings
PB - IEEE
ER -
TY - JOUR
T1 - A graph theoretic approach to construct desired cryptographic boolean functions
AU - Ghorbani, Modjtaba
AU - Dehmer, Matthias
AU - Taghvayi-Yazdelli, Vahid
AU - Emmert-Streib, Frank
PY - 2019/6/1
Y1 - 2019/6/1
N2 - In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictableWalsh spectrum. A lot of cryptographic properties of boolean functions can be presented by theirWalsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desiredWalsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
AB - In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictableWalsh spectrum. A lot of cryptographic properties of boolean functions can be presented by theirWalsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desiredWalsh spectrum and investigate their non-linearity, algebraic and correlation immunity.
KW - Algebraic immunity
KW - Boolean functions
KW - Cayley graphs
KW - Non-linearity
KW - Walsh spectrum
U2 - 10.3390/axioms8020040
DO - 10.3390/axioms8020040
M3 - Article
VL - 8
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 2
M1 - 40
ER -
TY - JOUR
T1 - A note on distance-based entropy of dendrimers
AU - Ghorbani, Modjtaba
AU - Dehmer, Matthias
AU - Zangi, Samaneh
AU - Mowshowitz, Abbe
AU - Emmert-Streib, Frank
PY - 2019
Y1 - 2019
N2 - This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs.
AB - This paper introduces a variant of entropy measures based on vertex eccentricity and applies it to all graphs representing the isomers of octane. Taking into account the vertex degree as well (degree-ecc-entropy), we find a good correlation with the acentric factor of octane isomers. In particular, we compute the degree-ecc-entropy for three classes of dendrimer graphs.
KW - Dendrimer
KW - Graph entropy
KW - Vertex eccentricity
U2 - 10.3390/axioms8030098
DO - 10.3390/axioms8030098
M3 - Article
VL - 8
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 3
M1 - 98
ER -
TY - JOUR
T1 - Continuum approach to high-cycle fatigue. The finite life-time case with stochastic stress history
AU - Orelma, H.
PY - 2019
Y1 - 2019
N2 - In this paper, we consider continuum approach for high-cycle fatigue in the case where life-time is finite. The method is based on differential equations and all basic concepts are explained. A stress history is assumed to be a stochastic process and this leads us to the theory of stochastic differential equations. The life-time is a quantity, which tells us when the breakdown of the material happens. In this method, it is naturally a random variable. The basic assumption is, that the distribution of the life-time is log-normal or Weibull. We give a numerical basic example to demonstrate the method.
AB - In this paper, we consider continuum approach for high-cycle fatigue in the case where life-time is finite. The method is based on differential equations and all basic concepts are explained. A stress history is assumed to be a stochastic process and this leads us to the theory of stochastic differential equations. The life-time is a quantity, which tells us when the breakdown of the material happens. In this method, it is naturally a random variable. The basic assumption is, that the distribution of the life-time is log-normal or Weibull. We give a numerical basic example to demonstrate the method.
KW - Evolution equation
KW - High-cycle fatigue
KW - Life-time
U2 - 10.14498/vsgtu1705
DO - 10.14498/vsgtu1705
M3 - Article
VL - 23
SP - 452
EP - 463
JO - Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Seriya Fiziko-Matematicheskie Nauki
JF - Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Seriya Fiziko-Matematicheskie Nauki
SN - 1991-8615
IS - 3
ER -
TY - GEN
T1 - Structural Similarity Index with Predictability of Image Blocks
AU - Ponomarenko, Mykola
AU - Egiazarian, Karen
AU - Lukin, Vladimir
AU - Abramova, Victoriya
N1 - JUFOID=72887
EXT="Lukin, Vladimir"
PY - 2018/9/10
Y1 - 2018/9/10
N2 - Structural similarity index (SSIM) is a widely used full-reference metric for assessment of visual quality of images and remote sensing data. It is calculated in a block-wise manner and is based on multiplication of three components: similarity of means of image blocks, similarity of contrasts and a correlation factor. In this paper, two modifications of SSIM are proposed. First, a fourth multiplicative component is introduced to SSIM (thus obtaining SSIM4) that describes a similarity of predictability of image blocks. A predictability for a given block is calculated as a minimal value of mean square error between the considered block and the neighboring blocks. Second, a simple scheme for calculating the metrics SSIM and SSIM4 for color images is proposed and optimized. Effectiveness of the proposed modifications is confirmed for the specialized image databases TID2013, LIVE, and FLT. In particular, the Spearman rank order correlation coefficient (SROCC) for the recently introduced FLT Database, calculated between the proposed metric color SSIM4 and mean opinion scores (MOS), has reached the value 0.85 (the best result for all compared metrics) whilst for SSIM it is equal to 0.58.
AB - Structural similarity index (SSIM) is a widely used full-reference metric for assessment of visual quality of images and remote sensing data. It is calculated in a block-wise manner and is based on multiplication of three components: similarity of means of image blocks, similarity of contrasts and a correlation factor. In this paper, two modifications of SSIM are proposed. First, a fourth multiplicative component is introduced to SSIM (thus obtaining SSIM4) that describes a similarity of predictability of image blocks. A predictability for a given block is calculated as a minimal value of mean square error between the considered block and the neighboring blocks. Second, a simple scheme for calculating the metrics SSIM and SSIM4 for color images is proposed and optimized. Effectiveness of the proposed modifications is confirmed for the specialized image databases TID2013, LIVE, and FLT. In particular, the Spearman rank order correlation coefficient (SROCC) for the recently introduced FLT Database, calculated between the proposed metric color SSIM4 and mean opinion scores (MOS), has reached the value 0.85 (the best result for all compared metrics) whilst for SSIM it is equal to 0.58.
KW - image visual quality assessment
KW - masking of unpredictable energy
U2 - 10.1109/MMET.2018.8460285
DO - 10.1109/MMET.2018.8460285
M3 - Conference contribution
SN - 9781538654385
VL - 2018-July
SP - 115
EP - 118
BT - 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory, MMET 2018 - Proceedings
PB - IEEE COMPUTER SOCIETY PRESS
ER -
TY - JOUR
T1 - Eigenstates and dynamics of Hookes atom
T2 - Exact results and path integral simulations
AU - Gholizadehkalkhoran, Hossein
AU - Ruokosenmäki, Ilkka
AU - Rantala, Tapio T.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.
AB - The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.
U2 - 10.1063/1.5028503
DO - 10.1063/1.5028503
M3 - Article
VL - 59
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 5
M1 - 052104
ER -
TY - JOUR
T1 - Toward measuring network aesthetics based on symmetry
AU - Chen, Zengqiang
AU - Dehmer, Matthias
AU - Emmert-Streib, Frank
AU - Mowshowitz, Abbe
AU - Shi, Yongtang
PY - 2017/6/1
Y1 - 2017/6/1
N2 - In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer's perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics.
AB - In this exploratory paper, we discuss quantitative graph-theoretical measures of network aesthetics. Related work in this area has typically focused on geometrical features (e.g., line crossings or edge bendiness) of drawings or visual representations of graphs which purportedly affect an observer's perception. Here we take a very different approach, abandoning reliance on geometrical properties, and apply information-theoretic measures to abstract graphs and networks directly (rather than to their visual representaions) as a means of capturing classical appreciation of structural symmetry. Examples are used solely to motivate the approach to measurement, and to elucidate our symmetry-based mathematical theory of network aesthetics.
KW - Aesthetical theory
KW - Aesthetics
KW - Entropy
KW - Network aesthetics
KW - Networks
U2 - 10.3390/axioms6020012
DO - 10.3390/axioms6020012
M3 - Article
VL - 6
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 2
M1 - 12
ER -
TY - JOUR
T1 - Search reliability and search efficiency of combined Lévy-Brownian motion
T2 - Long relocations mingled with thorough local exploration
AU - Palyulin, Vladimir V.
AU - Chechkin, Aleksei V.
AU - Klages, Rainer
AU - Metzler, Ralf
PY - 2016/9/8
Y1 - 2016/9/8
N2 - A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α <1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.
AB - A combined dynamics consisting of Brownian motion and Lévy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Lévy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Lévy flights with stable exponent α <1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Lévy flight component.
KW - Brownian motion
KW - first arrival
KW - first passage
KW - Lévy flights
KW - random search process
UR - http://www.scopus.com/inward/record.url?scp=84989172145&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/49/39/394002
DO - 10.1088/1751-8113/49/39/394002
M3 - Article
VL - 49
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 39
M1 - 394002
ER -
TY - JOUR
T1 - Hermitian one-particle density matrix through a semiclassical gradient expansion
AU - Bencheikh, K.
AU - Räsänen, E.
PY - 2015/12/9
Y1 - 2015/12/9
N2 - We carry out the semiclassical expansion of the one-particle density matrix up to the second order in h. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.
AB - We carry out the semiclassical expansion of the one-particle density matrix up to the second order in h. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.
KW - density matrix
KW - density-functional theory
KW - Wigner transform
U2 - 10.1088/1751-8113/49/1/015205
DO - 10.1088/1751-8113/49/1/015205
M3 - Article
VL - 49
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 1
M1 - 015205
ER -
TY - JOUR
T1 - Quantifying the non-ergodicity of scaled Brownian motion
AU - Safdari, Hadiseh
AU - Cherstvy, Andrey G.
AU - Chechkin, Aleksei V.
AU - Thiel, Felix
AU - Sokolov, Igor M.
AU - Metzler, Ralf
PY - 2015/9/18
Y1 - 2015/9/18
N2 - We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form $D(t)\simeq {t}^{\alpha -1}$. We compute the ergodicity breaking parameter EB in the entire range of scaling exponents α, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Δ the EB parameter as function of the scaling exponent α has no divergence at α = 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
AB - We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form $D(t)\simeq {t}^{\alpha -1}$. We compute the ergodicity breaking parameter EB in the entire range of scaling exponents α, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Δ the EB parameter as function of the scaling exponent α has no divergence at α = 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
KW - ageing
KW - anomalous diffusion
KW - scaled Brownian motion
UR - http://www.scopus.com/inward/record.url?scp=84940069543&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/48/37/375002
DO - 10.1088/1751-8113/48/37/375002
M3 - Article
VL - 48
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 37
M1 - 375002
ER -
TY - JOUR
T1 - Ageing first passage time density in continuous time random walks and quenched energy landscapes
AU - Krüsemann, Henning
AU - Godec, Aljaž
AU - Metzler, Ralf
PY - 2015/7/17
Y1 - 2015/7/17
N2 - We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function φ (t) ≃ t-1-α (0 ≤ α ≤ 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time ta, the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < α < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < α < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
AB - We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function φ (t) ≃ t-1-α (0 ≤ α ≤ 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time ta, the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < α < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < α < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
KW - anomalous diffusion
KW - first passage
KW - random walks
UR - http://www.scopus.com/inward/record.url?scp=84937118398&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/48/28/285001
DO - 10.1088/1751-8113/48/28/285001
M3 - Article
VL - 48
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 28
M1 - 285001
ER -
TY - JOUR
T1 - Conformational properties of complex polymers
T2 - Rosette versus star-like structures
AU - Blavatska, V.
AU - Metzler, R.
PY - 2015/4/7
Y1 - 2015/4/7
N2 - Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f1 loops (petals) and f2 linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius Rg and asphericity Â of typical conformation as functions of parameters f1, f2. In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.
AB - Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f1 loops (petals) and f2 linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius Rg and asphericity Â of typical conformation as functions of parameters f1, f2. In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.
KW - conformational properties
KW - path integration
KW - polymers
UR - http://www.scopus.com/inward/record.url?scp=84930681628&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/48/13/135001
DO - 10.1088/1751-8113/48/13/135001
M3 - Article
VL - 48
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 13
M1 - 135001
ER -
TY - JOUR
T1 - Localized nonlinear wavepackets with radial-azimuthal modulated nonlinearity and an external potential
AU - Zhong, Wei Ping
AU - Belić, Milivoj R.
AU - Assanto, Gaetano
PY - 2011/11
Y1 - 2011/11
N2 - We analytically investigated two-dimensional localized nonlinear waves in Kerr media with radial and azimuthal modulation of the nonlinearity and in the presence of an external potential. The solutions have been derived through the similarity transformation. We demonstrate that the properties of nonlinear waves are determined by two parameters: a whole number n (the index of the Jacobi elliptical waves) and an integer m (the topological charge). Our results indicate that the dynamic evolution, including cnoidal and snoidal waves, can be strongly affected by these two parameters, providing an approach to controlling nonlinear waves by an appropriate radial-azimuthal modulation of the nonlinearity, with an appropriate external potential.
AB - We analytically investigated two-dimensional localized nonlinear waves in Kerr media with radial and azimuthal modulation of the nonlinearity and in the presence of an external potential. The solutions have been derived through the similarity transformation. We demonstrate that the properties of nonlinear waves are determined by two parameters: a whole number n (the index of the Jacobi elliptical waves) and an integer m (the topological charge). Our results indicate that the dynamic evolution, including cnoidal and snoidal waves, can be strongly affected by these two parameters, providing an approach to controlling nonlinear waves by an appropriate radial-azimuthal modulation of the nonlinearity, with an appropriate external potential.
UR - http://www.scopus.com/inward/record.url?scp=80755143598&partnerID=8YFLogxK
U2 - 10.1088/0031-8949/84/05/055001
DO - 10.1088/0031-8949/84/05/055001
M3 - Article
VL - 84
JO - Physica Scripta
JF - Physica Scripta
SN - 0031-8949
IS - 5
M1 - 055001
ER -
TY - JOUR
T1 - Forward simulation and inverse dipole localization with the lowest order Raviart - Thomas elements for electroencephalography
AU - Pursiainen, S.
AU - Sorrentino, A.
AU - Campi, C.
AU - Piana, M.
PY - 2011/4
Y1 - 2011/4
N2 - Electroencephalography is a non-invasive imaging modality in which a primary current density generated by the neural activity in the brain is to be reconstructed based on external electric potential measurements. This paper focuses on the finite element method (FEM) from both forward and inverse aspects. The goal is to establish a clear correspondence between the lowest order Raviart-Thomas basis functions and dipole sources as well as to show that the adopted FEM approach is computationally effective. Each basis function is associated with a dipole moment and a location. Four candidate locations are tested. Numerical experiments cover two different spherical multilayer head models, four mesh resolutions and two different forward simulation approaches, one based on FEM and another based on the boundary element method (BEM) with standard dipoles as sources. The forward simulation accuracy is examined through column- and matrix-wise relative errors as well as through performance in inverse dipole localization. A closed-form approximation of dipole potential was used as the reference forward simulation. The present approach is compared to the BEM and indirectly also to the recent FEM-based subtraction approach regarding both accuracy, computation time and accessibility of implementation.
AB - Electroencephalography is a non-invasive imaging modality in which a primary current density generated by the neural activity in the brain is to be reconstructed based on external electric potential measurements. This paper focuses on the finite element method (FEM) from both forward and inverse aspects. The goal is to establish a clear correspondence between the lowest order Raviart-Thomas basis functions and dipole sources as well as to show that the adopted FEM approach is computationally effective. Each basis function is associated with a dipole moment and a location. Four candidate locations are tested. Numerical experiments cover two different spherical multilayer head models, four mesh resolutions and two different forward simulation approaches, one based on FEM and another based on the boundary element method (BEM) with standard dipoles as sources. The forward simulation accuracy is examined through column- and matrix-wise relative errors as well as through performance in inverse dipole localization. A closed-form approximation of dipole potential was used as the reference forward simulation. The present approach is compared to the BEM and indirectly also to the recent FEM-based subtraction approach regarding both accuracy, computation time and accessibility of implementation.
UR - http://www.scopus.com/inward/record.url?scp=79953662770&partnerID=8YFLogxK
U2 - 10.1088/0266-5611/27/4/045003
DO - 10.1088/0266-5611/27/4/045003
M3 - Article
VL - 27
JO - Inverse Problems
JF - Inverse Problems
SN - 0266-5611
IS - 4
M1 - 045003
ER -
TY - JOUR
T1 - Robustness in scale-free networks
T2 - Comparing directed and undirected networks
AU - Emmert-Streib, Frank
AU - Dehmer, Matthias
PY - 2008/5
Y1 - 2008/5
N2 - In this paper, scale-free networks and their functional robustness with respect to structural perturbations of the network are studied. Two types of perturbations are distinguished: random perturbations and attacks. The robustness of directed and undirected scale-free networks is studied numerically for two different measures and the obtained results are compared. For random perturbations, the results indicate that the strength of the perturbation plays a crucial role. In general, directed scale-free networks are more robust than undirected scale-free networks.
AB - In this paper, scale-free networks and their functional robustness with respect to structural perturbations of the network are studied. Two types of perturbations are distinguished: random perturbations and attacks. The robustness of directed and undirected scale-free networks is studied numerically for two different measures and the obtained results are compared. For random perturbations, the results indicate that the strength of the perturbation plays a crucial role. In general, directed scale-free networks are more robust than undirected scale-free networks.
KW - Functional robustness
KW - Markov chain
KW - Scale-free networks
UR - http://www.scopus.com/inward/record.url?scp=47049131368&partnerID=8YFLogxK
U2 - 10.1142/S0129183108012510
DO - 10.1142/S0129183108012510
M3 - Article
VL - 19
SP - 717
EP - 726
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
SN - 0129-1831
IS - 5
ER -
TY - JOUR
T1 - Nonextensivity and universality in the earthquake preparation process
AU - Papadimitriou, C.
AU - Kalimeri, M.
AU - Eftaxias, K.
N1 - EXT=”Kalimeri, Maria”
PY - 2008/3/3
Y1 - 2008/3/3
N2 - We suggest that the activation of a single fault by means of preseismic electromagnetic emissions (PEME) is well-described by recently introduced models for earthquake (EQ) dynamics, which have been rooted in a nonextensive framework starting from first principles. The analysis implies that the activation of a single fault is (i) a reduced self-affine image of the regional seismicity covering many geological faults, and (ii) a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we study whether characteristic signatures emerged in PEME indicating the transition to the last phase of the EQ preparation process. We use the q -Tsallis entropy as a measure of organization. Tsallis entropy gives evidence of state changes leading to the point of global instability: it detects the pattern of alterations in the preseismic electromagnetic signals and is able to discriminate between "injury levels" of the focal area. Importantly, a significant organization increase can be confirmed at the tail of the recorded PEME by means of Tsallis entropy, which is also accompanied by the appearance of persistency. We argue that these footprints may indicate the fracture of the backbone of strong entities that hinders the relative motion of the fault planes.
AB - We suggest that the activation of a single fault by means of preseismic electromagnetic emissions (PEME) is well-described by recently introduced models for earthquake (EQ) dynamics, which have been rooted in a nonextensive framework starting from first principles. The analysis implies that the activation of a single fault is (i) a reduced self-affine image of the regional seismicity covering many geological faults, and (ii) a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we study whether characteristic signatures emerged in PEME indicating the transition to the last phase of the EQ preparation process. We use the q -Tsallis entropy as a measure of organization. Tsallis entropy gives evidence of state changes leading to the point of global instability: it detects the pattern of alterations in the preseismic electromagnetic signals and is able to discriminate between "injury levels" of the focal area. Importantly, a significant organization increase can be confirmed at the tail of the recorded PEME by means of Tsallis entropy, which is also accompanied by the appearance of persistency. We argue that these footprints may indicate the fracture of the backbone of strong entities that hinders the relative motion of the fault planes.
UR - http://www.scopus.com/inward/record.url?scp=40949121412&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.77.036101
DO - 10.1103/PhysRevE.77.036101
M3 - Article
VL - 77
JO - Physical Review E
JF - Physical Review E
SN - 1539-3755
IS - 3
M1 - 036101
ER -
TY - JOUR
T1 - Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy
AU - Kalimeri, M.
AU - Papadimitriou, C.
AU - Balasis, G.
AU - Eftaxias, K.
N1 - EXT=”Kalimeri, Maria"
PY - 2008/2/15
Y1 - 2008/2/15
N2 - We investigate, within the framework of nonextensive Tsallis entropy, particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system: the focal area of an impending earthquake. The Tsallis-like time-dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence.
AB - We investigate, within the framework of nonextensive Tsallis entropy, particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system: the focal area of an impending earthquake. The Tsallis-like time-dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence.
KW - Hurst exponent
KW - Time series analysis
KW - Tsallis entropy
UR - http://www.scopus.com/inward/record.url?scp=36749093506&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2007.10.053
DO - 10.1016/j.physa.2007.10.053
M3 - Article
VL - 387
SP - 1161
EP - 1172
JO - Physica A: Statistical Mechanics and Its Applications
JF - Physica A: Statistical Mechanics and Its Applications
SN - 0378-4371
IS - 5-6
ER -
TY - JOUR
T1 - Nonlinear time series prediction based on a power-law noise model
AU - Emmert-Streib, Frank
AU - Dehmer, Matthias
PY - 2007/12
Y1 - 2007/12
N2 - In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.
AB - In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.
KW - time series prediction
KW - maximum likelihood
KW - Monte Carlo method
KW - feed-forward
KW - neural network.
KW - SELF-ORGANIZED CRITICALITY
KW - NEURAL-NETWORKS
KW - OPTIMIZATION
KW - EXPLANATION
UR - http://www.scopus.com/inward/record.url?scp=38149090517&partnerID=8YFLogxK
U2 - 10.1142/S0129183107011765
DO - 10.1142/S0129183107011765
M3 - Article
VL - 18
SP - 1839
EP - 1852
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
SN - 0129-1831
IS - 12
ER -
TY - JOUR
T1 - A heterosynaptic learning rule for neural networks
AU - Emmert-Streib, Frank
PY - 2006/10
Y1 - 2006/10
N2 - In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is ueurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the preand postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean learning time increases with the number of patterns to be learned polynomially, indicating efficient learning.
AB - In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is ueurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the preand postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean learning time increases with the number of patterns to be learned polynomially, indicating efficient learning.
KW - Biological reinforcement learning
KW - Hebb-like learning
KW - Heterosynaptic plasticity
KW - Neural networks
UR - http://www.scopus.com/inward/record.url?scp=33750574569&partnerID=8YFLogxK
U2 - 10.1142/S0129183106009916
DO - 10.1142/S0129183106009916
M3 - Article
VL - 17
SP - 1501
EP - 1520
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
SN - 0129-1831
IS - 10
ER -
TY - JOUR
T1 - Stochastic Sznajd Model in open community
AU - Emmert-Streib, Frank
PY - 2005/11
Y1 - 2005/11
N2 - We extend the Sznajd Model for opinion formation by introducing persuasion probabilities for opinions. Moreover, we couple the system to an environment which mimics the application of the opinion. This results in a feedback, representing single-state opinion transitions in opposite to the two-state opinion transitions for persuading other people. We call this model opinion formation in an open community (OFOC). It can be seen as a stochastic extension of the Sznajd model for an open community, because it allows for a special choice of parameters to recover the original Sznajd model. We demonstrate the effect of feedback in the OFOC model by applying it to a, scenario in which, e.g., opinion B is worse then opinion A but easier explained to other people. Casually formulated we analyzed the question, how much better one has to be, in order to persuade other people, provided the opinion is worse. Our results reveal a linear relation between the transition probability for opinion B and the influence of the environment on B.
AB - We extend the Sznajd Model for opinion formation by introducing persuasion probabilities for opinions. Moreover, we couple the system to an environment which mimics the application of the opinion. This results in a feedback, representing single-state opinion transitions in opposite to the two-state opinion transitions for persuading other people. We call this model opinion formation in an open community (OFOC). It can be seen as a stochastic extension of the Sznajd model for an open community, because it allows for a special choice of parameters to recover the original Sznajd model. We demonstrate the effect of feedback in the OFOC model by applying it to a, scenario in which, e.g., opinion B is worse then opinion A but easier explained to other people. Casually formulated we analyzed the question, how much better one has to be, in order to persuade other people, provided the opinion is worse. Our results reveal a linear relation between the transition probability for opinion B and the influence of the environment on B.
KW - Markov process
KW - Monte Carlo simulation
KW - Small-world network
KW - Sznajd Model
UR - http://www.scopus.com/inward/record.url?scp=29244483126&partnerID=8YFLogxK
U2 - 10.1142/S0129183105008217
DO - 10.1142/S0129183105008217
M3 - Article
VL - 16
SP - 1693
EP - 1699
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
SN - 0129-1831
IS - 11
ER -
TY - JOUR
T1 - Molecular dynamics investigation of the premelting effects of lennard-jones (111) surfaces
AU - Valkealahti, S.
AU - Nieminen, R. M.
PY - 1987/10/1
Y1 - 1987/10/1
N2 - Molecular dynamics simulations have been performed to study the premelting effects of noble-gas surfaces (argon) close to but below the bulk melting temperature. In particular, the increase of disorder as a function of temperature at (111) surface has been considered. The truncated Lennard-Jones (6-12) potential is used to describe the interactions between particles. Surface premelting has been analyzed by means of total energies, trajectory plots, mean sequare displacement functions, diffusion coefficients, vacancy concentrations and two-dimensional order parameters. The (111) surface starts to disorder by vacancy formation, which leads to the premelting of the surface layer far below the bulk melting temperature. Melting proceeds via a layer-by-layer mechanism, when temperature is further increased. This study supports the earlier observations of a melting that proceeds in the direction of high packing density.
AB - Molecular dynamics simulations have been performed to study the premelting effects of noble-gas surfaces (argon) close to but below the bulk melting temperature. In particular, the increase of disorder as a function of temperature at (111) surface has been considered. The truncated Lennard-Jones (6-12) potential is used to describe the interactions between particles. Surface premelting has been analyzed by means of total energies, trajectory plots, mean sequare displacement functions, diffusion coefficients, vacancy concentrations and two-dimensional order parameters. The (111) surface starts to disorder by vacancy formation, which leads to the premelting of the surface layer far below the bulk melting temperature. Melting proceeds via a layer-by-layer mechanism, when temperature is further increased. This study supports the earlier observations of a melting that proceeds in the direction of high packing density.
U2 - 10.1088/0031-8949/36/4/007
DO - 10.1088/0031-8949/36/4/007
M3 - Article
VL - 36
SP - 646
EP - 650
JO - Physica Scripta
JF - Physica Scripta
SN - 0031-8949
IS - 4
ER -