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In chronic lymphocytic leukemia (CLL), changes in the peripheral blood lymphocyte subsets play an important role in disease progression and infectious complications. The impact of chemoimmunotherapy (CIT) on these changes has not been extensively studied METHODS: We used multi-color flow cytometry, to prospectively measure absolute and relative numbers of CD4Our results indicate that naïve cell depletion and CD4

Purpose This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters. Design/methodology/approach The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction. Findings This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region. Practical implications The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions. Originality/value While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

Melting probe is an autonomous exploratory tool that uses heat, typically generated by a nuclear energy source, to penetrate through layers of ice. Working devices have been used in terrestrial conditions for some time, but the concept has a potential for space missions, especially those that aim to collect water samples from subsurface oceans on icy moons. This motivates computational study of the concept, one that could answer fundamental questions regarding time and power requirements of the melting probe mission.In this talk, which presents results obtained in collaboration with Ondřej Souček, a multi-physics modelling approach will be introduced. The model couples a mechanical problem, governed by the Navier-Stokes equations with temperature dependent material properties, together with a thermal problem, in the form of a non-linear heat equation reformulated in enthalpy that is capable of capturing the phase-change phenomena. Though complex, the versatility of such model enables a study of the fully-convective regime of the melting probe. Preliminary results show that the coupled problem formulated in the axisymmetric two-dimensional approximation is (computationally) tractable and, at the same time, estimates the rate of ice penetration based on the external conditions, i.e., ice temperature and viscosity, gravitational acceleration, etc. The results form a foundation for possible kinematic models of ice sheet penetration that lead to estimates of mission time requirements.So far, the problem was studied in the simple setting of a heated sphere with a fixed frame of reference (see Fig.1, Fig.2 for preliminary results of a test setting). The solution is approximated by the finite element method implemented within the FEniCS computational platform.This stage, which serves as the model's proof of concept, permits straightforward generalizations (e.g., realistic cylindrical geometries, water jets boundary conditions, Arbitrary Lagrangian–Eulerian kinematic description). A brief discussion of the extensions will demonstrate the utility of the model. Acknowledgement: The authors would like to express their gratitude toward Charles University Grant Agency, project GA UK n. 1062120 (J.M.) and Czech Science Foundation, project 22-20388S (O.S.). Figure 1. Preliminary results - three time stamps show the evolution of temperature (including melting temperature isotherm), dynamic viscosity, and velocity field around the heated sphere (test problem parameters setting). Figure 2. Preliminary results - time evolution of probe descent velocity

We are concerned with a system of partial differential equations (PDEs) describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (the so-called yield) stress depends on the internal pore pressure governed by an advection–diffusion equation. After providing the physical background of the considered model, paying attention to the assumptions involved in its derivation, we focus on the PDE analysis of the initial and boundary value problems. We give several equivalent descriptions for the considered class of fluids of Bingham type. In particular, we exploit the possibility to write such a response as an implicit tensorial constitutive equation, involving the pore pressure, the deviatoric part of the Cauchy stress and the velocity gradient. Interestingly, this tensorial response can be characterized by two scalar constraints. We employ a similar approach to treat stick-slip boundary conditions. Within such a setting we prove long-time and large-data existence of weak solutions to the evolutionary problem in three dimensions.

Geophysics-focused missions and improved geophysical data sets are critical for the future exploration of icy ocean worlds. Of particular interest is the exploration of the Galilean moon, Europa, and the Saturnian moons, Titan and Enceladus. These bodies likely have geologically active surfaces and may harbor habitable subsurface environments. Placing any candidate signatures for life in context requires further knowledge of the interior of these worlds. While the surfaces of these bodies have been mapped, their interiors remain poorly understood. Geophysical approaches such as geodesy, seismology, ice-penetrating radar and altimetry measurements, and electromagnetometry would provide critical information regarding the interior of these icy ocean worlds. The approaches described below would answer key science questions regarding ice shell and ocean dynamics, internal structure and interior layer thicknesses, near-surface structure, and how material from the deep interior might be exchanged with the surface. Here we outline the geophysical environments of Enceladus, Europa, and Titan; some outstanding science questions that remain to be addressed; and examples of the geophysical approaches that can provide the context to better understand icy ocean worlds.

Sputnik Planitia, a 1000 km wide, Pluto-dominating feature, is located very close to Pluto-Charon tidal axis. To explain its position, a reorientation driven by a postimpact uplift of a subsurface ocean was proposed. Since pure water ice shell relaxes too quickly to maintain the reorientation up to the present, an insulating layer of high viscosity clathrates at the ice/ocean interface was proposed. Here, we solve Pluto’s ice shell evolution in a 2D spherical axisymmetric geometry with an evolving free surface, assuming a viscous rheology of both ice and clathrates. Our results show that the thermal effect of the impact and nonlinear rheology substantially decrease the relaxation timescales. Introduction Sputnik Planitia basin is situated only 400 km from the tidal axis. Since a position this close to the tidal axis is very unlikely, reorientation of the whole body was proposed [1]. Facing towards the tidal axis, Sputnik Planitia should be a positive gravity anomaly [1]. Pluto is believed to be differentiated into a rocky core and a hydrosphere [2], therefore isostatic uplift of a liquid ocean might have compensated the basin’s negative topography. Impact origin ejecta blanket and accumulated nitrogen would then provide an additional positive mass [3]. Due to the basin’s likely age of 4 Gyr [4], the gravity anomaly has to be positive up to the present. Since the warm ice close to the melting point is expected to relax quickly, Kamata et al. [5] proposed the presence of an insulating layer of high viscosity clathrates. Here, we study the effect of impact heating [6] and nonlinear ice and clathrate rheology [7] on the relaxation timescale. Numerical model We solve the thermal evolution of Pluto’s ice shell in a 2D spherical axisymmetric geometry with time-evolving ice/ocean interface. The initial height of the isostatic uplift is evaluated assuming Airy isostasy, a 10 km deep basin at the surface and ocean water density of 1100 kg/m3 [8]. Free surface is prescribed at the bottom boundary and free slip is prescribed elsewhere. Temperature is fixed at the top and bottom boundary (40 and 265 K, respectively) and the side boundaries are kept adiabatic. The initial condition is steady-state conductive profile assuming clathrate layer of thickness 5 or 10 km. We use nonlinear viscosity of ice dependent on temperature, grain size and stress using the composite law [7], similarly for clathrates [9]. We prescribe temperature dependent thermal conductivity for ice [10] and a constant value (0.6 W/m/K) in the clathrate layer. We choose impactor velocity 4 km/s, diameter 400 km and density 920 kg/m3 in order to create a 900 km wide circular basin. The resulting temperature anomaly in the isobaric core is ∼ 80 K [6]. We use the Arbitrary Lagrangian-Eulerian formulation to address the moving boundary [11]. The problem is implemented in a freely available Finite Element Method library FEniCS [12]. Results We performed series of simulations combining different shell thicknesses H and clathrate layer thicknesses hc. Here, we present two combinations, which, according to Kamata et al. [5], should lead to the uplift relaxation times in the order of billion years. Models 1 and 2 represent the H/hc = 100/5 km and 200/10 km simulations, respectively, with parameters used in [5]. Models 3 and 4 are analogical to Models 1 and 2, however, with nonlinear rheology and impact heating. Note that Kamata et al. [5] define relaxation timescale as the time when the uplift volume decreases to 1/e of the initial volume, whereas we present the time when the uplift starts to subside rapidly, i.e., when it no longer supports the surface basin isostatically, which is crucial for reorientation. This timescale turns out to be substantially shorter than the timescale presented in [5]. Figure 1 shows the relaxation curves, i.e., uplift height at the axis of symmetry with respect to time. We can see that Models 3 and 4 relax faster than Models 1 and 2. At 1 Gyr, the uplift of Model 4 already subsided by a few km and relaxation of Model 3 is almost over. These preliminary results suggest that none of them can compensate the negative basin topography anymore. Figure 2 shows the moment when the uplift starts to subside rapidly for Models 3 and 4. Although the thin shell becomes quickly cold and rigid (Fig. 2a), its uplift starts to relax at t Conclusions We investigated viscous relaxation of an uplift below Pluto’s basin Sputnik Planitia, assuming an insulating, high-viscosity layer of clathrates at the base of the shell. We showed that the impact temperature anomaly and nonlinear ice and clathrate rheology can substantially reduce the relaxation timescale. Moreover, accumulation of the insulating solid nitrogen layer can cause the shell to warm up, therefore the relaxation timescale may be even shorter. Acknowledgements This research was supported by the Czech Science Foundation through project No. 19-10809S. M.K. acknowledges the support from the Charles University projects SVV-2020-260581 and 111-10/251851. K.K. and O.S. were supported by the Charles University Research program No. UNCE/SCI/023. References [1] Nimmo et al., 2016. Nature. 540. 94–96. [2] Stern et al., 2015, Science, 350, 1815. [3] Keane et al., 2016. Nature, 540, 90–93. [4] Greenstreet et al., 2015. Icarus, 258, 267–288. [5] Kamata et al., 2019. Nature Geoscience, 12, 407–410. [6] Monteux et al., 2014. Icarus, 237, 377–387. [7] Goldsby and Kohlstedt, 2001. JGR: Solid Earth, 106, 11017–11030. [8] Johnson et al., 2016. Geophys. Res. Lett., 43, 10068–10077. [9] Durham et al., 2010. SSR. 153. 273–298. [10] Hobbs, 1974. Ice Physics. Clarendon Press, Oxford. [11] Scovazzi and Hughes, 2007. Sandia National Laboratories. [12] Logg et al., 2012. The FEniCS Book, Springer–Verlag

Analysis of Enceladus’ gravity, topography and libration data suggests that the thickness of the ice crust significantly varies, which may have important consequences for the heat transfer across and the tidal dissipation within the ice shell. Understanding these processes is a critical prerequisite for analyzing Enceladus’ thermal evolution and assessing the long-term stability of its subsurface ocean. Here, we investigate the impact of ice shell thickness variations on the tidal deformation of the moon and the associated heat production using a finite-element model that includes faults (“tiger stripes”) in the south polar region (SPR). Since the tidal deformation and the thermal structure of the ice shell are coupled through temperature and deviatoric stress, we simultaneously solve the equations governing the anelastic deformation of ice and also equations which model conductive heat transfer in the ice shell. We find that tidal heating is concentrated in a narrow low viscosity zone near the base of the ice shell and along faults. Outside the SPR, the thickness of this zone is about 1/10 of the local ice thickness and the associated volumetric heating is ≲ 1 0 − 6 W/m 3 , corresponding to less than 1 GW of dissipated power. In the SPR, the tidal effects are enhanced by the combined action of faults and ice shell thinning. Although the volumetric heating in this relatively small region may be larger than 10 −4 W/m 3 , the total heat production in this region does not exceed 1.1 GW. Our computations show that tidal heating in the ice shell can explain only a small fraction of Enceladus’ heat production derived from astrometric observations, implying that Enceladus’ heat engine is powered by dissipation in the core or in the ocean.

We derive a thermodynamically consistent model of heterogeneous catalysis for chemically reacting fluid mixtures formulated in the framework of continuum thermodynamics. The model takes into account standard transport phenomena in the bulk domain and involves mass transfer of the species between the bulk and the catalytic (active) part of the boundary where the surface counterparts to the bulk transport processes take place. Concerning the balance laws on the catalytic surface, the model benefits from description of the active part of the boundary as an interface between the bulk domain and its exterior which allows to employ the framework of continuum mechanics with interfacial transport phenomena. The constitutive relations involving vectorial and tensorial quantities such as the Cauchy stress, energy and entropy fluxes and diffusive fluxes relevant to individual constituents are constructed in a systematic manner ensuring compatibility with the second law of thermodynamics. The constitutive procedure follows from the specification of constitutive equations for suitable thermodynamic potentials (free energies) of the mixture in the bulk and on the active part of the boundary and from the identification of the bulk and surface entropy productions. The active part of the boundary is described by means of statistical physics and this description then serves as a building block for the derivation of surface continuum thermodynamic potentials. The derived model is suitable for further mathematical, numerical and computational analysis of relevant initial and boundary value problems. While the model employs a relatively simple description of the active part of the boundary as a monolayer lattice with single-site Langmuir-type adsorption, its detailed derivation presented here provides clear guidelines for the incorporation of other sorption models.

We present a new model of Enceladus’ internal structure based on the recent shape model by Tajeddine et al. (2017) and the gravity model by Iess et al. (2014). Assuming that the rocky core is homogeneous and in hydrostatic equilibrium, we derive a set of structural models that accurately reproduce the main characteristics of Enceladus’ gravity field. In order to restrict the range of acceptable models we analyze the degree of compensation (ratio of the bottom to the surface load) at spherical harmonic degrees well constrained by the gravity data. In agreement with previous studies, we find that Enceladus’ ice shell is close to equilibrium, with the degree of compensation approaching one for models with a hydrostatic core having a radius between 190 km and 195 km. By computing the flow of ice driven by variations in hydrostatic pressure on the ice water/interface, we demonstrate that the ice shell is in steady state, as suggested by the gravity and shape data, only if the viscosity of ice at the melting temperature is equal to or higher than 3 × 1014 Pa s, corresponding to diffusion creep with a grain size of 1 mm or larger. The topographic anomalies are maintained by phase changes at the ice/water interface with a melting/freezing rate of a few mm/yr or smaller. This process is controlled by the heat flux at the top of the ocean, characterized by a strong degree-2 zonal component with amplitudes exceeding 60 mW/m2 in both south and north polar regions.

The surface of Pluto is dominated by the Sputnik Planitia basin, possibly caused by an impact ~ 4 Gyr ago. To explain basin's unlikely position close to tidal axis with Charon, a reorientation driven by the post-impact uplift of the subsurface ocean was proposed recently. To maintain the reorientation until today, relaxation of the ice/ocean interface topography has to be sufficiently slow. Here we study the thermo-mechanical viscous relaxation of Pluto's ice shell of uneven thickness. We show that for a pure H2O ice shell the topography relaxes quickly (~ tens of Myr). On the other hand, if a layer of methane-clathrates is present at the base of the ice shell, the relaxation is much slower. With at least 5 km of clathrates, the ice/ocean interface topography can be maintained for 4 Gyr. Introduction Pluto, the largest dwarf planet in the Kuiper belt, is probably differentiated into a rocky core and a hydrosphere [9]. Its surface is dominated by the enigmatic Sputnik Planitia basin, which has likely been produced by a giant impact. The basin that covers about 7 % of Pluto's surface is located very close to the Charon tidal axis. To explain this unlikely position, [7] suggested that it may be the result of a whole body reorientation, which requires the crater to be a positive gravity anomaly. Isostatic uplift of the subsurface ocean was thus suggested to compensate the crater's negative gravity and an observed nitrogen layer [6] at the crater's surface to provide the positive signature necessary for the reorientation. However, it is not clear whether the ice/ocean interface topography is stable on long time scales. Here, we study the thermo-mechanical viscous relaxation of Pluto's ice shell of uneven thickness. Numerical model We solve thermal convection of ice in 2D cartesian geometry with time-evolving bottom boundary (interface with the ocean). The initial height of the ice/ocean interface is evaluated assuming Airy isostasy and a 6 km deep basin at surface. The governing equations are following: Free surface is prescribed at the bottom boundary and free slip is prescribed elsewhere. Temperature is fixed at the top and bottom boundary (40 and 265 K) and the side boundaries are kept thermally insulating. The initial condition is steady-state conductive profile. In some simulations, a layer of methane-clathrate [4] of thickness hc is assumed. We use strongly nonlinear viscosity for ice dependent on temperature, grain size and stress using the composite law [2], and similarly for clathrates [1]. As a result, the viscosity of clathrate layer is at least one order of magnitude higher than the viscosity of ice immediately above. We prescribe temperature dependent thermal conductivity for ice [6] that gives values of 2.3 to 13 Wm-1K-1 at the ice/ocean interface and surface respectively. In the clathrate layer of thickness hc we prescribe constant thermal conductivity of 0.6 Wm-1K-1 [10]. We use the Arbitrary Lagrangian-Eulerian formulation to adress the moving boundary [8]. The problem is implemented in freely available Finite Element Method library FEniCS [5]. Results We performed series of simulations with ice shell thickness h=150 km and clathrate layer thickness hc= 0, 5 and 10 km. The initial height of the ice/ocean interface topography is 87 km and grain size is d=1mm in all simulations. Figure 1 shows the time evolution of temperature in the ice shell in case without clathrate hydrates layer (hc=0 km). We observe that the ice shell is relatively warm which results in low viscosities and thus relatively fast relaxation. In this setting, the ice/ocean interface topography disappears in about 5 Myr. Note that in this relatively warm, low-viscosity ice shell, thermal convection further increases the temperature (panels c and d). Figure 2 shows the temperature (top) and viscosity (bottom) in the ice shell with hc=10 km after 100 Myr of relaxation. The insulating layer of clathrates at the ocean interface leads to significantly colder ice shell than in the case without clathrates. Therefore, the viscosity is also very high and no significant relaxation is observed. Conclusions We investigated the thermo-mechanical viscous relaxation of Pluto's ice shell using a numerical model with moving boundary. We showed that if Pluto's ice shell is made of pure H2O ice, the ice/ocean interface topography cannot be maintained for longer than a few tens of Myr. If an insulating layer of methane-clathrates is present at the ice shell/ocean interface, it may significantly delay the topography relaxation. Future study will take into account a more realistic initial temperature condition resulting from the impact. In such case, one might expect that the effect of clathrates would be reduced and the relaxation would proceed faster. These results will be presented at the meeting. Acknowledgements This research was supported by the Czech Science Foundation through project No. 19-10809S. M.K. acknowledges the support from the Charles University projects SVV-2019-260447 and SVV-2020-260581. K.K. and O.S. were supported by the Charles University Research program No. UNCE/SCI/023. References [1] Durham et al. (2010). SSR. 153. 273-298.[2] Goldsby Kohlstedt. (2001). JGR Solid Earth. 106. 11,017-11,030[3] Hobbs (1974). Ice Physics. Clarendon Press, Oxford.[4] Kamata et al. (2019). Nature Geoscience. 12. 407-410. [5] Logg et al. (2012). The FEniCS Book, Springer-Verlag [6] McKinnon et al. (2016), Nature, 534, 82-85.[7] Nimmo et al. (2016). Nature. 540. 94-96.[8] Scovazzi Hughes (2007), Sandia National Laboratories.[9] Stern et al. (2015), Science, 350, 1815.[10] Waite et al. (2006). GJI. 169. 767-774.

We present preliminary results of a numerical study of tidally induced deformation of Enceladus’s ice shell containing fissures (Tiger Stripes) in the south polar region (SPR). It is a follow-up study of Souček et al. (2016), which brings in a more realistic description of the faults' behavior. In particular, the fault zone is described by a model of effectively visco-elasto-plastic material with yield stress depending on the stress state. Such a model mimics the Coulomb-type friction contact at idealized fault surfaces. We show the basic features of the model and discuss the importance of fault description on the predicted tidal deformation and stress field within Enceladus's ice shell. Introduction In Souček et al. (2016), we have numerically demonstrated a profound effect of faults (Tiger Stripes) on the tidally induced deformation and stress fields in the south polar region of Enceladus. In Běhounková et al. (2017), we showed how this effect can be further enhanced in a synergetic way, when combined with a realistic thinning of the ice shell in the SPR for a shell thickness model based on inversion of gravity and libration data (Čadek et al., 2016). In both these studies, the faults were modelled as zones with significantly reduced elastic moduli. Effectively, such description corresponds to faults being described as narrow slots partially filled with water (compensating the overburden pressure within the layer). Such description of the faults is oversimplified since it does not take into account any friction at the faults. We attempt to circumvent this deficiency in the new study. Model We solve equations of deformation of a 3D Maxwell visco-elastic planetary shell containing faults in the SPR. The shell's deformation is driven by the incremental tidal potential and at the fault, Coulomb, type response is considered. The Coulomb-type friction is mimicked by a continuum model of a fault zone of finite thickness with stress limiting viscosity. The stress limiter is given by the yield stress, composed of (hydro)static contribution due to overburden pressure and a dynamic contribution due to normal stress variations during the tidal period. Results We present preliminary results with one active fault in the SPR, corresponding to the Baghdad Sulcus. In Figure 1, we plot the displacement in SPR for four instants during the tidal period, colors indicate the amplitude of normal displacement, vectors show the horizontal displacement. Compared to the case with frictionless faults, the model with Coulomb-type friction exhibits asymmetry - the lateral motion is facilitated during the opening phase and suppressed during the closing (compressional) phase of the period. Acknowledgements The research leading to these results received funding from the Czech Science Foundation through project No. 19-10809S. The computations were carried out in IT4Innovations National Supercomputing Center (project no. LM2015070). The study was supported by the Charles University, project GA UK No. 304217, SVV-2019-260447 and SVV 115-09/260581 (K.S.), and by Charles University Research program No. UNCE/SCI/023 (O.S.). References Běhounková, M., Souček, O., Hron, J.and O. Čadek (2017), Plume activity and tidal deformation of Enceladus influenced by faults and variable ice shell thickness, Astrobiology, 17(9), 941-954, https://doi.org/10.1089/ast.2016.1629. Čadek, O., Tobie, G., van Hoolst, T., Massé, M., Choblet, G., Lefèvre, A., Mitri, G., Baland, R.-M., Běhounková, M., Bourgeois, O., and Trinh, A. (2016) Enceladus’s internal ocean and ice shell constrained from Cassini gravity, shape, and libration data. Geophys Res Lett 43:5653–5660. Souček, O., Hron, J., Běhounková, M., and O. Čadek (2016), Effect of the tiger stripes on the deformation of Saturn's moon Enceladus, Geophysical Research Letters, 43(14), 7417–7423, https://doi.org/10.1002/2016GL069415.

Introduction The smallest Galilean moon Europa is differentiated into an outer ice shell, subsurface ocean, silicate mantle and iron-rich core (J. D. Anderson et al., 1997; Khurana et al., 1998). Its young surface exhibits a multitude of superposed crosscutting lineaments (Kattenhorn & Hurford, 2009), on some of which a lateral offset of a few kilometres was identified (e.g. Schenk & McKinnon, 1989). On Earth, strike-slip motion, thus potentially lateral offset, occurs either through a primary shear failure or through reactivation of the pre-existing faults and fractures (E. Anderson, 1905). On Europa, the latter case was confirmed so far (Hoppa et al., 1999; Sarid et al., 2002; Kattenhorn, 2004; Rhoden et al., 2012) and a process nicknamed "tidal walking'' (Hoppa et al., 1999) was suggested as a possible mechanism for producing the strike-slip offset through the reactivation of faults via diurnal tidal stresses. In the simplest setting (see Figure 1), the tension opening the fault facilitates strike-slip motion in one direction, while in the reverse direction in the second half of the period, the motion is suppressed by compression. Consequently, after one period a certain strike-slip offset is accumulated. Our numerical model aims at testing the "tidal walking" model by simulation of the behaviour of Europan strike-slip fault and its surroundings. Model The model consists of two parts reflecting the two timescale nature of the considered process, i.e. the diurnal timescale (~3.5 days) of the forcing stresses and the formation timescale (taken as 100kyr). The tidal model describes the fault and its surroundings as a viscoelastic (Maxwell) body with a pre-existing fissure in the middle of the computational domain, cf. right panel of Figure 2. This model is forced by shear and normal stresses, and it quantifies the tidally-driven heat production. Heat sources are used as an input for the second - convection - model operating on the time scale of tens of thousand years, describing ice as a non-newtonian fluid. The computed thermal evolution affects the viscosity in the tidal model, providing (together with the tidal heating) the coupling between the two modules. Results We performed an extensive parametric study of the behaviour of Europan strike-slip fault and its surroundings, varying ice shell thickness (D), the amplitude of loading stresses (shear and normal, σ0), the phase shift between the shear and normal stresses and the coefficient of friction. The results depend strongly on the amplitude of the loading stresses and the ice shell thickness. Our calculations confirm previous results by Preblich et al., 2007 that the active part of the fault needs to reach a low viscosity zone or to penetrate to the ocean. The whole-shell penetration appears improbable as unrealistically thin (1km) shell and larger than present-day loading stresses would be required. However, our results indicate that a low viscosity zone at the base of the active part of the fault may form as a result of frictional and shear heating in the fault’s vicinity (D=5 km ice shell and σ0=6 x 105Pa loading amplitude). Such a scenario shows that the thermo-mechanical coupling is vital for the complete understanding of the behaviour of strike-slip faults. A third option for producing observable offset is to assume that the cracks are partially filled with water from the internal ocean, then the hydrostatic pressure is partially compensated by the water column. Thus the active part of the fault can reach the bottom of the shell much more easily, in this setting the production of a significant offset is possible even for the present-date estimates of the tidal forcing amplitudes and ice-shell thickness of less or equal to ten kilometres. Acknowledgements The research leading to these results received funding from the Czech Science Foundation through project No. 19-10809S. The computations were carried out in IT4Innovations National Supercomputing Center (project no. LM2015070). The study was supported by the Charles University, project GA UK No. 304217 and SVV 115-09/260581 (K.S.), and by Charles University Research program No. UNCE/SCI/023 (O.S., K.K.). References Anderson, E. (1905). The dynamics of faulting. Transactions of the Edinburgh Geological Society, 8(3), 387–402. doi: 10.1144/transed.8.3.387 Anderson, J. D., Lau, E. L., Sjogren, W. L., Schubert, G., & Moore, W. B. (1997). Europa’s Differentiated Internal Structure: Inferences from Two Galileo Encounters. Science, 276(5316), 1236–1239. doi: https://doi.org/10.1126/science.276.5316.1236 Hoppa, G., Tufts, B. R., Greenberg, R., & Geissler, P. (1999). Strike-slip faults on Europa: Global shear patterns driven by tidal stress. Icarus, 141(2), 287–298. doi:https://doi.org/10.1006/icar.1999.6185 Kattenhorn, S. A. (2004). Strike-slip fault evolution on Europa: Evidence from tail- crack geometries. Icarus, 172(2), 582–602. doi: https://doi.org/10.1016/j.icarus .2004.07.005 Kattenhorn, S. A., & Hurford, T. (2009). Tectonics of Europa. In Europa (pp. 199– 236). University of Arizona Press. Khurana, K. K., Kivelson, M. G., Stevenson, J. D., Schubert, G., Russell, C. T., Walker, R. J., & Polanskey, C. (1998). Induced magnetic fields as evidence for subsurface oceans in Europa and Callisto. Nature, 424(July). doi: https://doi.org/10.1038/27394 Rhoden, A. R., Wurman, G., Huff, E. M., Manga, M., & Hurford, T. A. (2012). Shell tectonics: A mechanical model for strike-slip displacement on Europa. Icarus, 218(1), 297 - 307. doi: https://doi.org/10.1016/j.icarus.2011.12.015 Sarid, A. R., Greenberg, R., Hoppa, G. V., Hurford, T. A., Tufts, B., & Geissler, P. (2002). Polar Wander and Surface Convergence of Europa’s Ice Shell: Evidence from a Survey of Strike-Slip Displacement. Icarus, 158(1), 24 - 41. doi: https://doi.org/10.1006/icar.2002.6873 Schenk, P. M., & McKinnon, W. B. (1989). Fault offsets and lateral crustal move- ment on Europa: Evidence for a mobile ice shell. Icarus, 79(1), 75–100. doi: https://doi.org/10.1016/0019-1035(89)90109-7 Sládková, K., Souček, O., Kalousová, K., & Bĕhounková, M. (2020). Tidal walking on Europa's strike slip faults ‐ insight from numerical modeling. Journal of Geophysical Research: Planets, 125, e2019JE006327. https://doi.org/10.1029/2019JE006327

The role of the immune system as an integral component of the inflammatory response in the pathophysiology of migraine remains unclear. The aim of this study was to evaluate the differences in immune system parameters (acquired immunity parameters) in patients with episodic migraine (EM) and in healthy controls. In EM patients, we aimed to determine whether the changes found in peripheral blood parameters were related to migraine severity according to the standardised MIDAS and HIT-6 tests. Forty-nine patients with EM and 50 healthy controls were included in this study. The authors compared different lymphocyte parameters obtained by multicolor flow cytometry in the EM and control groups by performing statistical tests. The relationship between the changes in peripheral blood parameters and migraine severity in EM patients was investigated using correlation and regression analysis. EM patients showed higher values than healthy controls, especially in nine parameters: relative count of lymphocytes, relative and absolute counts of CD3 T cells, relative and absolute counts of CD8 suppressor cytotoxic T cells, relative and absolute counts of CD4 + TEMRA (terminally differentiated helper T lymphocytes), absolute count of CD8 naïve T cells, and absolute count of CD19 switched memory B cells. Among the lymphocyte parameters, CD4 + TEM (effector memory helper T lymphocytes) and CD8 + TEMRA (terminally differentiated cytotoxic T lymphocytes) were statistically significantly associated with HIT-6. Patients with a CD4 + TEM value below 15 had a high probability (90%) that the HIT-6 value would be higher than 60. The results of this study show that EM patients have changes in immune system parameters measured in the peripheral blood. Changes in the abundance of CD4 + TEM could be used as a biomarker for disease severity.

Zanětliva střevni onemocněni (IBD) jsou chronicke choroby předevsim střevni sliznice, s opakovanými relapsy aktivity, kteremohou postupně vest k destrukci střeva. Soucasti komplikaci těchto onemocněni může být nedostatek vitaminu D a vapniku.Tento clanek shrnuje soucasne nazory o potřebě suplementace vitaminu D u děti s IBD.

Geophysical data from the Cassini spacecraft imply the presence of a global ocean underneath the ice shell of Enceladus 1 , only a few kilometres below the surface in the South Polar Terrain 2–4 . Chemical analyses indicate that the ocean is salty 5 and is fed by ongoing hydrothermal activity 6–8 . In order to explain these observations, an abnormally high heat power (>20 billion watts) is required, as well as a mechanism to focus endogenic activity at the south pole 9,10 . Here, we show that more than 10 GW of heat can be generated by tidal friction inside the unconsolidated rocky core. Water transport in the tidally heated permeable core results in hot narrow upwellings with temperatures exceeding 363 K, characterized by powerful (1–5 GW) hotspots at the seafloor, particularly at the south pole. The release of heat in narrow regions favours intense interaction between water and rock, and the transport of hydrothermal products from the core to the plume sources. We are thus able to explain the main global characteristics of Enceladus: global ocean, strong dissipation, reduced ice-shell thickness at the south pole and seafloor activity. We predict that this endogenic activity can be sustained for tens of millions to billions of years. Tidal forcing within a very porous (unconsolidated) core can generate enough energy to drive all the observed global features of Enceladus. This activity can be sustained up to several billion years.

We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for incompressible viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally calls for the formulation of a temperature evolution equation that would accompany the evolution equations for the mechanical quantities. The evolution equation for the temperature is explicitly formulated, and it is shown to be consistent with the laws of thermodynamics and the evolution equations for the mechanical quantities. The temperature evolution equation contains terms that are ignored or even not thought of in most of the practically oriented (computational) works dealing with this class of fluids. The impact of the additional terms in the temperature evolution equation on the flow dynamics is documented by the solution of simple initial/boundary value problems.

Jupiter's moon Europa has a very young surface with the abundance of unique terrains that indicate recent endogenic activity. Morphological models as well as spectral observations suggest that it might possess shallow lenses of liquid water within its outer ice shell. Here we investigate the generation and possible accumulation of liquid water below the tidally activated strike-slip faults using a numerical model of two-phase ice-water mixture in two-dimensional Cartesian geometry. Our results suggest that generation of shallow partially molten regions underneath Europa's active strike-slip faults is possible, but their lifetime is constrained by the formation of Rayleigh-Taylor instabilities due to the negative buoyancy of the melt. Once formed, typically within a few million years, these instabilities efficiently transport the meltwater through the shell. Consequently, the maximum water content in the partially molten regions never exceeds 10% which challenges their possible detection by future exploration mission.

Suspensions, solutions and colloids are physical systems that can be generally denoted as “multicomponent systems” or “mixtures”. Physical systems of this type are frequently met in many industrial applications which rises the need for numerical simulations of the behaviour of such complex systems. A particular practical example of such system is glass/tin/nitrogen system that must be studied in modelling of the float glass process (Pilkington process) that partly motivated this research. The aim of this paper is to discuss the numerical challenges along with some practical issues concerning the implementation of a chosen Cahn–Hilliard–Navier–Stokes type model that showed up to be particularly suitable for the description of three-component systems. The discretization of the system of governing partial differential equations is based on the finite element method using the FEniCS Project. Numerical experiments carried out in two and three spatial dimensions verify our straightforward implementation that uses parallel direct sparse solvers to resolve the intermediate linear systems of algebraic equations. Possible improvements of the current implementation are briefly outlined within the paper.

We study a nonlinear elliptic system with prescribed inner interface conditions. These models are frequently used in physical system where the ion transfer plays the important role, for example, in modeling of nano-layer growth or Li-on batteries. The key difficulty of the model consists of the rapid or very slow growth of nonlinearity in the constitutive equation inside the domain or on the interface. While on the interface, one can avoid the difficulty by proving a kind of maximum principle of a solution, inside the domain such regularity for the flux is not available in principle since the constitutive law is discontinuous with respect to the spatial variable. The key result of the paper is the existence theory for these problems, where we require that the leading functional satisfies either the delta-two or the nabla-two condition. This assumption is applicable in case of fast (exponential) growth as well as in the case of very slow (logarithmically superlinear) growth.

Hypofosfatazie (HPP) je vzacne onemocněni způsobene nedostatecnou produkci alkalicke fosfatazy (ALP). V důsledku toho dochazi k demineralizaci skeletu a objevuji se zavažne extraskeletalni symptomy: respiracni insuficience, křece, opožďovani v psychomotorickem vývoji, kraniosynostoza, nefrokalcinoza. Diagnostika je založena na nizke koncentraci ALP v seru v kombinaci s charakteristickými klinickými znamkami. Od roku 2015 je dostupna substitucni enzymaticka terapie pomoci rekombinantni ALP, ktera změnila životni prognozu těchto pacientů. Clanek shrnuje soucasne poznatky o etiologii, formach, diagnostice a terapii HPP s důrazem na ulohu pediatrů při rozpoznavani tohoto onemocněni.

Enceladus is a small icy moon of Saturn with active jets of water emanating from fractures around the south pole, informally called tiger stripes, which might be connected to a subsurface water ocean. The effect of these features on periodic tidal deformation of the moon has so far been neglected because of the difficulties associated with implementation of faults in continuum mechanics models. Here we estimate the maximum possible impact of the tiger stripes on tidal deformation and heat production within Enceladus's ice shell by representing them as narrow zones with negligible frictional and bulk resistance passing vertically through the whole ice shell. Assuming a uniform ice shell thickness of 25 km, consistent with the recent estimate of libration, we demonstrate that the faults can dramatically change the distribution of stress and strain in Enceladus's south polar region, leading to a significant increase of the heat production in this area.

We investigate a model of a fluidized bed reactor decomposing liquid formic acid and producing gaseous mixture of carbon dioxide and hydrogen in the presence of microscopic solid catalytic particles. We describe the system, contained in a fixed control volume, as a mixture composed of four constituents-formic acid ( F A ), catalyst micro-particles ( C a t ), carbon dioxide (CO2) and hydrogen (H2). For the individual mixture components, we distinguish partial densities and momenta, while we only consider one common temperature field for the mixture as a whole. We reduce the four-constituents model to a binary mixture model of liquid phase ( C a t + F A ) and gaseous phase (CO2+H2) which forms bubbles.Liquid phase is considered as a compressible viscous fluid with temperature-dependent density and viscosity depending on both the temperature (Arrhenius model) and the volume fraction of the catalyst particles. Physical interaction between the bubbles and the liquid is modeled under simplifying assumptions by the pressure-drag balance. The chemical rates satisfy mass-action law and undergo Arrhenius kinetics. The model was implemented numerically in COMSOL Multiphysics and we present several simulations addressing primarily the role of liquid viscosity and imposed wall temperature on the performance and flow regime inside the reactor.

We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarantees that the derived boundary conditions are compatible with the second law of thermodynamics. The starting assumption of our approach is to describe the boundary of the domain as the membrane separating two different continua, one inside the domain, and the other outside the domain. With this viewpoint one may employ the framework of continuum thermodynamics involving singular surfaces. This approach allows us to identify, for various classes of surface Helmholtz free energies, the corresponding surface entropy production mechanisms. By establishing the constitutive relations that guarantee that the surface entropy production is non-negative, we identify a new class of boundary conditions, which on one hand generalizes in a nontrivial manner the Navier’s slip boundary conditions, and on the other hand describes dynamic and static contact angle conditions. We explore the general model in detail for a particular case of a Korteweg fluid where the Helmholtz free energy in the bulk is that of a van der Waals fluid. We perform a series of numerical experiments to document the basic qualitative features of the novel boundary conditions and their practical applicability to model phenomena such as the contact angle hysteresis.

Background: Multiple sclerosis (MS) is a neurodegenerative disease that affects the central nervous system. The cause of MS is still unknown, and the role of innate immunity is still poorly understood. Objective: The goal of this study was to understand whether, compared to healthy controls, the elements of innate immunity are altered in the blood of MS patients in the remitting phase. Methods: A total of 77 na&iuml, ve MS patients and 50 healthy controls were included in this cohort study. Peripheral blood samples were collected and analyzed. All the calculations were performed with the statistical system R (r-project.org). Results: The results showed that MS patients had significantly lower relative representations of granulocytes than healthy controls, while the relative representations of monocytes remained unchanged. CD64- and PD-L1-positive granulocytes exhibited a nonsignificant decreasing trend, while granulocytes with other membrane markers remained noticeably unchanged. Conclusion: The results of this study suggest that studies of the causes of MS and its treatment should also be focused on the elements of the innate immune response.

Iapetus possesses two spectacular characteristics: (i) a high equatorial ridge which is unique in the Solar System and (ii) a large flattening ( a - c = 34 km) inconsistent with its current spin rate. These two main characteristics have probably been acquired in Iapetus’ early past as a consequence of coupled interior-rotation evolution. Previous models have suggested that rapid despinning may result either from enhanced internal dissipation due to short-lived radioactive elements or from interactions with a sub-satellite resulting from a giant impact. For the ridge formation, different exogenic and endogenic hypotheses have also been proposed, but most of the proposed scenarios have not been tested numerically. In order to model simultaneously internal heat transfer, tidal despinning and shape evolution, we have developed a two-dimensional axisymmetric thermal convection code with a deformable surface boundary, coupled with a viscoelastic code for tidal dissipation. The model includes centrifugal and buoyancy forces, a composite non-linear viscous rheology as well as an Andrade rheology for the dissipative part. By considering realistic rheological properties and by exploring various grain size values, we show that, in the absence of additional external interactions, despinning of a fast rotating Iapetus is impossible even for warm initial conditions ( T > 250 K). Alternatively, the impact of a single body with a radius of 250–350 km at a velocity of 2 km/s may be sufficient to slow down the rotation from a period of 6–10 h to more than 30 h. By combining despinning due to internal dissipation and an abrupt change of rotation due to a giant impact, we determined the parameters leading to a complete despinning and we computed the corresponding shape evolution. We show that stresses arising from shape change affect the viscosity structure by enhancing dislocation creep and can lead to the formation of a large-scale ridge at the equator as a result of rapid rotation change for initial rotation periods of 6 h.

The floor of Isidis Planitia, a giant impact basin located close to the martian equator, exhibits a landform assemblage, nicknamed Thumbprint Terrain, made of Arcuate Ridges, Aligned Cones, Isolated Cones, Cone Fields, associated with a peripheral network of Sinuous Ridges, Linear Depressions, and Mounds. From a new comprehensive mapping initiative of these landforms and from comparisons with terrestrial analogues (ribbed moraines, dirt cones, kettle holes, eskers, tunnel valleys and moraine plateaux), we demonstrate that this distinctive assemblage is a glacial landsystem inherited from the presence of a massive polythermal ice sheet over the basin during the Hesperian. The flow of the ice sheet was controlled by its basal thermal regime. Wet-based conditions led to the formation of Arcuate Ridges and Aligned Cones in most parts of the basin, while a negative geothermal anomaly due to impact-related crustal thinning was responsible for cold-based conditions in its central part, where only Isolated Cones and Cones Fields are present. Sinuous Ridges, Linear Depressions and Mounds at the basin margins are interpreted as relicts of a radial network of subglacial channels, which drained the glacial meltwater produced within the interior of the ice sheet across its cold-based periphery.

We present a two-phase model for the generation of meltwater and its propagation through the outer shells of icy satellites such as Europa, Enceladus or Titan. We exploit the analogy with the process of partial melt generation in the Earth’s interior by adopting the formalism of two-phase flow developed in the mantle-dynamics community, and by means of scaling analysis we derive a reduced system appropriate for our planetary application. The resultant system couples Darcy’s law with the deformation of the viscous ice matrix. We numerically investigate the system in a simplified one-dimensional geometry, corresponding to a laterally uniform ice layer, and analyze the role of various physical parameters. We focus on the leading-order effects, namely (i) the key importance of ice permeability, (ii) the role of complex ice rheology depending on temperature, deformation mechanisms and water content, (iii) the possible contribution of surface tension and (iv) the effects of mechanical coupling between the phase...

We investigated the effect of variations in ice shell thickness and of the tiger stripe fractures crossing Enceladus' south polar terrain on the moon's tidal deformation by performing finite element calculations in three-dimensional geometry. The combination of thinning in the polar region and the presence of faults has a synergistic effect that leads to an increase of both the displacement and stress in the south polar terrain by an order of magnitude compared to that of the traditional model with a uniform shell thickness and without faults. Assuming a simplified conductive heat transfer and neglecting the heat sources below the ice shell, we computed the global heat budget of the ice shell. For the inelastic properties of the shell described by a Maxwell viscoelastic model, we show that unrealistically low average viscosity of the order of 1013 Pa s is necessary for preserving the volume of the ocean, suggesting the important role of the heat sources in the deep interior. Similarly, low viscosity is required to predict the observed delay of the plume activity, which hints at other delaying mechanisms than just the viscoelasticity of the ice shell. The presence of faults results in large spatial and temporal heterogeneity of geysering activity compared to the traditional models without faults. Our model contributes to understanding the physical mechanisms that control the fault activity, and it provides potentially useful information for future missions that will sample the plume for evidence of life. Key Words: Enceladus—Tidal deformation—Faults—Variable ice shell thickness—Tidal heating—Plume activity and timing. Astrobiology 17, 941–954.

A theory describing the behavior of chemically non-reacting binary mixtures can be based on a detailed formulation of the governing equations for the individual components of the mixture or on treating the mixture as a single homogenized continuous medium. We argue that if we accept that both approaches can be used to describe the behavior of the given mixture, then the requirement on the equivalence of these approaches places restrictions on the possible structure of the internal energy, entropy, Helmholtz potential, and also of the diffusive, energy, and entropy fluxes. (The equivalence of the approaches is understood in the sense that the quantities used in one approach can be interpreted in terms of the quantities used in the other approach and vice versa. Further, both approaches must lead to the same predictions concerning the evolution of the physical system under consideration). In the case of a general chemically non-reacting binary mixture of components at the same temperature, we show that these restrictions can indeed be obtained by purely algebraic manipulations. An important outcome of this analysis is, for example, a general form of the evolution equation for the diffusive flux. The restrictions can be further exploited in the specification of thermodynamically consistent constitutive relations for quantities such as the interaction (drag) force or the Cauchy stress tensor. As an example of the application of the current framework, we derive, among others, a generalization of Fick’s law and we recover several non-trivial results obtained by other techniques. The qualitative features of the derived generalization of Fick’s law are demonstrated by a numerical experiment.