Phase separation in driven granular gases: exploring the elusive character of nonequilibrium steady states.

The emergence of patterns and phase separation in many-body systems far from thermal equilibrium is discussed using the example of driven granular gases. It is shown that phase separation follows a similar mechanism as in the systems of active Brownian particles. Depending on the quantities chosen for observation, it may or may not be easy to find functionals analogous to the free energy in equilibrium statistical physics. We argue that although such functionals can always be derived from the dynamics, it is of only limited value for predicting relevant aspects of the nonequilibrium steady state of the system. Consequently, although there is indeed a 'principle' governing the selection of collective nonequilibrium steady states (and the corresponding large deviation functional can be identified), it is not generally useful for predicting the behaviour of the system.

Universal phase diagram for wetting on mesoscale roughness.

The wetting properties of solid substrates with mesoscale (between van der Waals tails and the capillary length) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. It is shown that the well-known transition occurring at Wenzel's angle is accompanied by a transition line at which a jump in the adsorbed liquid volume occurs. This should be present generally on surfaces bearing homogeneous, isotropic random roughness. While a similar abrupt filling transition has been reported before for certain idealized groove or trough geometries, it is identified here as a universal phenomenon. Its location can be analytically calculated under certain mild conditions.

Wetting, spreading, and adsorption on randomly rough surfaces.

The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first-order transition in the adsorbed film thickness, which we term "Wenzel prewetting", occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting.

Morphological clues to wet granular pile stability.

When a granular material such as sand is mixed with a certain amount of liquid, the surface tension of the latter bestows considerable stiffness to the material, which enables, for example, sand castles to be sculpted. The geometry of the liquid interface within the granular pile is of extraordinary complexity and strongly varies with the liquid content. Surprisingly, the mechanical properties of the pile are largely independent of the amount of liquid over a wide range. We resolve this puzzle with the help of X-ray microtomography, showing that the remarkable insensitivity of the mechanical properties to the liquid content is due to the particular organization of the liquid in the pile into open structures. For spherical grains, a simple geometric rule is established, which relates the macroscopic properties to the internal liquid morphologies. We present evidence that this concept is also valid for systems with non-spherical grains. Hence, our results provide new insight towards understanding the complex physics of a large variety of wet granular systems including land slides, as well as mixing and agglomeration problems.

Fluidization of granular media wetted by liquid 4He.

We explore experimentally the fluidization of vertically agitated polymethylmethacrylate spheres wetted by liquid 4He . By controlling the temperature around the lambda point, we change the properties of the wetting liquid from a normal fluid (helium I) to a superfluid (helium II). For wetting by helium I, the critical acceleration for fluidization (Gamma_{c}) shows a steep increase close to the saturation of the vapor pressure in the sample cell. For helium II wetting, Gamma_{c} starts to increase at about 75% saturation, indicating that capillary bridges are enhanced by the superflow of the unsaturated helium film. Above saturation, Gamma_{c} enters a plateau regime where the capillary force between particles is independent of the bridge volume. The plateau value is found to vary with temperature and shows a peak at 2.1K , which we attribute to the influence of the specific heat of liquid helium.

Equation of state of wet granular matter.

An expression for the near-contact pair correlation function of D -dimensional weakly polydisperse hard spheres is presented, which arises from elementary free-volume arguments. Its derivative at contact agrees very well with our simulations for D=2 . For jammed states, the expression predicts that the number of exact contacts is equal to 2D, in agreement with established simulations. When the particles are wetted, they interact by the formation and rupture of liquid capillary bridges. Since formation and rupture events of capillary bonds are well separated in configuration space, the interaction is hysteretic with a characteristic energy loss Ecb. The pair correlation is strongly affected by this capillary interaction depending on the liquid-bond status of neighboring particles. A theory is derived for the nonequilibrium probability currents of the capillary interaction which determines the pair correlation function near contact. This finally yields an analytic expression for the equation of state, P=P(N/V,T), of wet granular matter for D=2, valid in the complete density range from gas to jamming. Driven wet granular matter exhibits a van der Waals-like unstable branch at granular temperatures T>T, is of relevance for aggregation in general, simulations have been performed which show very good agreement with the theoretically predicted coordination K of capillary bonds as a function of the bond length scrit. This result implies that particles that stick at the surface, scrit=0, form isostatic clusters. An extension of the theory in which the bridge coordination number K plays the role of a self-consistent mean-field is proposed.

Chaoticity of the wet granular gas.

In this work we derive an analytic expression for the Kolmogorov-Sinai entropy of dilute wet granular matter, valid for any spatial dimension. The grains are modeled as hard spheres and the influence of the wetting liquid is described according to the capillary model, in which dissipation is due to the hysteretic cohesion force of capillary bridges. The Kolmogorov-Sinai entropy is expanded in a series with respect to density. We find a rapid increase of the leading term when liquid is added. This demonstrates the sensitivity of the granular dynamics to humidity, and shows that the liquid significantly increases the chaoticity of the granular gas.

Dry and wet granular shock waves.

The formation of a shock wave in one-dimensional granular gases is considered, for both the dry and the wet cases, and the results are compared with the analytical shock wave solution in a sticky gas. Numerical simulations show that the behavior of the shock wave in both cases tends asymptotically to the sticky limit. In the inelastic gas (dry case) there is a very close correspondence to the sticky gas, with one big cluster growing in the center of the shock wave, and a step-like stationary velocity profile. In the wet case, the shock wave has a nonzero width which is marked by two symmetric heavy clusters performing breathing oscillations with slowly increasing amplitude. All three models have the same asymptotic energy dissipation law, which is important in the context of the free cooling scenario. For the early stage of the shock formation and asymptotic oscillations we provide analytical results as well.

Ripening of ordered breath figures

We have investigated the ripening of breath figures with variable initial order. A dramatic impact of the degree of order on the coalescence behavior is observed. As opposed to the two-droplet coalescence events common to the usual disordered droplet arrays, four-droplet coalescence cascades predominate in a perfectly hexagonal breath figure. Upon introduction of disorder, a gradual transition to a regime dominated by three-droplet cascades is observed. The statistics of coalescence cascades allows for detailed conclusions on the microscopic droplet dynamics.

Three-phase contact line energetics from nanoscale liquid surface topographies

The contact line tension of a three-phase system (solid-liquid-vapor) is determined from the liquid surface topography data obtained with scanning force microscopy. The data are analyzed in two completely complementary ways, one of which is based on the modified Young equation, the other on the effective interface potential derived from the profile of the liquid-vapor interface in the three-phase region. The two methods agree quite well for the systems investigated. Contact line tensions are in the range of 10(-11) to 10(-10) J/m, which is consistent with theory.

Cutoff value of choline concentration reliably reveals high-grade brain tumors among other contrast-enhancing brain lesions.

BACKGROUND AND AIM: To evaluate whether there is a cutoff value for a metabolite concentration measured by 1 H MR spectroscopy (MRS), which can be used to differentiate malignant brain tumors (high-grade gliomas, primary CNS lymphomas [PCNSL] and metastases) from other contrast-enhancing lesions like low-grade gliomas and non-neoplastic lesions. MATERIAL AND METHODS: 1 H MRS was performed in 252 consecutive patients with space-occupying brain lesions which were enhanced with application of a contrast agent. Concentrations of N-acetyl-aspartate, total creatine, choline containing metabolites (total choline, tCho), lipids, and lactate were evaluated from the contrast-enhancing part of the lesions and from the normal appearing brain tissue. Linear discriminant analysis was used to find the best predictor for malignant brain tumors. In addition, receiver operating characteristic analysis (ROC) was performed to determine a cutoff value for the best predictor in detecting malignant brain tumors with a specificity of >95%. RESULTS: All brain tumors and 20 out of 47 nonneoplastic lesions were examined histopathologically. The remaining 27 diagnoses were based on MR imaging, clinical findings, and follow-up. The final diagnosis was 134 high-grade gliomas (WHO grade III/IV), 36 metastases, 9 PCNSL, 8 low-grade gliomas (WHO grade I/II), 34 infections, 9 infarctions, 2 hematomas, and 2 vasculitides. 18 patients were excluded due to insufficient spectral quality. The tCho concentration was the best predictor to differentiate malignant brain tumors from enhancing low-grade gliomas or non-neoplastic lesions (F=26.6 [df: 25.833], p<0.0005). The ROC revealed that a cutoff tCho value, based on an increase of ≥40% compared to normal, yielded a specificity of 100% and a sensitivity of 89.4% to correctly diagnose a malignant brain tumor. CONCLUSION: 1 H MRS reliably differentiates malignant brain tumors from other contrast-enhancing brain lesions. At least a 40% increase of tCho compared to normal brain tissue indicates a malignant tumor (WHO grade III/IV gliomas, PCNSL, metastases) with >90% specificity and sensitivity.

Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths.

Nonequilibrium steady states of Markov processes give rise to nontrivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here we present an iterative cycle decomposition exhibiting a natural dynamics on the space of cycles that satisfies detailed balance. Expectation values of observables can be expressed as cycle "averages," resembling the cycle representation of expectation values in dynamical systems. We illustrate our approach in terms of an analogy to a simple model of mass transit dynamics. Symmetries are reflected in our approach by a reduction of the minimal number of cycles needed in the decomposition. These features are demonstrated by discussing a variant of an asymmetric exclusion process. Intriguingly, a continuous change of dominant flow paths in the network results in a change of the structure of cycles as well as in discontinuous jumps in cycle weights.

Fluidization of wet granulates under shear.

Small amounts of a wetting liquid render sand a stiff and moldable material. The cohesive forces between the sand grains are caused by capillary bridges at the points of contact. Due to the finite strength of these bridges wet sand undergoes a transition from an arrested (i.e., solidified) to a fluidized state under an externally applied shear force. The transition between these two dynamic states is studied in a MD-type simulation of a two-dimensional assembly of bidisperse frictionless disks under the action of a cosine force profile. In addition to soft core repulsion the disks interact through a hysteretic and short ranged attractive force modeling the effect of the capillary bridges. In this model the transition between the fluidized and the arrested state is discontinuous and hysteretic. The parameter dependence of the critical force for solidification is modeled by combining theoretical arguments with a detailed numerical exploration of the transition. We address a range of densities from slightly below close packing until slightly above densities where the system approaches a shear-banded state. Differences and similarities of the transition in wet granulates to the jamming transition are also addressed.

Diagnostic impact of proton MR-spectroscopy versus image-guided stereotactic biopsy.

BACKGROUND: The aim of this study was to compare the diagnostic accuracy of (1)H MR-spectroscopy versus image-guided stereotactic biopsy. METHOD: A cohort of 83 consecutive patients with a broad spectrum of brain lesions were examined. Prior to stereotactic biopsy, the patients were subjected to (1)H MR-spectroscopy examination. Diagnostic accuracy of (1)H MR-spectroscopy and image guided stereotactic biopsy was determined for the largest diagnostic subgroups. Each diagnostic procedure was tested for concordance in every subgroup. FINDINGS: The subgroups of patients comprised: low grade glioma, high grade glioma (grades III and IV), lymphoma and metastasis. For the sensitivity of (1)H MR-spectroscopy ranged from 87.7 in high grade glioma to 92.3% in metastasis and for specificity from 93.3% for high grade glioma to 100% in low grade glioma. The highest positive predictive value of 100% was reached in the subgroup of low grade glioma. The highest negative predictive value was reached in lymphoma and metastasis, 100%. The kappa values were highly significant for all comparisons (p<0.001). The co-efficient ranged from 0.68 to 0.84. It was lowest in assessing high grade glioma and highest in lymphoma. CONCLUSION: Compared with each other (1)H MR-spectroscopy and image-guided stereotactic biopsy showed a moderate to good, statistically highly significant concordance. In patients in whom operation is at an increased risk e.g., due to severe medical illness, (1)H MR-spectroscopy as a noninvasive procedure may be sufficient to assess the diagnosis.

Unclustering transition in freely cooling wet granular matter.

The free cooling of one-dimensional wet granular matter is presented in the framework of the minimal capillary model. We demonstrate analytically and by extensive simulations that above a critical density, the clustering of wet granular matter is not monotonic in time, but undergoes a sharp unclustering transition. This precipitation of granular droplets out of the gas takes place when the granular temperature comes close to the energy scale set by the capillary interaction.

Free cooling of the one-dimensional wet granular gas.

The free cooling behavior of a wet granular gas is studied in one dimension. We employ a particularly simple model system in which the interaction of wet grains is characterized by a fixed energy loss assigned to each collision. Macroscopic laws of energy dissipation and cluster formation are studied on the basis of numerical simulations and mean-field analytical calculations. We find a number of remarkable scaling properties which may shed light on earlier unexplained results for related systems.