Physical Review Letters, ISSN 0031-9007, 11/2015, Volume 115, Issue 21, p. 215301

We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap...

OPTICAL LATTICE | ULTRACOLD ATOMS | PHYSICS, MULTIDISCIPLINARY | FERMIONS | SYSTEMS | IMPENETRABLE BOSONS | TONKS-GIRARDEAU GAS | Antiferromagnetism | Accuracy | Particle spin | Chains | Mathematical models | Wave functions | Orientation | Cold atoms | Physics - Quantum Gases | Annan fysik | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences | Other Physics Topics

OPTICAL LATTICE | ULTRACOLD ATOMS | PHYSICS, MULTIDISCIPLINARY | FERMIONS | SYSTEMS | IMPENETRABLE BOSONS | TONKS-GIRARDEAU GAS | Antiferromagnetism | Accuracy | Particle spin | Chains | Mathematical models | Wave functions | Orientation | Cold atoms | Physics - Quantum Gases | Annan fysik | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences | Other Physics Topics

Journal Article

2.
Full Text
Correlation functions in the prethermalized regime after a quantum quench of a spin chain

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 05/2013, Volume 87, Issue 20

Results are presented for a two-point correlation function of a spin chain after a quantum quench for an intermediate time regime where inelastic effects are weak...

PHYSICS, CONDENSED MATTER | HEISENBERG ANTIFERROMAGNETIC CHAIN | SYSTEMS | RELAXATION | ULTRACOLD GASES | CUPRATE | Physics - Strongly Correlated Electrons

PHYSICS, CONDENSED MATTER | HEISENBERG ANTIFERROMAGNETIC CHAIN | SYSTEMS | RELAXATION | ULTRACOLD GASES | CUPRATE | Physics - Strongly Correlated Electrons

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 8/2019, Volume 2019, Issue 8, pp. 1 - 31

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions...

Lattice Integrable Models | Conformal Field Theory | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STRINGS | ADS | SL(2,R) WZW MODEL | PHASE | ANTIFERROMAGNETIC TRANSITION | POTTS-MODEL | Q-OPERATORS | STAGGERED 6-VERTEX MODEL | PHYSICS, PARTICLES & FIELDS | Hypergeometric functions | Chains | Scaling | Differential equations

Lattice Integrable Models | Conformal Field Theory | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | STRINGS | ADS | SL(2,R) WZW MODEL | PHASE | ANTIFERROMAGNETIC TRANSITION | POTTS-MODEL | Q-OPERATORS | STAGGERED 6-VERTEX MODEL | PHYSICS, PARTICLES & FIELDS | Hypergeometric functions | Chains | Scaling | Differential equations

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 09/2014, Volume 2014, Issue 9, pp. P09005 - 17

Using the density-matrix renormalization group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely...

quantum wires (theory) | ladders and planes (theory) | quantum phase transitions (theory) | optical lattices | spin chains | MATRIX RENORMALIZATION-GROUP | SOLUBLE MODEL | MECHANICS | ANTIFERROMAGNETIC CHAIN | PHYSICS, MATHEMATICAL | ULTRACOLD | Exchange | Optical lattices | Liquids | Algorithms | Anisotropy | Liquid phases | Chains | Constants | Ferromagnetism

quantum wires (theory) | ladders and planes (theory) | quantum phase transitions (theory) | optical lattices | spin chains | MATRIX RENORMALIZATION-GROUP | SOLUBLE MODEL | MECHANICS | ANTIFERROMAGNETIC CHAIN | PHYSICS, MATHEMATICAL | ULTRACOLD | Exchange | Optical lattices | Liquids | Algorithms | Anisotropy | Liquid phases | Chains | Constants | Ferromagnetism

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2017, Volume 50, Issue 41, p. 414002

The spin-1/2 Heisenberg chain exhibits a quantum critical regime characterized by quasi long-range magnetic order at zero temperature...

Heisenberg model | probability distribution function | XXZ spin chain | sine-Gordon model | staggered magnetization | magnetization | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | QUANTUM | CORRELATION AMPLITUDE | NOISE | MODEL | ANTIFERROMAGNETIC CHAIN | PHYSICS, MATHEMATICAL | KONDO PROBLEM | Physics - Statistical Mechanics

Heisenberg model | probability distribution function | XXZ spin chain | sine-Gordon model | staggered magnetization | magnetization | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | QUANTUM | CORRELATION AMPLITUDE | NOISE | MODEL | ANTIFERROMAGNETIC CHAIN | PHYSICS, MATHEMATICAL | KONDO PROBLEM | Physics - Statistical Mechanics

Journal Article

Physical review letters, ISSN 0031-9007, 2013, Volume 111, Issue 13, p. 137205

The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor,...

FNWI top publication | ORDERED PHASE | SPIN DYNAMICS | PHYSICS, MULTIDISCIPLINARY | TRANSITION RATES | COMPOUND KCUF3 | QUANTUM | DYNAMICAL CORRELATION-FUNCTION | NEUTRON-SCATTERING | MAGNETIC-FIELD | ANTIFERROMAGNETIC CHAIN | BETHE-ANSATZ | Physics - Strongly Correlated Electrons

FNWI top publication | ORDERED PHASE | SPIN DYNAMICS | PHYSICS, MULTIDISCIPLINARY | TRANSITION RATES | COMPOUND KCUF3 | QUANTUM | DYNAMICAL CORRELATION-FUNCTION | NEUTRON-SCATTERING | MAGNETIC-FIELD | ANTIFERROMAGNETIC CHAIN | BETHE-ANSATZ | Physics - Strongly Correlated Electrons

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 04/2019, Volume 941, pp. 794 - 837

We study a Y junction of spin-1/2 Heisenberg chains with an interaction that breaks both time-reversal and chain exchange symmetries, but not their product nor SU(2) symmetry...

TRIANGULAR-LATTICE | PHASE | TRANSPORT | FUSION RULES | MODELS | BOUNDARY-CONDITIONS | LIQUID | DYNAMICS | HEISENBERG ANTIFERROMAGNETIC CHAIN | CONFORMAL-FIELD-THEORY | PHYSICS, PARTICLES & FIELDS | Monte Carlo method | Physics - Strongly Correlated Electrons

TRIANGULAR-LATTICE | PHASE | TRANSPORT | FUSION RULES | MODELS | BOUNDARY-CONDITIONS | LIQUID | DYNAMICS | HEISENBERG ANTIFERROMAGNETIC CHAIN | CONFORMAL-FIELD-THEORY | PHYSICS, PARTICLES & FIELDS | Monte Carlo method | Physics - Strongly Correlated Electrons

Journal Article

Physical Review Letters, ISSN 0031-9007, 02/2012, Volume 108, Issue 8, p. 081601

We introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-Hermitian "Hamiltonian'' and show, using mostly analytical techniques, that it is described at low energies by the SL(2, R)/U(1...

SYSTEM | LATTICE POTTS-MODEL | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | ANTIFERROMAGNETIC TRANSITION | 1-DIMENSIONAL CHAIN | CONTINUUM-LIMIT | HIGH-ENERGY QCD

SYSTEM | LATTICE POTTS-MODEL | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | ANTIFERROMAGNETIC TRANSITION | 1-DIMENSIONAL CHAIN | CONTINUUM-LIMIT | HIGH-ENERGY QCD

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 06/2016, Volume 85, Issue 6, p. 63704

We investigate the ground-state phase diagram of the bond-alternating S = 2 quantum spin chain with the XXZ and on-site anisotropies...

SYSTEMS | TRANSITIONS | NEAREST-NEIGHBOR INTERACTIONS | PHYSICS, MULTIDISCIPLINARY | ANTIFERROMAGNETIC HEISENBERG CHAIN

SYSTEMS | TRANSITIONS | NEAREST-NEIGHBOR INTERACTIONS | PHYSICS, MULTIDISCIPLINARY | ANTIFERROMAGNETIC HEISENBERG CHAIN

Journal Article

Nature, ISSN 0028-0836, 01/2019, Volume 565, Issue 7737, pp. 56 - 60

...-imbalanced Hubbard chains using fully spin- and density-resolved quantum gas microscopy. Doping is found to induce a linear change in the spin...

EXCITATIONS | LUTTINGER-LIQUID | MULTIDISCIPLINARY SCIENCES | ANTIFERROMAGNETIC CORRELATIONS | MODEL | SPIN-CORRELATION | PAIR | Magnetism | Research | Fermions | Particle spin | Lattice dynamics | Magnetization | Magnetic fields | Analysis | Nuclear physics | Antiferromagnetism | Optical lattices | Correlation | Computer simulation | Domain walls | Doping | Heisenberg theory | Chains | Density | Physics | Statistical models | Microscopy | Correlation analysis | Spin density waves | Physics - Quantum Gases

EXCITATIONS | LUTTINGER-LIQUID | MULTIDISCIPLINARY SCIENCES | ANTIFERROMAGNETIC CORRELATIONS | MODEL | SPIN-CORRELATION | PAIR | Magnetism | Research | Fermions | Particle spin | Lattice dynamics | Magnetization | Magnetic fields | Analysis | Nuclear physics | Antiferromagnetism | Optical lattices | Correlation | Computer simulation | Domain walls | Doping | Heisenberg theory | Chains | Density | Physics | Statistical models | Microscopy | Correlation analysis | Spin density waves | Physics - Quantum Gases

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 08/2011, Volume 84, Issue 8

We study spinless fermions in a flux threaded AB(2) chain taking into account nearest-neighbor Coulomb interactions...

PHASE-SEPARATION | PHYSICS, CONDENSED MATTER | LUTTINGER-LIQUID | ELECTRON GROUND-STATES | BOND-CHARGE INTERACTION | ANTIFERROMAGNETIC HEISENBERG-MODEL | TWISTED BOUNDARY-CONDITIONS | T-J MODEL | 8-VERTEX MODEL | HUBBARD-MODEL | LATTICE STATISTICS | Physics - Strongly Correlated Electrons

PHASE-SEPARATION | PHYSICS, CONDENSED MATTER | LUTTINGER-LIQUID | ELECTRON GROUND-STATES | BOND-CHARGE INTERACTION | ANTIFERROMAGNETIC HEISENBERG-MODEL | TWISTED BOUNDARY-CONDITIONS | T-J MODEL | 8-VERTEX MODEL | HUBBARD-MODEL | LATTICE STATISTICS | Physics - Strongly Correlated Electrons

Journal Article

Physical Review Letters, ISSN 0031-9007, 09/2010, Volume 105, Issue 11, p. 116805

.... Despite the Laughlin state being bulk gapped while the antiferromagnetic spin chain state is bulk gapless, we show that the S...

HEISENBERG ANTIFERROMAGNETIC CHAIN | STATES | EXCITATIONS | PHYSICS, MULTIDISCIPLINARY | INCOMPRESSIBLE QUANTUM FLUID | INVARIANT | EXCITATION | MULTIPLICITY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL MODELS | ANTIFERROMAGNETISM | DIMERIZATION | QUANTUM ENTANGLEMENT | POLYMERIZATION | ENERGY LEVELS | ENERGY-LEVEL TRANSITIONS | PARTICLE PROPERTIES | QUANTUM NUMBERS | FIELD THEORIES | SPACE | CRYSTAL MODELS | MAGNETISM | ANGULAR MOMENTUM | CHEMICAL REACTIONS | HALL EFFECT | SPECTRA | HEISENBERG MODEL | GROUND STATES

HEISENBERG ANTIFERROMAGNETIC CHAIN | STATES | EXCITATIONS | PHYSICS, MULTIDISCIPLINARY | INCOMPRESSIBLE QUANTUM FLUID | INVARIANT | EXCITATION | MULTIPLICITY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL MODELS | ANTIFERROMAGNETISM | DIMERIZATION | QUANTUM ENTANGLEMENT | POLYMERIZATION | ENERGY LEVELS | ENERGY-LEVEL TRANSITIONS | PARTICLE PROPERTIES | QUANTUM NUMBERS | FIELD THEORIES | SPACE | CRYSTAL MODELS | MAGNETISM | ANGULAR MOMENTUM | CHEMICAL REACTIONS | HALL EFFECT | SPECTRA | HEISENBERG MODEL | GROUND STATES

Journal Article

Physica B: Physics of Condensed Matter, ISSN 0921-4526, 09/2017, Volume 520, pp. 65 - 68

We use bond operator method to study the dimerized ferrimagnetic spin chain. With the dimerization parameter g from 1 to 0, the model describes the system from normal ferrimagnetic state to dimer state...

Bond operator method | Dimerization parameter | Dimerized ferrimagnetic spin chain | PHYSICS, CONDENSED MATTER | MEAN-FIELD THEORY | MAGNETIZATION | MODEL | ANTIFERROMAGNETIC CHAINS | ANISOTROPY

Bond operator method | Dimerization parameter | Dimerized ferrimagnetic spin chain | PHYSICS, CONDENSED MATTER | MEAN-FIELD THEORY | MAGNETIZATION | MODEL | ANTIFERROMAGNETIC CHAINS | ANISOTROPY

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 01/2010, Volume 81, Issue 1

The minimal model to describe many spin-chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest-neighbor coupling J(1...

PHYSICS, CONDENSED MATTER | HEISENBERG ANTIFERROMAGNETIC CHAIN | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | SUSCEPTIBILITY | Physics - Strongly Correlated Electrons

PHYSICS, CONDENSED MATTER | HEISENBERG ANTIFERROMAGNETIC CHAIN | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | SUSCEPTIBILITY | Physics - Strongly Correlated Electrons

Journal Article

J Phys Soc Jpn, ISSN 0031-9015, 4/2011, Volume 80, Issue 4, pp. 043703 - 043703-4

The ground-state properties of the $S = 1/2$ frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method...

Quantum spin chain | Ferrimagnetism | DMRG | Exact diagonalization | Frustration | DELTA-CHAIN | PHYSICS, MULTIDISCIPLINARY | frustration | NEAREST-NEIGHBOR | quantum spin chain | COMPETING INTERACTIONS | exact diagonalization | QUANTUM RENORMALIZATION-GROUPS | DISTORTED DIAMOND CHAIN | ANTIFERROMAGNETIC INTERACTIONS | SYSTEMS | ferrimagnetism | GROUND-STATE PROPERTIES | CU3CL6(H2O)CENTER-DOT-2HCSO | CU-3(CO3)(OH) | Physics - Strongly Correlated Electrons

Quantum spin chain | Ferrimagnetism | DMRG | Exact diagonalization | Frustration | DELTA-CHAIN | PHYSICS, MULTIDISCIPLINARY | frustration | NEAREST-NEIGHBOR | quantum spin chain | COMPETING INTERACTIONS | exact diagonalization | QUANTUM RENORMALIZATION-GROUPS | DISTORTED DIAMOND CHAIN | ANTIFERROMAGNETIC INTERACTIONS | SYSTEMS | ferrimagnetism | GROUND-STATE PROPERTIES | CU3CL6(H2O)CENTER-DOT-2HCSO | CU-3(CO3)(OH) | Physics - Strongly Correlated Electrons

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 0163-1829, 04/2000, Volume 61, Issue 14, pp. 9558 - 9606

...) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1...

EXCHANGE INTERACTIONS | SPIN | MONTE CARLO METHOD | THEORETICAL DATA | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | ANTIFERROMAGNETIC MATERIALS | SIMULATION | ANTIFERROELECTRIC MATERIALS | ENERGY GAP | TEMPERATURE RANGE 0065-0273 K | ELECTRON EXCHANGE | SPECIFIC HEAT | THERMODYNAMICS | TEMPERATURE RANGE 0013-0065 K | MAGNETIC SUSCEPTIBILITY | CHAINS | HEISENBERG MODEL | EXPERIMENTAL DATA | ENTROPY

EXCHANGE INTERACTIONS | SPIN | MONTE CARLO METHOD | THEORETICAL DATA | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | ANTIFERROMAGNETIC MATERIALS | SIMULATION | ANTIFERROELECTRIC MATERIALS | ENERGY GAP | TEMPERATURE RANGE 0065-0273 K | ELECTRON EXCHANGE | SPECIFIC HEAT | THERMODYNAMICS | TEMPERATURE RANGE 0013-0065 K | MAGNETIC SUSCEPTIBILITY | CHAINS | HEISENBERG MODEL | EXPERIMENTAL DATA | ENTROPY

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 04/2009, Volume 79, Issue 13

We investigate theoretically and experimentally the static magnetic properties of single crystals of the molecular-based single-chain magnet of formula [Dy(hfac)(3)NIT(C6H4OPh)](infinity...

molecular magnetism | weak ferromagnetism | STATISTICAL-MECHANICS | PHYSICS, CONDENSED MATTER | antiferromagnetic materials | PHASE-TRANSITIONS | BEHAVIOR | Heisenberg model | RELAXATION | magnetic anisotropy | MODEL | magnetic moments | exchange interactions (electron) | ANTI-FERROMAGNETS | ab initio calculations | NITRONYL NITROXIDE | DYNAMICS | CHEMISTRY | canted spin arrangements | magnetic susceptibility | NANOWIRES | Physics - Materials Science

molecular magnetism | weak ferromagnetism | STATISTICAL-MECHANICS | PHYSICS, CONDENSED MATTER | antiferromagnetic materials | PHASE-TRANSITIONS | BEHAVIOR | Heisenberg model | RELAXATION | magnetic anisotropy | MODEL | magnetic moments | exchange interactions (electron) | ANTI-FERROMAGNETS | ab initio calculations | NITRONYL NITROXIDE | DYNAMICS | CHEMISTRY | canted spin arrangements | magnetic susceptibility | NANOWIRES | Physics - Materials Science

Journal Article

Physical Review Letters, ISSN 0031-9007, 04/2011, Volume 106, Issue 13, p. 137202

NMR measurements of the Si-29 spin-lattice relaxation time T-1 were used to probe the spin-1/2 random Heisenberg chain compound BaCu2(Si1-xGex)(2)O-7...

MODEL | PHYSICS, MULTIDISCIPLINARY | ANTIFERROMAGNETIC CHAIN | QUANTUM SPIN CHAINS | WILLIAMS-WATTS | Physics - Strongly Correlated Electrons

MODEL | PHYSICS, MULTIDISCIPLINARY | ANTIFERROMAGNETIC CHAIN | QUANTUM SPIN CHAINS | WILLIAMS-WATTS | Physics - Strongly Correlated Electrons

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 08/2009, Volume 80, Issue 2, p. 024404

We report a detailed examination of the magnetic structure of anhydrous cupric chloride CuCl2 carried out by powder neutron diffraction, magnetic...

LOW-TEMPERATURE CALORIMETRY | long-range order | WEAK FERROMAGNETISM | 300 DEGREES K | solid-state phase transformations | TOTAL-ENERGY CALCULATIONS | specific heat | SPIN-EXCHANGE INTERACTIONS | PHASE-TRANSITION | neutron diffraction | ferromagnetic materials | multiferroics | PHYSICS, CONDENSED MATTER | antiferromagnetic materials | frustration | Heisenberg model | exchange interactions (electron) | copper compounds | ANTIFERROMAGNETIC UNIFORM | density functional theory | crystal structure | Neel temperature | magnetic susceptibility | magnetic structure | LAYERED-TRIANGULAR LATTICE | WAVE BASIS-SET | HEAT-CAPACITY | Condensed Matter | Physics | Superconductivity

LOW-TEMPERATURE CALORIMETRY | long-range order | WEAK FERROMAGNETISM | 300 DEGREES K | solid-state phase transformations | TOTAL-ENERGY CALCULATIONS | specific heat | SPIN-EXCHANGE INTERACTIONS | PHASE-TRANSITION | neutron diffraction | ferromagnetic materials | multiferroics | PHYSICS, CONDENSED MATTER | antiferromagnetic materials | frustration | Heisenberg model | exchange interactions (electron) | copper compounds | ANTIFERROMAGNETIC UNIFORM | density functional theory | crystal structure | Neel temperature | magnetic susceptibility | magnetic structure | LAYERED-TRIANGULAR LATTICE | WAVE BASIS-SET | HEAT-CAPACITY | Condensed Matter | Physics | Superconductivity

Journal Article

Journal of Magnetism and Magnetic Materials, ISSN 0304-8853, 04/2016, Volume 404, pp. 91 - 118

.... We investigate the onset of modulational instability of a plane wave in a discrete ferromagnetic spin chain with physically significant higher order dispersive octupole–dipole and dipole–dipole interactions...

Modulational instability | Molecular dynamics simulations | Discrete breather | Ferromagnet | PHYSICS, CONDENSED MATTER | MATERIALS SCIENCE, MULTIDISCIPLINARY | NONLINEAR SCHRODINGER-EQUATION | EASY-PLANE ANISOTROPY | DISCRETE LATTICES | MODES | SOLITONS | BIQUADRATIC EXCHANGE | MAGNETIC-ANISOTROPY | HEISENBERG-FERROMAGNET | WAVE-GUIDE ARRAYS | ANTIFERROMAGNETIC CHAINS | Molecular dynamics | Analysis | Ferromagnetism | Dispersion (wave) | Stability | Mathematical analysis | Chains | Instability | Mathematical models | Position (location)

Modulational instability | Molecular dynamics simulations | Discrete breather | Ferromagnet | PHYSICS, CONDENSED MATTER | MATERIALS SCIENCE, MULTIDISCIPLINARY | NONLINEAR SCHRODINGER-EQUATION | EASY-PLANE ANISOTROPY | DISCRETE LATTICES | MODES | SOLITONS | BIQUADRATIC EXCHANGE | MAGNETIC-ANISOTROPY | HEISENBERG-FERROMAGNET | WAVE-GUIDE ARRAYS | ANTIFERROMAGNETIC CHAINS | Molecular dynamics | Analysis | Ferromagnetism | Dispersion (wave) | Stability | Mathematical analysis | Chains | Instability | Mathematical models | Position (location)

Journal Article