2,307 research outputs found
Anomalous diffusion and Tsallis statistics in an optical lattice
We point out a connection between anomalous quantum transport in an optical
lattice and Tsallis' generalized thermostatistics. Specifically, we show that
the momentum equation for the semiclassical Wigner function that describes
atomic motion in the optical potential, belongs to a class of transport
equations recently studied by Borland [PLA 245, 67 (1998)]. The important
property of these ordinary linear Fokker--Planck equations is that their
stationary solutions are exactly given by Tsallis distributions. Dissipative
optical lattices are therefore new systems in which Tsallis statistics can be
experimentally studied.Comment: 4 pages, 1 figur
ΠΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΡΡ ΠΊΠ»Π΅ΡΠΎΡΠ½ΡΡ Π°Π²ΡΠΎΠΌΠ°ΡΠΎΠ² Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π²Π½ΡΡΡΠ΅Π½Π½Π΅ΠΉ ΡΡΡΡΠΊΡΡΡΡ ΡΠ½Π΄ΠΎΠΏΡΠΎΡΠ΅Π·Π° ΡΠ°Π·ΠΎΠ±Π΅Π΄ΡΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΡΡΡΠ°Π²Π° ΡΠ΅Π»ΠΎΠ²Π΅ΠΊΠ°
ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΡΡ
ΠΊΠ»Π΅ΡΠΎΡΠ½ΡΡ
Π°Π²ΡΠΎΠΌΠ°ΡΠΎΠ² ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΠΈΠ·ΡΡΠ΅Π½ΠΈΠ΅ Π²Π»ΠΈΡΠ½ΠΈΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΎΠ½Π½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ ΡΠ½Π΄ΠΎΠΏΡΠΎΡΠ΅Π·Π° ΡΠ°Π·ΠΎΠ±Π΅Π΄ΡΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΡΡΡΠ°Π²Π° ΡΠ΅Π»ΠΎΠ²Π΅ΠΊΠ° Π½Π° Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΈ ΠΏΡΠΎΡΠ½ΠΎΡΡΠ½ΡΠ΅ ΡΠ²ΠΎΠΉΡΡΠ²Π°, Π° ΡΠ°ΠΊΠΆΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ ΠΈ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ "ΡΡΡΡΠ°Π²-ΡΠ½Π΄ΠΎΠΏΡΠΎΡΠ΅Π·-Π±Π΅Π΄ΡΠ΅Π½Π½Π°Ρ ΠΊΠΎΡΡΡ". Π‘ΡΡΡΠΊΡΡΡΠ° ΠΏΡΠΎΡΠ΅Π·Π° ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π»Π°ΡΡ Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ΠΌ Π² ΡΠ΅ΠΉΠΊΡ Π΄Π΅ΠΌΠΏΡΠΈΡΡΡΡΠΈΡ
Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΠΉ ΠΈ Π½Π°Π½Π΅ΡΠ΅Π½ΠΈΠ΅ΠΌ ΠΏΠΎΠΊΡΡΡΠΈΡ Π½Π° Π½ΠΎΠΆΠΊΡ ΠΈΠΌΠΏΠ»Π°Π½ΡΠ°ΡΠ°. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π½Π°Π»ΠΈΡΠΈΠ΅ ΡΠ°ΠΊΠΈΡ
Π²ΠΊΠ»ΡΡΠ΅Π½ΠΈΠΉ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈ Π½Π΅ ΠΈΠ·ΠΌΠ΅Π½ΡΠ΅Ρ ΠΏΡΠΎΡΠ½ΠΎΡΡΡ ΡΠΈΡΡΠ΅ΠΌΡ, Π½ΠΎ ΠΏΡΠΈ ΡΡΠΎΠΌ Π²Π΅Π΄Π΅Ρ ΠΊ Π·Π°ΠΌΠ΅ΡΠ½ΠΎΠΌΡ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΠΎΠΉ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΡΡΡΡΠΊΡΡΡΡ "ΠΊΠΎΡΡΡ - ΠΏΡΠΎΡΠ΅Π·", Π° ΡΠ°ΠΊΠΆΠ΅ ΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π° Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΡ Π·Π°ΡΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΠΈ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΏΠΎΠ²ΡΠ΅ΠΆΠ΄Π΅Π½ΠΈΠΉ Π² ΠΊΠΎΡΡΠ½ΠΎΠΉ ΡΠΊΠ°Π½ΠΈ
On the theory of double quantum NMR in polymer systems: The second cumulant approximation for many spin i = 1/2 systems
General analytical expressions for Double Quantum Nuclear Magnetic Resonance (DQ NMR) kinetic curves of many-spin I = 1/2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the initial part of the kinetic curves and provide a reasonable approximation up to times of about the effective spin-relaxation time. For the case when the system contains two isolated spins, this result exactly reproduces known expressions. In the case of polymer melts, the intermolecular magnetic dipole-dipole interactions significantly influence the time dependence of the DQ NMR kinetic curves. Β© 2013 AIP Publishing LLC
Segmental Dynamics of Entangled Poly(ethylene oxide) Melts: Deviations from the Tube-Reptation Model
Β© 2018 American Chemical Society. The dynamics of entangled polymer melts not only is of fundamental theoretical interest but also has wide-reaching consequences for developing a theoretical foundation for investigating biological macromolecules and complex systems relevant to material sciences. Despite several decades of intensive experimental and theoretical research in this field, open questions remain regarding segmental dynamics over the wide range of time scales from local to global motion. This work employs a novel approach based on nuclear magnetic relaxation to scrutinize the character of dipolar interactions in entangled polymer melts, thereby accessing unique information about segmental diffusion and rotation. The main focus is set on the separate consideration of intra- and intermolecular contributions to the proton dipolar interactions, which have been previously shown to possess a different, nontrivial time dependence. A combination of well-established field-cycling T1 relaxometry and recently developed methods based on spin echo is utilized to investigate dipolar couplings in entangled poly(ethylene oxide) melts of various molecular weights. Isolation of the intermolecular contributions to the corresponding experimental quantities provides a means to observe segmental translations taking place during more than 6 orders of magnitude in time. Time dependences of the mean-square displacement obtained in this way revealed apparent exponents of the power laws significantly deviating from predictions of the widely used tube-reptation model of polymer dynamics in the regime of entangled motion. In addition to that, the relative ratio of intermolecular dipolar interactions over the intramolecular counterpart is probed through their corresponding contributions to the transverse relaxation rate. A strong deviation from the tube-reptation model predictions for the evolution of this quantity is observed in the whole range probed experimentally. The obtained data do not reflect the restricted character of segmental motion anticipated in the corresponding time regime. It is emphasized that similar results, both in amplitude and in qualitative behavior, have been previously demonstrated in polybutadiene and polyethylene-alt-propylene, thereby allowing to discuss the universality of the observed deviation
Technoβeconomic assessment and comparison of different plastic recycling pathways: A German case study
Greenhouse gas (GHG) emissions need to be reduced to limit global warming. Plastic production requires carbon raw materials and energy that are associated today with predominantly fossil raw materials and fossil GHG emissions. Worldwide, the plastic demand is increasing annually by 4%. Recycling technologies can help save or reduce GHG emissions, but they require comparative assessment. Thus, we assess mechanical recycling, chemical recycling by means of pyrolysis and a consecutive, complementary combination of both concerning Global Warming Potential (GWP) [CO2e], Cumulative Energy Demand (CED) [MJ/kg], carbon efficiency [%], and product costs [β¬] in a processβoriented approach and within defined system boundaries. The developed technoβeconomic and environmental assessment approach is demonstrated in a case study on recycling of separately collected mixed lightweight packaging (LWP) waste in Germany. In the recycling paths, the bulk materials polypropylene (PP), polyethylene (PE), polyvinylchloride (PVC), and polystyrene (PS) are assessed. The combined mechanical and chemical recycling (pyrolysis) of LWP waste shows considerable saving potentials in GWP (0.48 kg CO2e/kg input), CED (13.32 MJ/kg input), and cost (0.14 β¬/kg input) and a 16% higher carbon efficiency compared to the baseline scenario with stateβofβtheβart mechanical recycling in Germany. This leads to a combined recycling potential between 2.5 and 2.8 million metric tons/year that could keep between 0.8 and 2 million metric tons/year additionally in the (circular) economy instead of incinerating them. This would be sufficient to reach both EU and German recycling rate targets (EC 2018). This article met the requirements for a goldβsilver JIE data openness badge described at http://jie.click/badges
Π―Π·ΡΠΊΠΎΠ²Π°Ρ ΡΠ΅ΠΏΡΠ΅Π·Π΅Π½ΡΠ°ΡΠΈΡ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠ° Β«ΠΠΎΠ½Π³ΠΎΠ»ΠΈΡΒ» Π² ΡΡΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠΌ Π΄ΠΈΡΠΊΡΡΡΠ΅ (Π½Π° ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Π΅ ΠΎΡΠ·ΡΠ²ΠΎΠ² ΡΠΎΡΡΠΈΠΉΡΠΊΠΈΡ ΡΡΡΠΈΡΡΠΎΠ² ΠΎ ΠΠΎΠ½Π³ΠΎΠ»ΠΈΠΈ)
ΠΠ°Π½Π½ΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈΠ²Π½ΠΎΡΡΡΡ ΡΠ°Π·ΡΠ°Π±Π°ΡΡΠ²Π°Π΅ΠΌΠΎΠ³ΠΎ Π² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΌ ΡΠ·ΡΠΊΠΎΠ·Π½Π°Π½ΠΈΠΈ Π°Π½ΡΡΠΎΠΏΠΎΡΠ΅Π½ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° ΠΊ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΡΠ·ΡΠΊΠ°, Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡΡ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠΈ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΠΊΠΎΠ³Π½ΠΈΡΠΈΠ²Π½ΠΎΠΉ Π»ΠΈΠ½Π³Π²ΠΈΡΡΠΈΠΊΠΈ ΠΈ Π»ΠΈΠ½Π³Π²ΠΎΠΊΡΠ»ΡΡΡΡΠΎΠ»ΠΎΠ³ΠΈΠΈ, ΡΡΠΈΠ»Π΅Π½ΠΈΠ΅ΠΌ Π²Π½ΠΈΠΌΠ°Π½ΠΈΡ ΠΈ ΠΏΠΎΡΡΠ΅Π±Π½ΠΎΡΡΡΡ ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠΎΠ·Π½Π°Π½ΠΈΡ Π² ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΠΊΠ»ΡΡΠ΅Π²ΡΡ
ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΎΠ² ΠΊΡΠ»ΡΡΡΡΡ, ΠΊ ΠΊΠΎΡΠΎΡΡΠΌ ΠΎΡΠ½ΠΎΡΠΈΡΡΡ ΠΈ ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΠΌΡΠΉ ΠΊΠΎΠ½ΡΠ΅ΠΏΡ "ΠΠΎΠ½Π³ΠΎΠ»ΠΈΡ", ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡΠΈΠΉ ΡΠΎΠ±ΠΎΠΉ ΠΎΠ΄Π½Ρ ΠΈΠ· Π½Π΅ΡΡΡΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΎΠ±ΡΠ°Π·Π° ΠΌΠΈΡΠ°, Π³Π»ΠΎΠ±Π°Π»ΡΠ½ΡΡ ΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ Π΅Π΄ΠΈΠ½ΠΈΡΡ Π² ΡΠΎΡΡΠ°Π²Π΅ ΡΡΡΡΠΊΠΎΠΉ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΎΡΡΡΠ΅ΡΡ. ΠΠ΅ΡΠΌΠΎΡΡΡ Π½Π° ΡΠΎ, ΡΡΠΎ Π»Π΅ΠΊΡΠΈΠΊΠΎ-ΡΠ΅ΠΌΠ°Π½ΡΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΏΠΎΠ»Π΅ ΠΠΎΠ½Π³ΠΎΠ»ΠΈΡ β ΠΎΠ΄Π½ΠΎ ΠΈΠ· ΡΠ°ΠΌΡΡ
ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅Π»ΡΠ½ΠΎ Π½Π°ΡΡΡΠ΅Π½Π½ΡΡ
ΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠ°ΡΠΏΠ΅ΠΊΡΠ½ΠΎ ΠΈΠ½ΡΠ΅ΠΏΡΠ΅ΡΠΈΡΡΠ΅ΠΌΡΡ
, Π»ΠΈΠ½Π³Π²ΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΠΉ Π°ΡΠΏΠ΅ΠΊΡ ΡΡΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠ° ΡΠ°ΡΠΊΡΡΡ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ, ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ΄Π²Π΅ΡΠ³Π»ΠΈΡΡ Π»ΠΈΡΡ ΠΎΡΠ΄Π΅Π»ΡΠ½ΡΠ΅ ΠΎΠ±Π»Π°ΡΡΠΈ Π±ΠΎΠ³Π°ΡΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠΈΡΠ° Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠ°.This study is determined by the productivity of the anthropocentric approach to describing the language developed in modern linguistics, the need to develop theoretical theories of cognitive linguistics and linguoculturology,and also by increasing attention and the need for modern linguistics in the study of key concepts of culture, which includes the described concept "Mongolia", which is one from the bearing designs of the image of the world, the global mental unit within the Russian conceptosfrera. Despite the fact that the lexical and semantic field of Mongolia is one of the most meaningfully saturated and multi-faceted interpretations, the linguistic aspect of this concept is not sufficiently disclosed, only certain areas of the rich linguistic world of this concept have been explore
On the theory of the proton free induction decay and Hahn echo in polymer systems: The role of intermolecular magnetic dipole-dipole interactions and the modified Anderson-Weiss approximation
The influence of the intermolecular magnetic dipole-dipole interaction on the free induction decay (FID) as well as on the Hahn-echo of proton spins in polymer melts is investigated. It is shown that for isotropic models of polymer dynamics, when polymer segment displacements do not correlate with an initial chain conformation, the influence of the intermolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing more rapidly with evolution time than the corresponding influence of the intramolecular magnetic dipole-dipole interactions. On the other hand, the situation is inverted for the tube-reptation model: here the influence of the intramolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing faster with time than the contribution from intermolecular interactions. A simple expression for the relative mean squared displacements of polymer segments from different chains is obtained from the intermolecular contribution to the FID. A modified Anderson-Weiss approximation, taking into account flip-flop transitions between different spins, is proposed and on that basis, the conditions for extracting the relative intermolecular mean squared displacements of polymer segments from the intermolecular contribution to the proton FID is established. Systematic investigations of intermolecular contributions, which were considered as an unimportant factor for FID and Hahn echo in polymer systems by most previous works, actually cannot be considered as negligible and opens a new dimension for obtaining information about polymer dynamics in the millisecond regime. Β© 2012 American Institute of Physics
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