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Recently, it was demonstrated that electrochemical doping fronts in organic semiconductors exhibit a new fundamental instability growing from multidimensional perturbations [ Bychkov et al.  Phys. Rev. Lett. 107 016103 (2011)]. In the instability development, linear growth of tiny perturbations goes over into a nonlinear stage of strongly distorted doping fronts. Here we develop the nonlinear theory of the doping front instability and predict the key parameters of a corrugated doping front, such as its velocity, in close agreement with the experimental data. We show that the instability makes the electrochemical doping process considerably faster. We obtain the self-similar properties of the front shape corresponding to the maximal propagation velocity, which allows for a wide range of controlling the doping process in the experiments. The developed theory provides the guide for optimizing the performance of organic optoelectronic devices such as light-emitting electrochemical cells.

The concept of a front plays a decisive role in various elds in physics and beyond. In the present thesis we study key aspects of front dynamics and stability in the context of laser plasmas, organic semiconductors and quantum media.

In laser plasmas, we investigate the hydrodynamic instabilities developing at the fronts of laser deagration (ablation). Using direct numerical simulations, we nd noticeable velocity increase of the Rayleigh-Taylor bubble at a deagration front in comparison with that arising at an inert interface. We study the Darrieus-Landau instability of laser deagration accounting for the specific features of the fusion plasmas: strong temperature dependence of the thermal conduction and sonic velocities of the plasma flow. We find that these features of the laser plasmas make the Darrieus-Landau instability stronger by a factor of 3 in comparison with the well-known case of slow flames. We clarify the experimental conditions required for observations of the Darrieus-Landau instability in laser plasmas.

In quantum plasmas, we study interplay of the classical and quantum eects for shock waves and for the pseudo-ferrouid instability. For shocks in quantum plasmas, we demonstrate transition from a monotonic Burgers classical shock structure to the train of oscillations (solitons) in the quantum limit. We obtain also a counterpart of the ferrouid instability in quantum magnetized plasmas due to collective spin-dynamics in an external magnetic eld. We discuss importance of the instability for thermonuclear explosions of white dwarfs in the Supernovae Ia events.

In organic semiconductors, we develop the theoretical and numerical model of the electrochemical doping fronts. The study is based on the modifed mobilitydiffusion approach to the complex semiconductor plasmas consisting of holes, electrons, positive and negative ions. The m odel describes the doping front structure and predicts the front velocity in a very good agreement with the experiments. We discover a new fundamental instability, which distorts the doping fronts and speeds-up the process considerably. We demonstrate how the instability may be controlled and used to improve performance of optoelectronic devices.

Finally, we study avalanches of spin-switching in crystals of nanomagnets, which may be described as magnetic deagration and detonation due to striking resemblance to the respective combustion phenomena. We find that magnetic deflagration becomes unstable and propagates in a pulsating regime when potential barrier of the spin-switching is sufficiently high in comparison with the energy release in the process. We also demonstrate the possibility of magnetic detonation in the crystals, which explains the astounding effect of ultra-fast spin-avalanches encountered in recent experiments. We find that magnetic detonation does not destroy the unique properties of the crystals, a very important conclusion in view of possible applications of nanomagnets in quantum computing.

Konceptet med en utbredningsfront spelar en avgörande roll inom många olika områden i fysik. I denna avhandling studeras centrala aspekter av utbredningsfronters dynamik och deras stabilitet i för laser-plasmaväxelverkan, organiska halvledare samt kvantmedier. 

För laser-plasmaväxelverkan har vi undersökt de hydrodynamiska instabiliteter, som t ex Rayleigh-Taylor-instabiliteten, vilka utvecklas vid deflagrationsfronter (under så kallad laserablation). Med hjälp av direkta numeriska simuleringar har vi hittat en märkbar hastighetökning av Rayleigh-Taylor bubblan i en deaflgrationsfront jämfört med det som kan ses vid ett inert gränssnitt. Vi har även studerat Darrieus-Landau-instabiliteten vid laserdeflagration, speciellt hur denna påverkas av de specifika egenskaperna hos ett fusionsplasma: ett starkt temperaturberoende hos värmeledningen samt plasmaflödet som uppnår ljudhastighet.

Vi har funnit att dessa egenskaper hos laser-plasmasystem gör Darrieus-Landau instabilitet starkare jämfört med det vanliga fallet av långsamma flammor. Vi har även klargjort de experimentella förutsättningar som krävs för observationer av Darrieus-Landau instabilitet i laser-plasmasystem. 

Vi har studerat samspelet mellan klassiska och kvantmekaniska aspekter i kvantplasmor. Specifikt har vi undersökt chockvågors utbredning och dynamik samt instabiliteter i pseudo-ferrofluider. För chocker i kvantplasmor har vi visat att en övergång från Burgers klassiska monotona chockstruktur till ett vågtåg av solitoner sker i kvantgränsen. Vi för också en motsvarighet till ferrofluidinstabiliter i magnetiserade plasmor  på grund av dess kollektiva spinn-dynamik i ett yttre magnetfält. Vi har diskuterar instabilitetens roll för termonukleära explosioner hos vita dvärgar i supernovor av typ Ia.  

I organiska halvledare har vi utvecklat en teoretisk och numerisk modell av elektrokemiska dopningsfronter. Studien är baserad på en modifierade drift-diffusiondmodell för komplexa dopade halvledare, vilka består av hål, elektroner, positiva och negativa joner. Modellen beskriver dopningsstrukturen och gör det möjligt att beräkna dopningsfrontens hastighet med värden som överensstämmer mycket väl med experimenten. Vi har även upptäckt en ny grundläggande instabilitet, vilket gör dopningsfronter anisotrop och snabbar upp processen betydligt. Vi visar hur instabilitet kan styras och användas för att förbättra optoelektronisk utrustning.  

Slutligen studerar vi laviner av spin-växlingar i kristaller bestående av nanomagneter. Denna process kan beskrivas i termer av ett nytt analogt koncept, så kallad magnetiska deflagration och detonation, på grund av de slående likheter dessa har till motsvarande förbränningsfenomen. Vi har funnit att magnetiska deflagration blir instabil och propagerar i en pulserande regim när potentialbarriären för spin-växling är tillräckligt hög i jämförelse med frigörelsen av energi i processen. Vi visar också möjlighet till magnetisk detonation i dessa  kristaller, vilket förklarar de ultrasnabba spin-laviner man stött på under vid experiment helt nyligen. Denna magnetiska detonation förstör inte de unika egenskaperna hos kristallerna, en mycket viktig slutsats med tanke på möjliga tillämpningar av nanomagneter i kvantdatorer.

The internal structure of electrochemical doping fronts in organic semiconductors is investigated using an extended drift-diffusion model for ions, electrons, and holes. The model also involves the injection barriers for electrons and holes in the partially doped regions in the form of the Nernst equation, together with a strong dependence of the electron and hole mobility on concentrations. It is shown that the internal structure of the doping fronts is controlled by a balance between the diffusion and mobility processes. The asymptotic behavior of the concentrations and the electric field is studied analytically inside the doping fronts. The numerical solution for the front structure confirms the most important findings of the analytical theory: a sharp head of the front in the undoped region, a smooth relaxation tail in the doped region, and a plateau at the critical point of transition from doped to undoped regions. The theoretically predicted complex structure of the doping fronts is in agreement with the previous experimental data. The acceleration of the p- and n-fronts toward each other in light-emitting electrochemical cells is described. The theoretical predictions for the planar front acceleration are in a good quantitative agreement with the experimental measurements for the backside of the curved doping fronts.

The stability of a magnetic deflagration front in a media of molecular magnets, such as Mn₁₂ acetate, is considered. It is demonstrated that stationary deflagration is unstable with respect to one-dimensional perturbations if the energy barrier of the magnets is sufficiently high in comparison with the release of Zeeman energy at the front; their ratio may be interpreted as an analog to the Zeldovich number, as found in problems of combustion. When the Zeldovich number exceeds a certain critical value, a stationary deflagration front becomes unstable and propagates in a pulsating regime. Analytical estimates for the critical Zeldovich number are obtained. The linear stage of the instability is investigated numerically by solving the eigenvalue problem. The nonlinear stage is studied using direct numerical simulations. The parameter domain required for experimental observations of the pulsating regime is discussed.

The dynamics of doping transformation fronts in organic semiconductor plasma is studied for application in light-emitting electrochemical cells. We show that new fundamental effects of the plasma dynamics can significantly improve the device performance. We obtain an electrodynamic instability, which distorts the doping fronts and increases the transformation rate considerably. We explain the physical mechanism of the instability, develop theory, provide experimental evidence, perform numerical simulations, and demonstrate how the instability strength may be amplified technologically. The electrodynamic plasma instability obtained also shows interesting similarity to the hydrodynamic Darrieus-Landau instability in combustion, laser ablation, and astrophysics.

Recent experiments [W. Decelle et al., Phys. Rev. Lett. 102 027203 (2009)] have discovered ultrafast propagation of spin avalanches in crystals of nanomagnets, which is 3 orders of magnitude faster than the traditionally studied magnetic deflagration. The new regime has been hypothetically identified as magnetic detonation. Here we demonstrate unequivocally the possibility of magnetic detonation in the crystals, as a front consisting of a leading shock and a zone of Zeeman energy release. We study the key features of the process and find that the magnetic detonation speed only slightly exceeds the sound speed in agreement with the experimental observations. For combustion science, our results provide a unique physical example of extremely weak detonation.

From a magnetofluid description with intrinsic magnetization, a new plasma instability is obtained. The plasma magnetization is produced by the collective electron spin. The instability develops in a nonuniform plasma when the electron concentration and temperature vary along an externally applied magnetic field. Alfvén waves play an important role in the instability. The instability properties are numerically investigated for a particular example of an ultrarelativistic degenerate plasma in exploding white dwarfs.

We develop a model describing the electrochemical conversion of an organic semiconductor (specifically, the active material in a light-emitting electrochemical cell) from the undoped nonconducting state to the doped conducting state. The model, an extended Nernst-Planck-Poisson model, takes into account both strongly concentration-dependent mobility and diffusion for the electronic charge carriers and the Nernst equation in the doped conducting regions. The standard Nernst-Planck-Poisson model is shown to fail in its description of the properties of the doping front. Solving our extended model numerically, we demonstrate that doping front progression in light-emitting electrochemical cells can be accurately described.

The main characteristics of the linear Darrieus-Landau instability in the laser ablation flow are investigated. The dispersion relation of the instability is found numerically as a solution to an eigenvalue stability problem, taking into account the continuous structure of the flow. The results are compared to the classical Darrieus- Landau instability of a usual slow flame. The difference between the two cases is due to the specific features of laser ablation: sonic velocities of hot plasma and strong temperature dependence of thermal conduction. It is demonstrated that the Darrieus-Landau instability in laser ablation is much stronger than in the classical case. In particular, the maximum growth rate in the case of laser ablation is about three times larger than that for slow flames. The characteristic length scale of the Darrieus-Landau instability in the ablation flow is comparable to the total distance from the ablation zone to the critical zone of laser light absorption. The possibility of experimental observations of the Darrieus-Landau instability in laser ablation is discussed.

We investigate influence of magnetic field on the Rayleigh–Taylor instability in quantum plasmas with para- and ferromagnetic properties. Magnetization of quantum plasma happens due to the collective electron spin behavior at low temperature and high plasma density. In the classical case, without magnetization, magnetic field tends to stabilize plasma perturbations with wave numbers parallel to the field and with sufficiently short wavelengths. Paramagnetic effects in quantum plasma make this stabilization weaker. The stabilization disappears completely for short wavelength perturbations in the ferromagnetic limit, when the magnetic field is produced by intrinsic plasma magnetization only. Still, for perturbations of long and moderate wavelength, certain stabilization always takes place due to the nonlinear character of quantum plasma magnetization.