Treatment of Elderly Patients With Dorsopathy

Камчатнов, П Р; Евзельман, М. А.; Чугунов, А В

doi:10.21518/2079-701x-2016-9-28-32

Cited by 7 publications

(10 citation statements)

References 22 publications

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“…An ideal MHD soliton, as defined in [13,24], is a static configuration of magnetic field B, fluid velocity u, and pressure p that satisfies the ideal, incompressible MHD equations. The fluid field and pressure that solve this can be inferred from the momentum equation, which can be written as:…”

Section: Plasma Torus Knotsmentioning

confidence: 99%

“…It is remarkable how abstract topological concepts are directly relevant to many branches of science. A prime example is the Hopf map [1], a non-trivial topological structure that has found applications in liquid crystals [2], molecular biology [3], superconductors [4], superfluids [5], Bose-Einstein condensates [6,7], ferromagnets [8], optics [9][10][11], and plasma physics [12,13]. This article deals with topological aspects of novel persistent plasma configurations that emerge from decaying plasma torus knots.…”

mentioning

confidence: 99%

“…In 1982 Kamchatnov described an intrinsically stable plasma configuration [13] with a magnetic topology based on fibers of the Hopf map [18]. This type of MHD equilibrium, where the fluid velocity is parallel to the field and equal to the local Alfvén speed, was shown by Chandrasekhar to be stable [19], even in specific cases in the presence of dissipative forces [20].…”

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Magnetic surface topology in decaying plasma knots

et al. 2017

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Torus-knot solitons have recently been formulated as solutions to the ideal incompressible magnetohydrodynamics (MHD) equations. We investigate numerically how these fields evolve in resistive, compressible, and viscous MHD. We find that certain decaying plasma torus knots exhibit magnetic surfaces that are topologically distinct from a torus. The evolution is predominantly determined by a persistent zero line in the field present when the poloidal winding number ¹ n 1 p . Dependence on the toroidal winding number n t is less pronounced as the zero line induced is contractible and disappears. The persistent zero line intersects the new magnetic surfaces such that, through the Hopf-Poincaré index theorem, the sum of zeroes on the new surfaces equals their (in general non-zero) Euler characteristic. Furthermore we observe the formation of magnetic islands between the surfaces. These novel persistent magnetic structures are of interest for plasma confinement, soliton dynamics and the study of dynamical systems in general.It is remarkable how abstract topological concepts are directly relevant to many branches of science. A prime example is the Hopf map [1], a non-trivial topological structure that has found applications in liquid crystals [2], molecular biology [3], superconductors [4], superfluids [5], Bose-Einstein condensates [6,7], ferromagnets [8], optics [9][10][11], and plasma physics [12,13]. This article deals with topological aspects of novel persistent plasma configurations that emerge from decaying plasma torus knots.Due to the generally high electrical conductivity of plasma described by magnetohydrodynamics (MHD), large electrical currents can flow and plasmas are heavily influenced by the resulting magnetic forces. The zerodivergence magnetic fields can lead to closed magnetic field lines, field lines that ergodically fill a magnetic surface, and field lines that chaotically fill a region of space. In ideal (zero-resistance) MHD the magnetic flux through a perfect conducting fluid element cannot change, leading to frozen in magnetic fields in the plasma [14]. This implies that in ideal MHD magnetic topology and magnetic helicity is conserved [15][16][17].In 1982 Kamchatnov described an intrinsically stable plasma configuration [13] with a magnetic topology based on fibers of the Hopf map [18]. This type of MHD equilibrium, where the fluid velocity is parallel to the field and equal to the local Alfvén speed, was shown by Chandrasekhar to be stable [19], even in specific cases in the presence of dissipative forces [20]. Quasi stable self-organizing magnetic fields with similar magnetic topology to Kamchatnov's field (but different flow) have recently been demonstrated to occur in full-MHD simulations [12]. Here the final configuration is not a Taylor state, which is consistent with recent findings in [21].Recently the class of topologically non-trivial solutions to Maxwell's equations has been extended by including torus knotted fields [22]. Another way of obtaining such solutions, for massles...

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Section: Plasma Torus Knotsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Magnetic surface topology in decaying plasma knots

et al. 2017

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“…It is a solution of Maxwell's equations in vacuum [1,2] where the electric and magnetic field lines form closed loops each of them linked to another. Such fields have also appeared as solitons in MHD [3] and generalised later [4,5]. The hopfion is deeply connected to non-null twistors [6,7] and its properties have been studied [8,9] extensively.…”

Section: Introductionmentioning

confidence: 99%

Collision of two hopfions

Arrayás¹,

Trueba²

2017

J. Phys. A: Math. Theor.

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We study the collision of two hopfions or Hopf-Rañada electromagnetic fields. The superposition of two of such fields, travelling in opposite directions, yields different topology for the electric and magnetic field lines. Controlling the angular momentum of such fields, we can control the topology of the flow associated to the field lines, and the energy distribution. The concept of electromagnetic helicity and the exchange between its magnetic and electric components are used to explain the different behaviours observed when the angular momentum is reversed.

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“…Преимуществом формы препарата Вольтарен Эмульгель 2%-ный является пролонгированное действие однократной дозы до 12 ч [14]. Вольтарен Эмульгель 2%-ный назначается преимущественно больным с хрони-ческой болью в суставах, а благодаря более высокой кон-центрации диклофенака и формуле, усиливающей про-никновение, действует дольше, чем Вольтарен Эмульгель 1%-ный [15].…”

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Efficacy of Local Nsaids Therapy With Osteoarthritis Different Localization

Шавловская¹

2017

Med. sov.

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Современные стандарты лечения предпочитают один из самых популярных неселективных НПВП -диклофенак, который по соотношению «эффективность/безопасность» по праву называют «золотым стандартом» анальгетической терапии. В последние годы при лечении болей в суставах широкое применение получил Вольтарен Эмульгель 1% и 2%. В настоя-щее время имеется убедительная доказательная база, свидетельствующая о его анальгетическом и противовоспалитель-ном действии как при травматических повреждениях связок и мышц, сопровождающихся выраженным болевым синдро-мом, так и при хронических воспалительных процессах в суставах у пациентов всех возрастов.Ключевые слова: нестероидные противовоспалительные препараты, диклофенак, Вольтарен Эмульгель, остеоартроз, болевой синдром. O.A. SHAVLOVSKAYA, MD, Sechenov First Moscow State Medical University EFFICACY OF LOCAL NSAIDS THERAPY WITH OSTEOARTHRITIS DIFFERENT LOCALIZATIONModern standards of treatment prefer one of the most popular non-selective NSAIDs -diclofenac, which is the ratio efficiency/ safety is rightly called the «gold standard» analgesic therapy. In recent years in the treatment of joint pain widely used Voltaren Emulgel 1% and 2%. Currently, there is a convincing evidence base testifying to its analgesic and anti-inflammatory action, as in traumatic injuries of the ligaments and muscles, accompanied by severe pain syndrome, and chronic inflammatory processes in the joints, patients of all ages.

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Treatment of Elderly Patients With Dorsopathy

Cited by 7 publications

References 22 publications

Magnetic surface topology in decaying plasma knots

Magnetic surface topology in decaying plasma knots

Collision of two hopfions

Efficacy of Local Nsaids Therapy With Osteoarthritis Different Localization

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