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We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under Grant Agreement No. 633053. Peer Reviewed Article signat per 497 autors/es: Thomas Sunn Pedersen1,2,∗ , I. Abramovic3, P. Agostinetti4, M. Agredano Torres1, S. Äkäslompolo1, J. Alcuson Belloso1, P. Aleynikov1, K. Aleynikova1, M. Alhashimi1, A. Ali1, N. Allen5, A. Alonso6, G. Anda7, T. Andreeva1, C. Angioni8, A. Arkhipov8, A. Arnold1, W. Asad8, E. Ascasibar6, M.-H. Aumeunier9, K. Avramidis10, E. Aymerich11, S.-G. Baek3, J. Bähner1, A. Baillod12, M. Balden1, M. Balden8, J. Baldzuhn1, S. Ballinger3, M. Banduch1, S. Bannmann1, A. Banon Navarro8, A. Bañon Navarro ´ 1, T. Barbui13, C. Beidler1, C. Belafdil9, A. Bencze7, A. Benndorf1, M. Beurskens1, C. Biedermann1, O. Biletskyi14, B. Blackwell15, M. Blatzheim1, T. Bluhm1, D. Böckenhoff1, G. Bongiovi16, M. Borchardt1, D. Borodin17, J. Boscary8, H. Bosch1,18, T. Bosmann19, B. Böswirth8, L. Böttger1, A. Bottino8, S. Bozhenkov1, R. Brakel1, C. Brandt1, T. Bräuer1, H. Braune1, S. Brezinsek17, K. Brunner1, S. Buller1, R. Burhenn1, R. Bussiahn1, B. Buttenschön1, A. Buzás7, V. Bykov1, I. Calvo6, K. Camacho Mata1, I. Caminal20, B. Cannas11, A. Cappa6, A. Carls1, F. Carovani1, M. Carr21, D. Carralero6, B. Carvalho22, J. Casas20, D. Castano-Bardawil17, F. Castejon6, N. Chaudhary1, I. Chelis23, A. Chomiczewska24, J.W. Coenen13,17, M. Cole1, F. Cordella25, Y. Corre9, K. Crombe26, G. Cseh7, B. Csillag7, H. Damm1, C. Day10, M. de Baar27, E. De la Cal6, S. Degenkolbe1, A. Demby13, S. Denk3, C. Dhard1, A. Di Siena8,28, A. Dinklage12, T. Dittmar17, M. Dreval14, M. Drevlak1, P. Drewelow1, P. Drews17, D. Dunai7, E. Edlund3, F. Effenberg29, G. Ehrke1, M. Endler1, D.A. Ennis5, F.J. Escoto6, T. Estrada6, E. Fable8, N. Fahrenkamp1, A. Fanni11, J. Faustin1, J. Fellinger1, Y. Feng1, W. Figacz4, E. Flom13, O. Ford1, T. Fornal24, H. Frerichs13, S. Freundt1, G. Fuchert1, M. Fukuyama30, F. Füllenbach1, G. Gantenbein10, Y. Gao1, K. Garcia13, J.M. García Regaña6, I. García-Cortés6, J. Gaspar31, D.A. Gates29, J. Geiger1, B. Geiger13, L. Giudicotti32, A. González6, A. Goriaev26,33, D. Gradic1, M. Grahl1, J.P. Graves12, J. Green13, E. Grelier9, H. Greuner8, S. Groß1, H. Grote1, M. Groth34, M. Gruca24, O. Grulke1,35, M. Grün1, J. Guerrero Arnaiz1, S. Günter8, V. Haak1, M. Haas1, P. Hacker1, A. Hakola36, A. Hallenbert1, K. Hammond29, X. Han17,37, S.K. Hansen3, J.H. Harris38, H. Hartfuß1, D. Hartmann1, D. Hathiramani1, R. Hatzky8, J. Hawke39, S. Hegedus7, B. Hein8, B. Heinemann8, P. Helander12, S. Henneberg1, U. Hergenhahn8,40, C. Hidalgo6, F. Hindenlang8, M. Hirsch1, U. Höfel1, K.P. Hollfeld17, A. Holtz1, D. Hopf8, D. Höschen17, M. Houry9, J. Howard19, X. Huang41, M. Hubeny17, S. Hudson29, K. Ida9, Y. Igitkhanov10, V. Igochine8, S. Illy10, C. Ionita-Schrittwieser42, M. Isobe39, M. Jabłczynska ´ 24, S. Jablonski24, B. Jagielski1, M. Jakubowski1, A. Jansen van Vuuren1, J. Jelonnek10, F. Jenko8, F. Jenko8, T. Jensen35, H. Jenzsch1, P. Junghanns8, J. Kaczmarczyk24, J. Kallmeyer1, U. Kamionka1, M. Kandler8, S. Kasilov43, Y. Kazakov26, D. Kennedy1, A. Kharwandikar1, M. Khokhlov1, C. Kiefer8, C. Killer1, A. Kirschner17, R. Kleiber1, T. Klinger12, S. Klose1, J. Knauer1, A. Knieps17, F. Köchl44, G. Kocsis7, Ya.I. Kolesnichenko45, A. Könies1, R. König1, J. Kontula34, P. Kornejew1, J. Koschinsky, M.M. Kozulia14, A. Krämer-Flecken17, R. Krampitz1, M. Krause1, N. Krawczyk24, T. Kremeyer1, L. Krier10, D.M. Kriete5, M. Krychowiak1, I. Ksiazek46, M. Kubkowska24, M. Kuczynski1, G. Kühner1, A. Kumar15, T. Kurki-Suonio34, S. Kwak1, M. Landreman47, P.T. Lang8, A. Langenberg1, H.P. Laqua12, H. Laqua1, R. Laube1, S. Lazerson1, M. Lewerentz1, C. Li17, Y. Liang17, Ch. Linsmeier17, J. Lion1, A. Litnovsky17,48, S. Liu37, J. Lobsien1, J. Loizu12, J. Lore38, A. Lorenz1, U. Losada6, F. Louche26, R. Lunsford29, V. Lutsenko45, M. Machielsen12, F. Mackel8, J. Maisano-Brown3, O. Maj8, D. Makowski49, G. Manduchi50, E. Maragkoudakis6, O. Marchuk17, S. Marsen1, E. Martines4, J. Martinez-Fernandez6, M. Marushchenko1, S. Masuzaki41, D. Maurer5, M. Mayer8, K.J. McCarthy6, O. Mccormack4, P. McNeely1, H. Meister8, B. Mendelevitch8, S. Mendes1, A. Merlo1, A. Messian26, A. Mielczarek49, O. Mishchenko1, B. Missal1, R. Mitteau9, V.E. Moiseenko14, A. Mollen1, V. Moncada9, T. Mönnich1, T. Morisaki41, D. Moseev1, G. Motojima41, S. Mulas6, M. Mulsow1, M. Nagel1, D. Naujoks1, V. Naulin35, T. Neelis19, H. Neilson29, R. Neu8, O. Neubauer17, U. Neuner1, D. Nicolai17, S.K. Nielsen35, H. Niemann1, T. Nishiza1, T. Nishizawa1, T. Nishizawa8, C. Nührenberg1, R. Ochoukov8, J. Oelmann17, G. Offermanns17 K. Ogawa41, S. Okamura41, J. Ölmanns17, J. Ongena26, J. Oosterbeek1, M. Otte1, N. Pablant29, N. Panadero Alvarez6, N. Panadero Alvarez6, A. Pandey1, E. Pasch1, R. Pavlichenko14, A. Pavone1, E. Pawelec46, G. Pechstein1, G. Pelka24, V. Perseo1, B. Peterson41, D. Pilopp1, S. Pingel1, F. Pisano11, B. Plöckl8, G. Plunk1, P. Pölöskei1, B. Pompe2, A. Popov51, M. Porkolab3, J. Proll19, M.J. Pueschel19,27, M.-E. Puiatti52, A. Puig Sitjes1, F. Purps1, K. Rahbarnia1, M. Rasinski ´ 17, J. Rasmussen35, A. Reiman29, F. Reimold1, M. Reisner8, D. Reiter17, M. Richou9, R. Riedl8, J. Riemann1, K. Riße1, G. Roberg-Clark1, V. Rohde8, J. Romazanov17, D. Rondeshagen1, P. Rong1, L. Rudischhauser1, T. Rummel1, K. Rummel1, A. Runov1, N. Rust1, L. Ryc24, P. Salembier20, M. Salewski35, E. Sanchez6, S. Satake41, G. Satheeswaran17, J. Schacht1, E. Scharff1, F. Schauer8, J. Schilling1, G. Schlisio1, K. Schmid8, J. Schmitt5, O. Schmitz13, W. Schneider1, M. Schneider1, P. Schneider8, R. Schrittwieser42, T. Schröder1, M. Schröder1, R. Schroeder1, B. Schweer26, D. Schwörer1, E. Scott1, E. Scott8, B. Shanahan1, G. Sias11, P. Sichta29, M. Singer1, P. Sinha29, S. Sipliä34, C. Slaby1, M. Sleczka53, H. Smith1, J. Smoniewski54, E. Sonnendrücker8, M. Spolaore4, A. Spring1, R. Stadler8, D. Stanczak24, T. Stange1, I. Stepanov26, L. Stephey13, J. Stober8, U. Stroth8,55, E. Strumberger8, C. Suzuki41, Y. Suzuki41, J. Svensson1, T. Szabolics7, T. Szepesi7, M. Szücs7, F.L. Tabares6, N. Tamura41, A. Tancetti35, C. Tantos10, J. Terry3, H. Thienpondt6, H. Thomsen1, M. Thumm10, J.M. Travere9, P. Traverso5, J. Tretter8, E. Trier8, H. Trimino Mora1, T. Tsujimura41, Y. Turkin1, A. Tykhyi45, B. Unterberg17, P. van Eeten1, B.Ph. van Milligen6, M. van Schoor26, L. Vano1, S. Varoutis10, M. Vecsei7, L. Vela56, J.L. Velasco6, M. Vervier17, N. Vianello50, H. Viebke1, R. Vilbrandt1, G. Vogel8, N. Vogt1, C. Volkhausen1, A. von Stechow1, F. Wagner1, E. Wang17, H. Wang57, F. Warmer1, T. Wauters26, L. Wegener1, T. Wegner1, G. Weir1, U. Wenzel1, A. White3, F. Wilde1, F. Wilms1, T. Windisch1, M. Winkler1, A. Winter1, V. Winters1, R. Wolf118, A.M. Wright29, G.A. Wurden39, P. Xanthopoulos1, S. Xu17, H. Yamada58, H. Yamaguchi41, M. Yokoyama41, M. Yoshinuma41, Q. Yu8, M. Zamanov14, M. Zanini1, M. Zarnstorff29, D. Zhang1, S. Zhou17, J. Zhu1, C. Zhu29, M. Zilker8, A. Zocco1, H. Zohm8, S. Zoletnik7 and L. Zsuga7 // 1 Max Planck Institute for Plasma Physics, Garching and Greifswald, Germany: 2 University of Greifswald, Greifswald, Germany; 3 Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States of America; 4 Consorzio RFX, Corso Stati Uniti, 4-35127 Padova, Italy; 5 Auburn University, Auburn, AL 36849, United States of America; 6 CIEMAT, Avenida Complutense, 40, 28040 Madrid, Spain; 7 Center for Energy Research, Konkoly-Thegeut 29-33, 1121 Budapest, Hungary; 8 Max-Planck-Institute for Plasma Physics, Boltzmannstraße 2, 85748 Garching bei München, Germany; 9 CEA Cadarache, 13115 Saint-Paul-lez-Durance, France; 10 Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany; 11 University of Cagliari, Via Universita, 40, 09124 Cagliari, Italy; 12 École Polytechnique Fédérale de Lausanne, Swiss Plasma Center, CH-1015 Lausanne, Switzerland; 13 University of Wisconsin–Madison, Engineering Drive, Madison, WI 53706, United States of America; 14 Institute of Plasma Physics, National Science Center ‘Kharkiv Institute of Physics and Technology’, Kharkiv, Ukraine; 15 The Australian National University, Acton ACT 2601, Canberra, Australia; 16 Department of Engineering, University of Palermo, Viale delle Scienze, Edificio 6, Palermo, 90128, Italy; 17 Forschungszentrum Jülich GmbH, Institut für Energie-und Klimaforschung—Plasmaphysik, 52425 Jülich, Germany; 18 Technical University of Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany; 19 Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands; 20 Universitat Politècnica de Catalunya. BarcelonaTech, C. Jordi Girona, 31, 08034 Barcelona, Spain; 21 Culham Center for Fusion Energy, Abingdon OX14 3EB, United Kingdom; 22 Instituto de Plasmas e Fusao Nuclear, Av. Rovisco Pais, 1049-001 Lisboa, Portugal; 23 Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece; 24 Institute of Plasma Physics and Laser Microfusion, 23 Hery Str., 01-497 Warsaw, Poland; 25 ENEA—Centro Ricerche Frascati, Via Enrico Fermi, 45, 00044 Frascati RM, Italy; 26 Laboratory for Plasma Physics, LPP-ERM/KMS, TEC Partner, B-1000 Brussels, Belgium; 27 Dutch Institute for Fundamental Energy Research, PO Box 6336, 5600 HH Eindhoven, Netherlands; 28 University of Texas, Austin, TX, United States of America; 29 Princeton Plasma Physics Laboratory, Princeton, NJ 08543, United States of America; 30 Kyushu University, 744 Motooka Nishi-ku, Fukuoka 819-0395, Japan; 31 Aix-Marseille University, Jardin du Pharo, 58 Boulevard Charles Livon, 13007, Marseille, France; 32 Department of Physics and Astronomy, Padova University, Via Marzolo 8, 35131 Padova, Italy; 33 Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41 B4, 9000 Ghent, Belgium; 34 Aalto University, 02150 Espoo, Finland; 35 Department of Physics, Technical University of Denmark, Anker Engelunds Vej, 2800 Kgs Lyngby, Denmark; 36 VTT Technical Research Center of Finland Ltd., PO Box 1000, FI-02044 VTT, Finland; 37 Institute of Plasma Physics, Chinese Academy of Sciences, 230031 Hefei, Anhui, China; 38 Oak Ridge National Laboratory, 1 Bethel Valley Rd, Oak Ridge, TN 37830, United States of America; 39 Los Alamos National Laboratory, NM 87545, United States of America; 40 Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany; 41 National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki, Gifu Prefecture 509-5292, Japan; 42 Institute for Ion Physics and Applied Physics, University of Innsbruck, Innsbruck, Austria; 43 Graz University of Technology, Rechbauerstraße 12, 8010 GRAZ, Austria; 44 Austrian Academy of Science, Doktor-Ignaz-Seipel-Platz 2, 1010 Wien, Austria; 45 Institute for Nuclear Research, prospekt Nauky 47, Kyiv 03028, Ukraine; 46 University of Opole, plac Kopernika 11a, 45-001 Opole, Poland; 47 University of Maryland, Paint Branch Drive, College Park, MA 20742, United States of America; 48 National Research Nuclear University MEPhI, 115409 Moscow, Russian Federation; 49 Department of Microelectronics and Computer Science, Lodz University of Technology, Wolczanska 221/223, 90-924 Lodz, Poland; 50 Consiglio Nazionale delle Ricerche, Piazzale Aldo Moro, 7, 00185 Roma, Italy; 51 Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 26 Politekhnicheskaya, St Petersburg 194021, Russian Federation; 52 Istituto di Fisica del Plasma Piero Caldirola, Via Roberto Cozzi, 53, 20125 Milano, Italy; 53 University of Szczecin, 70-453, aleja Papieza Jana Pawła II 22A, Szczecin, Poland; 54 Lawrence University, 711 E Boldt Way, Appleton, WI 54911, United States of America; 55 Physik-Department E28, Technische Universität München, 85747 Garching, Germany; 56 Universidad Carlos III de Madrid, Av. de la Universidad, 30 Madrid, Spain; 57 Yale University, New Haven, CT 06520, United States of America; 58 University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chhiab 277-0882, Japan Objectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant Objectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.a - Per a 2030, augmentar la cooperació internacional per tal de facilitar l’accés a la investigació i a les tecnolo­gies energètiques no contaminants, incloses les fonts d’energia renovables, l’eficiència energètica i les tecnologies de combustibles fòssils avançades i menys contaminants, i promoure la inversió en infraestructures energètiques i tecnologies d’energia no contaminant

The kinetic and thermal processes occurring during the separation of model solutions using electrodialysis equipment have been investigated. The design drawbacks of the developed apparatus that can affect the efficiency and quality of the solutions separation have been revealed.

The design of a roll-type electrobaromembrane apparatus has been developed, in which a high efficiency of mixing of multicomponent solutions is ensured when separating colloidal process fluids and waste water from chemical industries. A method for calculating the total area of membranes in an electrobaromembrane apparatus, taking into account the areas of roll and tubular elements, has been developed.

This paper presents the results of a study of the initiation of explosive transformation of flat charges 40 mm in diameter and 5 mm thick, made of a low-density ( $$\rho$$ $$\approx$$ 0.9 g/cm3) light-sensitive explosive composition based on fine RDX and aluminum. It is shown that laser radiation (LR) can be used to initiate explosive transformation over a large area ( $$\approx$$ 1 000 mm2) with a small time difference in the arrival of the detonation wave front. It is determined that at an LR energy density $$Q_\text{opt}$$ = 10 J/cm2) over the entire LR spot on the charge surface, the time difference in the arrival of the detonation wave front at the rear surface of the charge is not more than 50 ns.

The composite materials features and characteristic defects in the obtaining apertures by machining are considered. A new method for forming apertures in fibrous polymer composite materials is proposed. The optimal shape of a tool for piercing holes is determined. The profiles of the pointed part of the tool are compared using numerical modeling.

It is demonstrated that the PT-symmetric terahertz photoconductivity observed in heterostructures based on thick Hg1 – xCdxTe films in the topological phase is due to the photoexcitation of charge carriers in the film bulk. At the same time, the place of localization of the effect is the topological film–trivial buffer layer heterointerface. The model describing such a spatial separation of the source of nonequilibrium charge carriers and the effect localization is discussed.

A tubular electrochemical membrane apparatus that enables efficient mixing of chemical plant solutions to be separated and of colloidal process solutions is designed and a procedure for calculating the total working area of the membranes in a tubular electrobaromembrane apparatus is developed. The areas of the cathodic and anodic membranes are calculated.

The selective modification of upper layers of a Ni/Al multilayer nanostructure irradiated by a single femtosecond laser pulse has been studied. The analysis of surface topography indicates that either partial or complete removal of two upper layers is possible depending on the absorbed energy. The surface has been scanned by an atomic force microscope. The numerical simulation of the phenomenon with a two-temperature hydrodynamic code has revealed an asynchronous dynamics of the electron subsystems of Ni and Al and an inhomogeneous heating of ion subsystems. As a result, a complex combination of compression and rarefaction waves is initiated in the multilayer target. It has been shown numerically that, as the absorbed energy increases, the first nickel layer is initially ruptured because of the localization of tensile stresses. The experimental and numerical thicknesses of the separated layer and the threshold energy are in agreement with each other. Consequently, the parameters of two-temperature models of nickel and aluminum are selected correctly.

An analysis of the I–V characteristics makes it possible to determine the mechanisms of conduction corresponding to different states of the flow channels upon resistive switching in porphyrazine films. A variation in the temperature, the structure of the dielectric matrix, and the type of majority charge carriers makes it possible to estimate the applicability of the model of conducting filaments for describing transport and determining the mechanisms of conduction for each state of the system.

In nanoscale communications, high-frequency surface acoustic waves are becoming effective data carriers and encoders. On-chip communications require acoustic wave propagation along nanocorrugated surfaces which strongly scatter traditional Rayleigh waves. Here, we propose the delivery of information using subsurface acoustic waves with hypersound frequencies of ∼20 GHz, which is a nanoscale analogue of subsurface sound waves in the ocean. A bunch of subsurface hypersound modes are generated by pulsed optical excitation in a multilayer semiconductor structure with a metallic nanograting on top. The guided hypersound modes propagate coherently beneath the nanograting, retaining the surface imprinted information, at a distance of more than 50 μm which essentially exceeds the propagation length of Rayleigh waves. The concept is suitable for interfacing single photon emitters, such as buried quantum dots, carrying coherent spin excitations in magnonic devices and encoding the signals for optical communications at the nanoscale.

The effect of two successive laser pulses on silicon placed in glycerol has been studied experimentally and numerically with electromagnetic, hydrodynamic, and atomistic simulation programs. It has been shown that a microbubble in the liquid is formed on the surface after the first pulse; then, the second pulse whose width is comparable with the diameter of the microbubble is diffracted on this microbubble. The calculated diffraction pattern and light intensity distribution on the silicon surface indicate that the maximum intensity at the diffraction peaks can be noticeably higher than the intensity on the axis of the incident Gaussian beam. An increase in the intensity concentrated in one bright narrow ring around the microbubble results in the formation of a characteristic groove surrounded by ridges on silicon. The molecular dynamics simulation has shown that intense heating at the diffraction peak is responsible for the melting and displacement of the melt from the center of heating. This leads to the formation of grooves with ridges having a profile similar to that measured in the experiment.

Applicability indicators of the linear viscoelasticity constitutive relation for isotropic time-dependent materials with arbitrary shear and bulk creep compliances are considered. General properties of the creep curve families for volumetric, longitudinal, and lateral strains generated by this linear relation under constant uniaxial tension and constant hydrostatic pressure are studied analytically. It is proved that the linear theory of viscoelasticity is able to describe the effect of (monotonic) expansion of a linear behavior range of material qualitatively as the hydrostatic pressure grows; more precisely, the effect of expansion of a range of axial stress values under which the axial compliance is independent of the stress level. The analysis reveals a number of specific features of the theoretical creep and compliance curves that can be conveniently employed as the applicability or non-applicability indicators of the linear viscoelasticity theory by the data of material creep tests under action of tensile load and hydrostatic pressure.

Hybrid quantum dot solar cell (HQDSC) based on solution-processed blends of poly(3-hexylthiophene) (P3HT) with PbS quantum dots (QDs) is a potential candidate toward practical use for its low material cost and simple fabrication process. However, P3HT is highly incompatible with oleic acid (OA)-capped PbS QDs (OA-PbS QDs) due to strong phase separation, giving poor quality in the desired bi-continuous networks morphology and thus leading to inefficient charge collection. Here, for the first time, a block copolymer of P3HT with polystyrene (P3HT-b-PS) was confirmed to improve the miscibility between the polymers and OA-PbS QDs, leading to the formation of a desirable bi-continuous network morphology, as predicted by us via dissipative dynamic simulations previously. The bi-continuous network morphology for charge transport is an ideal morphology in bulk heterojunction solar cells. For the active layer, using the block copolymer P3HT-b-PS as the donor and PbS QDs as the acceptor at the weight ratio of 1 : 20, the power conversion efficiency (PCE) of HQDSC was found to be 4.18%, which is higher than P3HT and PbS QDs (3.66%) having the same weight ratio even though the content of the P3HT component in P3HT-b-PS was 28% less than that of homo-polymer of P3HT. The formation of the desired morphology for electron and hole collections of the device with the block copolymer was confirmed via scanning electron microscopy. Further, the addition of P3HT into the blend of the block copolymer with OA-PbS QDs still retains the desired morphology. Therefore, further improvement of PCE was made by taking the blend of P3HT and P3HT-b-PS at the weight ratio of 0.7 : 0.3 as the donor, thus achieving the PCE of 4.91%, which is better than that of P3HT alone by 1.25% and P3HT-b-PS alone by 0.73%. Thus, this methodology could be applicable for hybrid solar cells with a low bandgap molecular or polymeric material as the donor.

A series of new random terpolymers was synthesized by copolymerization of one electron-donor alkyl-substituted benzodithiophene unit and two electron-acceptor units, diketopyrrolopyrrole (DPP) and bis(4,5-dodecylthiophen-2-yl)-[1,2,5]thiadiazol[3,4-i]dithieno[3,2-a:2',3'-c]phenazine (DF). The influence of the DPP/DF ratio on the thermal, optoelectronic, and electrochemical properties of the terpolymers was investigated using thermogravimetric analysis, UV-Vis spectroscopy, and cyclic voltammetry. The optical properties of the synthesized terpolymers were controlled by varying the DPP/DF ratio. An increase in the DF mole fraction in the polymer chain caused an increase in absorption intensity in the 300‒600 and 600‒1100 nm ranges, while increasing mole fraction of DPP resulted in stronger absorption in the 600‒900 nm range and lower absorption intensity in the 350‒600 nm range. The terpolymers exhibited broad and intense absorption over the spectral range from 300 to 1100 nm. The results demonstrate that random terpolymers with complementary absorption spectra have a great potential for increasing the photocurrent and efficiency of polymer solar cells.

The development of conjugated polymers with wide absorption spectra is imperative to achieve high efficiency in polymer solar cells (PSCs), since most of these polymers usually absorb only a limited range of the solar spectrum. Random terpolymers consisting of three blocks (one electron-donor and two electron-acceptor blocks) are promising p-type polymers for PSCs, because the inclusion of a third block in the polymer macromolecules provides a synergistic effect of physical properties, such as absorption capacity, charge transfer, HOMO/LUMO energy levels, and photovoltaic characteristics. In this regard, we have developed and synthesized random terpolymers consisting of two different chromophores (DPP and BFCTP) with complementary absorption spectra as co-acceptor blocks in conjugated donor–acceptor (D–A) copolymers. Random copolymers exhibit both broad absorption and low HOMO levels favoring short-circuit current and idle voltage in PSCs. It is expected that new terpolymers consisting of one electron-donor unit and two electron-acceptor moieties will make a significant contribution to the development of highly efficient PSCs. It is expected that new ternary copolymers consisting of one electron-donor unit and two electron-acceptor fragments will make a significant contribution to the development of high-performance PSСs.

Iron and aluminum form a number of intermetallic phases, which have a quite high hardness and can be used for manufacturing parts of equipment operating under abrasive wear conditions. In addition, the advantage of applying iron–aluminum intermetallic alloys is a low cost and the lack of deficiency of the alloy components (aluminum, iron). However, all intermetallic compounds of this system have a high brittleness, and this fact restricts the region of applying the alloys based on iron–aluminum intermetallic phases. As an alternative to the parts made of the intermetallic alloys, steel–iron aluminide composites are proposed. The technology of manufacturing these composites is described. The studies performed in this work show that the proposed technology enables the formation of composite materials of adequate quality. The ultimate compressive strength of porous steel is ~145 MPa, and that of the composite material is higher than 435 MPa. The hardness of the intermetallic portions of the composite material is 385–400 HB, and the relative wear resistance of the composite material is ~6.

The phase transitions of poly(N-isopropylacrylamide) (PNIPAM) in water–methanol mixed solutions were studied in detail by high-sensitivity differential scanning calorimetry. From this study, the de...

Modern space-based telescopes operating in the terahertz (THz) spectral range require highly reflecting and cryogenically cooled optics ensuring extremely low noise. The idea of using high-temperature superconductor YBa 2 Cu 3 O 7-δ as a telescope's mirror coating for providing low dissipation and high reflectivity of the surface for the subTHz frequency band has been explored. We are presenting here some results of measurements of the reflection losses in YBa 2 Cu 3 O 7-δ at cryogenic and room temperatures (4.2-300 K) in the frequency band 0.166-0.23 THz. High-accuracy measurements of the absolute value of reflectivity have been performed with the help of the resonance technique. The measured reflection losses in the given frequency band were below 1%. For the same frequency range, these values are well above the reflection losses in normal metals such as copper or aluminum, which are normally used to cover mirrors of telescopes. We, therefore, conclude that the use of high-Tc superconductors YBa 2 Cu 3 O 7-δ as a highly reflecting coating for the THz telescope's mirror is not advisable.

An exact solution is constructed for the problem of creep and fracture of a hollow cylinder made of a physically nonlinear rheonomic isotropic incompressible material, which obeys Rabotnov’s constitutive viscoelasticity relation with two arbitrary material functions, under the action of internal and external pressures. Сlosed form equations for long-term strength curves are derived using three versions of a deformation fracture criterion, and the strain intensity, the maximum shear strain, or the maximum tensile strain is chosen as the measure of damage. Their properties are analytically investigated for arbitrary material functions of the constitutive relation.

Foam aluminium is a promising material with a unique combination of mechanical and operational properties: low specific gravity, low coefficient of thermal conductivity, ability to absorb acoustic ...

The results of studies of the optical and transport properties of epitaxial Pb0.74Sn0.26Te(In) films with a differently treated surface are presented. A comparative analysis of the results makes it possible to establish that the characteristic features of the photoconductivity spectra are defined by processes in the bulk while the surface states have practically no effect on the spectra. At the same time, the photoresponse kinetics and the rate of relaxation processes are heavily dependent on the state of the surface. The characteristic relaxation times of nonequilibrium charge carriers (about several milliseconds) are such that it is possible to use the methods of standard Fourier-transform spectroscopy to characterize optical transitions in the bulk.

In this paper, we report on photoconductivity induced by high-power laser radiation with a frequency of 2 THz in Hg0.87Cd0.13Te-based epitaxial structures. Experimental results obtained for a set of the samples with variable geometric parameters allow us to determine the photoresponse features of both bulk and nonlocal contributions to the net response. We show that the persistent photoconductivity effect originates from the non-equilibrium processes related to the bulk carrier excitation.

The development of energy-efficient methods of controlling the stress state of metallic materials and welded joints is topical for modern production. One of such methods is electrodynamic treatment (EDT). It is based on the passage of electric current pulses (ECP) through the metal, time-synchronized with an impact load initiated by electrodynamic forces. In this case, an electrodynamic deformation process and a process of formation of elastic strain waves occur simultaneously in the material being treated; they are defined as “electrodynamic impact”, the result of which is a local stress relaxation in the metal. The developed mathematical model of the formation of stress and strain fields during EDT, which is based on the motion of an elastoplastic medium, does not take into account the effect of ECPs on dynamic relaxation processes. A computational and experimental assessment of the effect of ECPs, which is based on the experimental assessment of the stress state and microindentation of AMg6 aluminum alloy plates after EDT without and with the passage of ECPs through the metal being treated, has been performed by the mathematical modeling of the EDT process taking into account microindentation results. The passage of ECPs contributes to an increase in tensile plastic strains and hence to an increase in residual compressive stresses (provided that the specimens to be treated are rigidly fixed). The reliability of the procedure has been confirmed by the results of evaluating the distribution of residual welding stresses in AMg6 alloy butt joints after EDT.

In this paper, we report on observation of a new effect—asymmetric in a magnetic field photoconductivity stimulated by radiofrequency pulses in heterostructures based on thick Hg1−xCdxTe films with composition x < 0.16 corresponding to the topological phase. At certain values of the excitation frequency, the photoconductivity may even change sign when the magnetic field is reversed. Possible mechanisms responsible for the effect appearance are discussed.

The synthesis of magnetite (Fe3O4) nanorods using reverse co-precipitation of Fe3+ and Fe2+ ions in the presence of a static magnetic field is reported in this work. The phase composition and crystal structure of the synthesized material were investigated using electron diffraction, Raman spectroscopy, and transmission electron microscopy. It was shown that the morphology of the reaction product strongly depends on the amount of OH− ions in the reaction mixture, varying from Fe3O4 nanorods to spherical Fe3O4 nanoparticles. Fe3O4 nanorods were examined using high-resolution transmission electron microscopy proving that they are single-crystalline and do not have any preferred crystallographic orientation along the axis of the rods. According to the data obtained a growth mechanism was proposed for the rods that consists of the dipole–dipole interaction between their building blocks (small hexagonal faceted magnetite nanocrystals), which are formed during the first step of the reaction. The study suggests a facile, green and controllable method for synthesizing anisotropic magnetic nanoparticles in the absence of stabilizers, which is important for further modification of their surfaces and/or incorporation of the nanoparticles into different media.

Laser ablation (i.e., the removal of target material upon irradiation) is under consideration; it is widely applied in some technologies. Physical models needed for an understanding of ablation have been developed since the invention of the first lasers. Some phenomena have been thoroughly investigated; however, there are still many problems that should be analyzed additionally. These poorly studied phenomena include surface structuring. The problems concerning ablation in liquid and laser forging/peening are not yet completely understood. They represent two sides of the same process: in the first case, the emphasis is on the description of motion of the substance beyond the target, whereas, in the case of laser forging, one abstracts from the plume and considers the elastoplastic transformations caused by a shock wave inside a target. The hydrodynamics of these processes differs radically with the transition from ultrashort to long pulses.

A measurement setup based on a transmission microscope with double acousto-optical wavelength selection is proposed for detection of high-quality spectral images with a size of 1920 × 1200 pixels in the visible wavelength range with a spectral resolution of 2.5 nm at a wavelength of 632 nm. The efficiency of the proposed approach and setup is demonstrated in the study of the transition of Misgurnus fossilis embryos from the 32nd to the 33rd stage. Correctness of the conclusions is proven in a comparison with the results of the corresponding ultrasonic study. Analysis of time dependences of the transmission spectra is performed for six spatial regions of the embryo including perivitelline space and head and tail sections. Such substantially different dependences can be used, in particular, for noninvasive monitoring and analysis of changes in the functional state of embryos related to the stage-to-stage transition.

A new oligomeric fluorophore, which combines the advantage of polycyclic aromatic compounds and fluorene structures has been synthesized. The new compound shows necessary film-forming properties, is readily soluble in the majority of organic solvents and emits in the blue range of solar light with maximum at 465 nm. The compound has a rather high quantum yield and can serve as both the electroluminescent dopant and the conducting light-emitting matrix for designing completely soluble blue and white OLEDs by both inkjet printing and spin coating. The new oligomeric fluorophore is a promising example of highly fluorescent oligomer, rarely used class of materials, in contrast to polymers and small molecules. Such oligomers can be useful for future completely soluble OLEDs.

Based on laws of theory of materials strengthening were discribed the experimentally obtained alloying effect in Mg-Ga system and shown using program for 3d atomic structures. As known from our experiments a homogeneous “wavy” microstructure of the diffusion zone forms as result of mass-transfer of molten gallium into the volume of magnesium alloys. SEM chemical composition shows Mg 65% wt. and Ga 35% wt. and X-ray spectra diffraction data - Mg5Ga2 intermetallic phase formation. Such intermetallic diffusion zone provides the significant strengthening effect of microstructure which was determined experimentally by the indentation method. The 3-d visualization shows the reaction and changing of an original crystal structure of magnesium atomic lattice upon diffusion doping with foreign atoms of gallium and then is shown the coalescence of Mg5Ga2 intermetallic crystal with crystals surfaces of Mg-matrix. So, investigated Mg-alloy strengthening at alloying with Ga explained by two main factors. At first is the formation of intermetallic phases with the ordering and consolidation of the crystal structure of the matrix by the ligature atoms, which is the key factor of the strengthening mechanism fixed experimentally. Second, when hexagonal and orthorhombic atomic structures growth according to their spatial type, a significant disorientation of structural fragments occurs, an increase in the density of the amorphous transition layer, a twinning of the structure in the interphase boundaries, which leads to the formation of intrinsic mutual deformation and a high level of internal stresses.

The mechanical properties of a layered foam aluminum–titanium composite material produced by the filling of Al melt into molds with pore-forming fluorine fluxes and titanium fixtures are investigated. The shear strength of the composite is determined by the adhesive bond between Al and Ti as well as by the strength of the intermetallic transition layer formed at the interface of the metals. To improve the adhesive bond, titanium is coated with aluminum, and the strength of the intermetallic transition layer is enhanced by alloying it with Co through an Al melt used for aluminizing of titanium. The effect of cobalt alloying on the wetting and spreading of Al melt in titanium during the formation of a composite material is studied. It is shown that alloying with 3% Co reduces the area of spreading of aluminum over titanium. When the titanium surface is activated with the K2TiF6 and K2ZrF6 flux, the wetting of titanium with the melt increases with an increase in the cobalt content, and when activated with KF-AlF3 eutectic, it decreases. Alloying with 2% Co increases the shear strength of the composite owing to the hardening of the intermetallic transition layer. When Ti surfaces are activated with K2ZrF6 flux, the shear strength of composites has the maximum value, which is due to alloying of the transition layer simultaneously with Co and Zr.

A tubular-type electro-baromembrane apparatus design has been developed, which makes it possible to efficiently separate chemical production solutions and differentially extract ions from multicomponent systems. A method for calculating the working area of membranes in the apparatus is proposed, which makes it possible to determine the area of near-cathode and near-anode membranes, as well as the total area of membranes in the apparatus.

The structural organization of the surface (active) layer and the state of water in composite ultrafiltration membranes have been investigated by means of the methods of vibrational IR spectroscopy and differential scanning calorimetry (DSC). Analysis of the shape of the absorption band of stretching vibrations of hydroxyl groups at ν = 3366.2 cm–1 with an asymmetry coefficient of ~1 and the activity of vibrations of methyl groups with ν = 2884.02 and 2942.35 cm—1 has demonstrated that the bulk supramolecular structure of a cellulose acetate layer of a dry sample is formed by two types of hydrogen bonds and dipole–dipole interactions of carbonyl groups. The interaction of macromolecules in the equatorial plane is formed by a lattice of hydrogen bonds of the (OH…O) type with participation of the only hydroxyl group of a pyranose ring in cellulose acetates. In the axial direction, the supramolecular structure is organized by hydrogen bonds between methine and carbonyl groups of the (CH…O=C) type and dipole interactions of coplanar ordered dipoles of (C=O) groups. The decrease in the intensity and the coefficient of asymmetry down to 0.81 of the absorption band of hydroxyl groups and the absorption band of methyl groups with frequencies ν = 2884.02–2942.35 cm–1 by 2.56 and 3.3 times in water-saturated samples occurs due to the destruction of the supramolecular structure and the reorganization of hydrogen bonds of active groups of cellulose acetate and water molecules blocking intermolecular interactions of the macromolecules. The manifestation of hydroxyl groups with frequencies of 3302.7 and 33 105 sh cm–1 and ν = 3600.6 and ν = 3598.8 sh cm–1 on the absorption band indicates the interaction of associated water molecules of the bound and capillary forms. The absence of the absorption band with ν = 873.53 cm–1 in the water-saturated sample is explained as an empirical indicator of the conformational transition of macromolecules into a linear form. Deconvolution of the endothermic peak on the DSC curve in the temperature range from 50 to 110°C into five Gaussians has demonstrated the multilevel structural organization of water molecules sorbed in pores and between macromolecules of the amorphous phase.

Ultradisperse polytetrafluoroethylene is separated into fractions soluble and insoluble in supercritical carbon dioxide. The initial polymer and its soluble and insoluble fractions are impregnated with silver(I) (1,5-cyclooctadiene)-1,1,1,5,5,5-hexafluoroacetylacetonate in supercritical carbon dioxide solution for 6.6 h under thermodynamic conditions at 65°С and 8 MPa followed by reduction of the metal in an atmosphere of hydrogen for 6 h at 65°С and 1.2 MPa. According to X-ray fluorescence analysis, the content of the metal attains 2.4 wt %. Ag-polymer composites are studied by X-ray fluorescence spectroscopy, transmission electron microscopy, small-angle X-ray scattering, and X-ray photoelectron spectroscopy. It is shown that silver in the form of nanoparticles with a size of 1.0–7.5 nm is localized largely in the soluble low molecular weight fraction.

The ionic compositions of lithium metaniobate and metatantalate nanopowders are modified in calcium-containing chloride melts. The reaction products are studied by X-ray diffraction, Raman spectroscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy, and elemental chemical analysis. The results of the studies show that the surface layer of the modified small-size particles of the lithium niobate or lithium tantalate powders is enriched in calcium metaniobate or metatantalate (CaNb2O6 or CaTa2O6) formed due to the isomorphic heterovalent substitution of calcium ions for lithium ions in molten LiCl–CaCl2 and KCl–CaCl2 mixtures at 700 and 750°C.

Titanium—aluminum, titanium—foam aluminum composites and bimetals obtained by liquid-phase methods, are increasingly used in industry. At the liquid-phase methods as result of the reaction diffusion of titanium and aluminum is formed transitional intermetallic layer at the phase boundary of the composite, which reduces the mechanical properties of titanium and composite. To reduce the growth rate of the intermetallic layer between the layers of the composite and increase its mechanical properties, it is proposed to alloy aluminum melt with nickel. The studies of the interaction of titanium and molten aluminum alloyed with nickel made it possible to establish the effect of temperature and aluminizing time on the thickness, chemical and phase compositions of the transition intermetallic layer. The tests showed the effect of the temperature of the aluminum melt, the nickel concentration on the strength properties of titanium—aluminum bimetal.

The mechanical and damping characteristics of titanium–aluminum foam composite materials obtained via casting of a mold with aluminum filled with pore-forming granules and titanium fittings are investigated in this work. Titanium reinforcement of aluminum foam is shown to increase the strength of a foamed material, slightly increasing its density. The damping properties of titanium–aluminum foam composites are close to those of a solid metal at an increase in the titanium content in the composite.

The monomer 1H,1H-perfluoro-4-methyl-3,6-dioxaoctyl methacrylate (PFMOM) has been synthesized for the first time. PFMOM–vinyl pivalate (VP) copolymers and PFMOM–VP–hydroxyethyl methacrylate (HEMA) terpolymers have been synthesized by radical polymerization in supercritical carbon dioxide, and the phase behavior of the resulting polymers in CO2 has been studied. The morphology and hydrophobic properties of copolymer coatings applied to textile substrates from solutions in supercritical CO2 have been examined.

Topological crystalline insulators form a class of semiconductors for which surface electron states with the Dirac dispersion relation are formed on surfaces with a certain crystallographic orientation. Pb1−xSnxTe alloys belong to the topological crystalline phase when the SnTe content x exceeds 0.35, while they are in the trivial phase at x < 0.35. For the surface crystallographic orientation (111), the appearance of topologically nontrivial surface states is expected. We studied the photoelectromagnetic (PEM) effect induced by laser terahertz radiation in Pb1−xSnxTe films in the composition range x = (0.11–0.44), with the (111) surface crystallographic orientation. It was found that in the trivial phase, the amplitude of the PEM effect is determined by the power of the incident radiation, while in the topological phase, the amplitude is proportional to the flux of laser radiation quanta. A possible mechanism responsible for the effect observed presumes damping of the thermalization rate of photoexcited electrons in the topological phase and, consequently, prevailing of electron diffusion, compared with energy relaxation.

The rate and pathways of relaxation of a magnetic medium to its equilibrium following excitation with intense and short laser pulses are the key ingredients of ultrafast optical control of spins. Here we study experimentally the evolution of the magnetization and magnetic anisotropy of thin films of a ferromagnetic metal galfenol (Fe$_{0.81}$Ga$_{0.19}$) resulting from excitation with a femtosecond laser pulse. From the temporal evolution of the hysteresis loops we deduce that the magnetization $M_S$ and magnetic anisotropy parameters $K$ recover within a nanosecond, and the ratio between $K$ and $M_S$ satisfies the thermal equilibrium's power law in the whole time range spanning from a few picoseconds to 3 nanoseconds. We further use the experimentally obtained relaxation times of $M_S$ and $K$ to analyze the laser-induced precession and demonstrate how they contribute to its frequency evolution at the nanosecond timescale., 8 pages, 7 figures

The article presents the results of studying the surface layers of structural steel samples alloyed with 48(WC–W 2 C) + 48Cr + 4Al powder materials mixture using laser-plasma alloying technology. ROFIN-SINAR Nd:YAG-laser DY044 (Germany) with irradiation wave length λ = 1.06 μm was used for laser alloying. Equipment and technologies of laser-plasma alloying were developed at the E.O. Paton Electric Welding Institute. Detailed studies at all structural levels of grain, subgrain, dislocation structures, including phase precipitates and their stoichiometric composition, were carried out using optical, scanning electron, and microdiffraction transmission electron microscopy. It was found that the formation of crack concentrators in the treated surfaces is due to such structural factors as coarse-grained structure, chemical inhomogeneity, and the formation of dislocation density gradients in grain-boundary areas. Under the optimal mode of laser-plasma alloying of the treated surfaces, a fine-grained structure is formed with a uniform distribution of the dislocation density. In this case, the dislocation substructure is characterized by a cellular type with a cell size of 50…110 nm and by the presence of dispersed phase precipitates up to 100 nm in size in the internal volumes of grains. Dispersion of the structure, the formation of a non-disoriented cellular dislocation substructure with a uniform distribution of dislocation density, the presence of dispersed phase precipitates (nanoscale type) will contribute to an increase in crack resistance and strength characteristics due to substructural and dispersion hardening.

We have shown that in heterostructures based on the topological phase Hg 1-x Cd x Te, the properties of two-dimensional topological states formed at the trivial buffer - topological film heterointerface differ from the states at the topological film - vacuum interface, and it is the former that are responsible for the appearance of PT-symmetric photoconductivity. It has been shown that the source of nonequilibrium electrons is the film bulk, while the place of manifestation of the effect is the trivial buffer - topological film heterointerface.

Two donor–acceptor (D–A) conjugated polymers designed on same 8,10-bis(2-octyldodecyl)-8,10-dihydro-9H-bisthieno[2′,3′:7,8;3″,2″:5,6]naphtho[2,3- d]imidazole-9-one donor and dissimilar acceptor uni...

We report data on the development of a polymer – salt method for the formation of aluminium yttrium garnet crystals doped with neodymium ions (YAG : Nd) inside the channels of a preform of microstructured fibre based on pure silica glass. The crystals are obtained by impregnating the channels with aqueous solutions of thermally decomposable salts (yttrium nitrate, aluminium nitrate, neodymium chloride) and an organic polymer, followed by drying and heat treatment at a temperature of 1100 °C. The resulting composite structure is drawn into the fibre at a temperature of 2000 °C. Using X-ray diffraction analysis, the presence of oriented YAG : Nd crystals ranging in size from 25 to 37 nm in the silica glass matrix of fibre is established. Measurements of the spectral dependence of optical losses in fibre show the presence of absorption bands of the optical signal, characteristic of Nd3+ ions. The shape of the luminescence spectra of nanocrystals is typical of YAG : Nd with a radiation peak at a wavelength of 1064 nm.

This paper is devoted to the jubilee of I.M. Khalatnikov, the founder and the first director of the Landau Institute for Theoretical Physics of the Russian Academy of Sciences. I.M. Khalatnikov organized a first-class institute the studies at which cover a broad spectrum of research directions. The plasma and lasers department of the Institute conducts research on plasma physics problems, laser–matter interaction, questions pertaining to laser applications, and hydrodynamics problems. Much attention is given to solid-state physics with an emphasis on the behavior of matter in extreme conditions under intense laser irradiation. A number of new results are presented: the behavior of metals in two-temperature states (when the temperature of the electron subsystem of a metal is much greater than the temperature of the ion subsystem due to ultrafast laser heating); determining the boundaries of existence of a single-wave propagation mode of elastoplastic shock waves in ductile metal crystals; the formation of a laser torch from target materials and liquids under metal laser ablation of a metal into the surrounding liquid; the physical–mechanical consequences (melting, capillarity, recrystallization) of nonuniform (along the irradiated surface) energy dissipation caused by the interference of plasmon–polariton and laser electromagnetic fields.

—A physically nonlinear constitutive equation with four arbitrary material functions for isotropic rheonomic materials is studied to determine the rheological effects simulated by it and the spheres of influence of the material functions. The properties of the volumetric, axial, and lateral creep curves generated by this equation and the dependence of the lateral strain coefficient (Poisson’s ratio) on the material functions, time, and stress during creep are analytically investigated. A general exact estimate of the upper and lower bounds of the Poisson’s ratio and criteria of its negativeness, increase, decrease, and constancy are obtained. The Poisson’s ratio of the model is proved not to be a nonmonotonic function of time.