Anomalous Diffusion

Texas -We study the process of random growth of surfaces approximating it by fractional Brownian motion (FBM) with scaling index H. The diffusion trajectories generated by the ballistic deposition (H = 1/3) and Edward-Wilkinson (H = 1/4) models are analyzed and the distribution of time intervals between two consecutive origin re-crossings are calculated numerically. This distribution follows the inverse power-law, ψ(τ ) ∝ 1/τ µ . For pure FBM µ = 2 -H if 1/3 < H < 1 and µ = 1 + 2H if 0 < H < 1/3. As was recently shown, the latter case is a direct manifestation of the infinite memory of the FBM trajectories. Our results demonstrate that because of friction, which is usually neglected in the processes of random growth of surfaces, the relation µ = 2 -H holds true for the Edward-Wilkinson model (H = 1/4). Thus, the new regime with persistency given by µ = 1 + 2H cannot be observed in the diffusion processes where even weak dissipation is present.

Texas -We study the process of random growth of surfaces approximating it by fractional Brownian motion (FBM) with scaling index H. The diffusion trajectories generated by the ballistic deposition (H = 1/3) and Edward-Wilkinson (H = 1/4) models are analyzed and the distribution of time intervals between two consecutive origin re-crossings are calculated numerically. This distribution follows the inverse power-law, ψ(τ ) ∝ 1/τ µ . For pure FBM µ = 2 -H if 1/3 < H < 1 and µ = 1 + 2H if 0 < H < 1/3. As was recently shown, the latter case is a direct manifestation of the infinite memory of the FBM trajectories. Our results demonstrate that because of friction, which is usually neglected in the processes of random growth of surfaces, the relation µ = 2 -H holds true for the Edward-Wilkinson model (H = 1/4). Thus, the new regime with persistency given by µ = 1 + 2H cannot be observed in the diffusion processes where even weak dissipation is present.

In this paper we discuss the connection between trajectory and density memory. The first form of memory is a property of a stochastic trajectory, whose stationary correlation function shows that the fluctuation at a given time depends on the earlier fluctuations. The density memory is a property of a collection of trajectories, whose density time evolution is described by a time convoluted equation showing that the density time evolution depends on its past history. We show that the trajectory memory does not necessarily yields density memory, and that density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory. We focus our attention on a time-convoluted diffusion equation, when the memory kernel is an inverse power law with (i) negative and (ii) positive tail. In case (i) there exist both renewal trajectories and trajectories with memory, compatible with this equation. Case (ii), which has eluded so far a convincing interpretation in terms of trajectories, is shown to be compatible only with trajectory memory.

The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates k(off) (k(on)). The tracer particle is restricted to diffuse with rate k(D) on the lattice and the density of crowders is constant (on average). The unbinding rate k(off) is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (k(off) ≫ k(D)) to the non-Markovian case (k(off) ≪ k(D)) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DN...

des Milieux H•t•rog•nes, ESPCI, Unitd de recherches associde au CNRS 857, Paris We present an experimental study and a model of the diffusion of sinusoidal pressure waves through porous media. We show that measurements of the hydraulic admittance A(w) in the sine wave mode allow us to probe the structure of porous samples with an adjustable investigation depth depending on the frequency w. The variations of A (w) in heterogeneous media with a percolationlike geometry are modeled numerically on two-dimensional p•ercolation networks. One obtains a transition from normal diffusion at low frequencies ( A(•o)l o• w r/2) to anomalous diffusion at higher frequencies (A(w) o• toø'7). At the transition, the penetration depth of the wave is of the order of the percolation correlation length. The hydraulic admittance and transmittance of 20% porosity pressed calcite have been investigated experimentally with sine wave excitations at pulsations w between 2 x 10 -4 and 0.42 rad/s. Both the modulus and the phase of the complex admittance A(w) display normal diffusive variations as ro increases. Increasing the viscosity reduces the frequency above which the diffusive behavior is observed. The measured diffusion coefficient is 25% higher than that computed from permeability and compressibility values measured independently; this difference may be associated with nonconnected porosity.

In living cell or its nucleus, the motions of molecules are complicated due to the large crowding and expected heterogeneity of the intracellular environment. Randomness in cellular systems can be either spatial (anomalous) or temporal (heterogeneous). In order to separate both processes, we introduce anomalous random walks on fractals that represented crowded environments. We report the use of numerical simulation and experimental data of single-molecule detection by fluorescence fluctuation microscopy for detecting resolution limits of different mobile fractions in crowded environment of living cells. We simulate the time scale behavior of diffusion times D( ) for one component, e.g. the fast mobile fraction, and a second component, e.g. the slow mobile fraction. The less the anomalous exponent the higher the geometric crowding of the underlying structure of motion that is quantified by the ratio of the Hausdorff dimension and the walk exponent w f d d / and specific for the

We report on fluorescence fluctuations of nanoparticles diffusing through a laser focus. Subject to an intensity threshold the fluorescence signal is transformed into time traces of on and off periods. The distribution functions of the experimental on and off times follow power laws t ÿ over several orders of magnitude with exponents ' 1:5 ÿ 2. At long times the distribution functions cross over to exponential decays. For the interpretation of the experimental data a diffusion-reaction equation is proposed which covers both, the diffusion controlled recurrence and the photon statistics as the relevant processes.

We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. We calculate both short-time and long-time concentrations, and compare and contrast the continuous and discrete cases. Our analysis is based on the fractional diffusion equation and its discrete analog.

Priprema za izvođenje nastavne jedinice dio je nastavnog kurikula. Pojmovi koji se navode u okviru glavnih sastavnica pripremanja nastavne teme (npr. ocekivana postignuca i ishodi) pa tako i u okviru sastavnica suvremenog kurikula, nisu usklađeni u hrvatskoj pedagoskoj literaturi ni u službenim dokumentima koji se koriste u odgojno- obrazovnom sustavu. U radu se navodi jedan od nacina na koji ih možemo formulirati te se daje primjer pripreme za izvođenje konkretne nastavne jedinice iz fizike.

• We use the evolution of distributions to characterize normal or anomalous diffusion. • We considered space and time dynamics to test different regimes of diffusion. • The width of the distribution is related to the parameters of the random walk. • This analysis is independent of the mechanism responsible for the diffusion. • The technique is specially useful in superdiffusion, where the variance diverges.

The mobility of water molecules confined in a silica pore is studied by computer simulation in the low hydration regime, where most of the molecules reside close to the hydrophilic substrate. A layer analysis of the single particle dynamics of these molecules shows an anomalous diffusion with a sublinear behaviour at long time. This behaviour is strictly connected to the long time decay of the residence time distribution analogously to water at contact with proteins. I.

In this paper, we solve a particular time-space fractional Stefan problem including fractional order derivatives in time and space variables in the Fourier heat conduction equation. For this, we consider fractional time derivative of order α ∈ (0, 1] and fractional space derivative of order 2β with β ∈ 1 2 , 1 , both in the Caputo sense. Including time and space fractional derivatives, the melt front advances as s ∼ t ξ , where ξ = ξ (α, β), and we can recover sub-diffusion, classical diffusion and super-diffusion behaviors. The result for the proposed problem depends on the choice of order of fractional derivatives α and β provided that the choice satisfies the relation α = 2β 1+β .

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Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) ∼ 2Dαtα, where Dα is the fractional diffusion constant and 0 &lt; α &lt; 2. In this article we show that both Dα and α can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function. This offers a simple method for the interpretation of quasielastic neutron scattering spectra from complex (bio)molecular systems, in which subdiffusive transport is frequently encountered. The approach is illustrated and validated by analyzing molecular dynamics simulations of molecular diffusion in a lipid POPC bilayer.

The paper describes an approach to anomalous diffusion within the framework of the generalized Langevin equation. Using a Tauberian theorem for Laplace transforms due to Hardy, Littlewood, and Karamata, generalized Kubo relations for the relevant transport coefficients are derived from the asymptotic form of the mean square displacement. In a second step conditions for anomalous diffusion are derived for the asymptotic forms of the velocity autocorrelation function and the associated memory function. Both spatially unconfined and confined diffusion processes are considered. The results are illustrated with semi-analytical examples.

We present a model for the local diffusion-relaxation dynamics of the Cα-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ⩾ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the Cα-atoms exceptionally well and reveals moreover a strong correlation between the residue&#39;s solvent-accessible surface and the fitted model parameters.

We study the motion of N = 2 overdamped Brownian particles in gravitational interaction in a space of dimension d = 2. This is equivalent to the simplified motion of two biological entities interacting via chemotaxis when time delay and degradation of the chemical are ignored. This problem also bears some similarities with the stochastic motion of two point vortices in viscous hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We analytically obtain the probability density of finding the particles at a distance r from each other at time t. We also determine the probability that the particles have coalesced and formed a Dirac peak at time t (i.e. the probability that the reduced particle has reached r = 0 at time t). Finally, we investigate the variance of the distribution r 2 and discuss the proper form of the virial theorem for this system. The reduced particle has a normal diffusion behavior for small times with a gravity-modified diffusion coefficient r 2 = r 2 0 + (4kB/ξµ)(T -T * )t, where kBT * = Gm1m2/2 is a critical temperature, and an anomalous diffusion for large times r 2 ∝ t 1-T * /T . As a by-product, our solution also describes the growth of the Dirac peak (condensate) that forms at large time in the post collapse regime of the Smoluchowski-Poisson system (or Keller-Segel model) for T < Tc = GM m/(4kB). We find that the saturation of the mass of the condensate to the total mass is algebraic in an infinite domain and exponential in a bounded domain. Finally, we provide the general form of the virial theorem for Brownian particles with power law interactions.

This paper investigates anomalous diffusion behavior for ultra low energy implants in the extension or tip of PMOS devices. Transient enhanced diffusion (TED) is minimal at these low energies, since excess interstitials are very close to the surface. Instead, interface induced uphill diffusion is found, for the first time, to dominate during low temperature thermal cycles. The interface pile-up dynamics can be taken advantage of to produce shallower junctions and improve short channel effect control in PMOS devices. Attempts to minimize TED before spacer deposition by inclusion of extra RTA anneals are shown to be detrimental to forming boron ultra shallow junctions.

In this paper, we are interested in approximating the solution to scalar conservation laws using systems of interacting stochastic particles. The scalar conservation law may involve a fractional Laplacian term of order α ∈ (0, 2]. When α ≤ 1 as well as in the absence of this term (inviscid case), its solution is characterized by entropic inequalities. The probabilistic interpretation of the scalar conservation is based on a stochastic differential equation driven by an α-stable process and involving a drift nonlinear in the sense of McKean. The particle system is constructed by discretizing this equation in time by the Euler scheme and replacing the nonlinearity by interaction. Each particle carries a signed weight depending on its initial position. At each discretization time we kill the couples of particles with opposite weights and positions closer than a threshold since the contribution of the crossings of such particles has the wrong sign in the derivation of the entropic inequalities. We prove convergence of the particle approximation to the solution of the conservation law as the number of particles tends to ∞ whereas the discretization step, the killing threshold and, in the inviscid case, the coefficient multiplying the stable increments tend to 0 in some precise asymptotics depending on whether α is larger than the critical level 1.

We simulated the invasion of a proliferating, diffusing tumor within different surrounding tissue conditions using a hybrid mathematical model. The in silico invasion of a tumor was addressed systematically for the first time within the framework of a generalized diffusion theory. Our results reveal that a tumor not only migrates using typical Fickian diffusion, but also migrates more generally using subdiffusion, superdiffusion, and even ballistic diffusion, with increasing mobility of the tumor cell when haptotaxis and chemotaxis toward the host tissue surrounding the proliferative tumor are involved. Five functional terms were included in the hybrid model and their effects on a tumor&#39;s invasion were investigated quantitatively: haptotaxis toward the extracellular matrix tissue that is degraded by matrix metalloproteinases; chemotaxis toward nutrients; cell-cell adhesion; the proliferation of the tumor; and the immune response toward the tumor. Haptotaxis and chemotaxis, which...

Density and temperature conditions in the solar core suggest that the microscopic diffusion of electrons and ions could be nonstandard: Diffusion and friction coefficients are energy dependent, collisions are not two-body processes and retain memory beyond the single scattering event. A direct consequence of nonstandard diffusion is that the equilibrium energy distribution of particles departs from the Maxwellian one (tails goes to zero more slowly or faster than exponentially) modifying the reaction rates. This effect is qualitatively different from temperature and/or composition modification: Small changes in the number of particles in the distribution tails can strongly modify the rates without affecting bulk properties, such as the sound speed or hydrostatic equilibrium, which depend on the mean values from the distribution. This mechanism can considerably increase the range of predictions for the neutrino fluxes allowed by the current experimental values (cross sections and solar properties) and can be used to reduce the discrepancy between these predictions and the solar neutrino experiments.

Density and temperature conditions in the solar core suggest that the microscopic diffusion of electrons and ions could be nonstandard: Diffusion and friction coefficients are energy dependent, collisions are not two-body processes and retain memory beyond the single scattering event. A direct consequence of nonstandard diffusion is that the equilibrium energy distribution of particles departs from the Maxwellian one (tails goes to zero more slowly or faster than exponentially) modifying the reaction rates. This effect is qualitatively different from temperature and/or composition modification: Small changes in the number of particles in the distribution tails can strongly modify the rates without affecting bulk properties, such as the sound speed or hydrostatic equilibrium, which depend on the mean values from the distribution. This mechanism can considerably increase the range of predictions for the neutrino fluxes allowed by the current experimental values (cross sections and solar properties) and can be used to reduce the discrepancy between these predictions and the solar neutrino experiments.

Density and temperature conditions in the solar core suggest that the microscopic diffusion of electrons and ions could be nonstandard: Diffusion and friction coefficients are energy dependent, collisions are not two-body processes and retain memory beyond the single scattering event. A direct consequence of nonstandard diffusion is that the equilibrium energy distribution of particles departs from the Maxwellian one (tails goes to zero more slowly or faster than exponentially) modifying the reaction rates. This effect is qualitatively different from temperature and/or composition modification: Small changes in the number of particles in the distribution tails can strongly modify the rates without affecting bulk properties, such as the sound speed or hydrostatic equilibrium, which depend on the mean values from the distribution. This mechanism can considerably increase the range of predictions for the neutrino fluxes allowed by the current experimental values (cross sections and solar properties) and can be used to reduce the discrepancy between these predictions and the solar neutrino experiments.

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to 2-loop order and, where available, compare them to numerical results.

We demonstrate that the 'microscopic' field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.

10 and 13 orders of magnitude concerning length and time scales are bridged. Are and how are all of these organization levels connected to fullfill their obvious functions, e. g. gene regulation or replication, since they are optimized by evolution ? -10 10 2 [s]

Applications at Erasmus MC: E.g. genome sequence analysis, protein structure simulations, chip/array analysis, epidemiology of viral infections, patient diagnostic image analysis (AMI). Applications at Erasmus MC: E.g. genome sequence analysis, protein structure simulations, chip/array analysis, epidemiology of viral infections, patient diagnostic image analysis (AMI). Applications at Erasmus MC: E.g. genome sequence analysis, protein structure simulations, chip/array analysis, epidemiology of viral infections, patient diagnostic image analysis (AMI). To develop an entire novel system-biology oriented genome browser, i.e. integrating the holistic complexity of genome organization in a single easy comprehensible platform has required completely new approaches to represent the genome architecture realistically in combination with the various types experimental data or instant analysis capabilities and annotation.

10 and 13 orders of magnitude concerning length and time scales are bridged. Are and how are all of these organization levels connected to fullfill their obvious functions, e. g. gene regulation or replication, since they are optimized by evolution ? -10 10 2 [s]

Fig..1: Two BACs 650 kbp appart were used to determine the overall architecture of the PWS/AS region, and within the PWS region four YACs with six trilaterable distances were used to detect the fine structure of the PWS locus and to test whether there is a difference between the (in-)active alleles. The difference between a random chromatin fiber and the measured spatial distances is obvious.

To overcome the "dare-to-share" attitude in respect to the inverse tragedy of the commons in the grid sector, a sustainable grid ecology within the e-Society is crucial for the success of the grid sector. I.e. that the e-Human Ecology of grid balances the integration of individual grid psychology with autopoietic e-Social sub-systems. Thus, the Human Ecology paradigm developed by Robert Park (1864-1944) and Ernest Burgess (1886-1966) evolving in Chicago in the 1920's concerning city development applies. Consequently, e-Human "Grid" Ecology provides a solution to the inverse tragedy of the commons as e.g. also GRID PSYCHOLOGY ECG With ever-new technologies emerging from research and development, also the amount of data, which has to be stored and analysed by advanced information technologies, is growing exponentially. In no other than the IT sector it is immanently simpler to share existing but unexploited resources. However, the resulting grid phenomenon and its implications show that this is similar complicated to the ecology/climate/environmental challange! C O N C LU S I O N Huge resources are availabe e.g. in the IT and the renewable energy sectors, but are not exploited due to the existence of an inverse tragedy of the commons. To exploit those resources both the autopoietic tragedy of social sub-subsystems and the individual risk psychology have to be integrated in a human ecology manner both on the micro and macro level. Consequently, the grid challenge in IT of virtualizing the huge and largely available hardware resources can be made achieved by e-Human "Grid" Ecology which on the operational level means the participative integration of individual applyers with the set-up of open and sustainable management structures complying to autopoietic e-Social sub-systems. Consequently, e-Human "Grid" Ecology can serve as a solution for the inverse tragedy of the commons and its challenge in many sectors as e.g. in the renewable energy sector and thus the climate problem.

The combination of genome sequence and structure, its annotation and experimental data in an accessible and comprehensible way is a major challenge. Increasingly there is a large number of extremely divergent data sets: the sequence itself, genes, regulatory regions, various forms of reoccurring sequence features and clone sets etc. Currently, one possibility to represent this information in a visual form -and thus to reveal its scientific meaning -is to use genome browsers such as "Ensembl" or "The UCSC Genome Browser". These browsers have been beneficial in the understanding of the complex organization of genomes. However, there are also limitations concerning their focus on linear presentation, standardized input and data bank accessibility. Also customizability by a remote user with special requirements is difficult. The GLOBE-Consortium is developing ways to visualize multi-dimensional data sets from various sources in an easily accessible way. This allows the integration of these data sets into a single holistic display system giving a biological oriented view of genomes and advancing basic research, diagnostics and new treatments.

Typical textbook illustration of the human cell nucleus: 1) human cell nuclei differ from spherical shape, 2) the DNA is not a closed pipe, 3) nucleosomes are not regularly organized into chromatin, 4) chromatin does not float around randomly in the nucleus. V. Hennings (illustrator) in Molecular and Cellular Biology by Stephen L. Wolfe, 1993.

and The different organization levels of genomes bridge several orders of magnitude concerning space and time. How all of these organization levels connect to processes like gene regulation, replication, embryogeneses, or cancer development is still unclear?

The combination of genome sequence and structure, its annotation and experimental data in an accessible and comprehensible way is a major challenge. Increasingly there is a large number of extremely divergent data sets: the sequence itself, genes, regulatory regions, various forms of reoccurring sequence features and clone sets etc. Currently, one possibility to represent this information in a visual form -and thus to reveal its scientific meaning -is to use genome browsers such as "Ensembl" or "The UCSC Genome Browser". These browsers have been beneficial in the understanding of the complex organization of genomes. However, there are also limitations concerning their focus on linear presentation, standardized input and data bank accessibility. Also customizability by a remote user with special requirements is difficult. The GLOBE-Consortium is developing ways to visualize multi-dimensional data sets from various sources in an easily accessible way. This allows the integration of these data sets into a single holistic display system giving a biological oriented view of genomes and advancing basic research, diagnostics and new treatments.

In VWCISC we propose a unique working and collaboration environment for international scientific communities. Science is increasingly collaborative at an international level, which enables projects to build teams of specialists best suited to the goals of the research effort, but which also puts heavy burdens on the scientists to communicate with one another. Email and international travel are primary collaboration tools, but increasingly specialist software is being developed to widen the collaboration channel. A number of software collaboration tools have been developed during the last 10 years, within the Grid and Cloud paradigms, that offer scientists easier and more functional ways to collaborate, and in Europe there has been very substantial funding for these efforts.

Frage 3 • Das Proposal schlägt vor, das PG als Teil von WissGrid zu konstituieren. Eine Darlegung, wie dies genau umgesetzt werden soll fehlt bisher. Das gilt insbesondere für das Verhältnis von dem WissGrid Fachberater Team (in AP2) und den im Antrag angestrebten Kompetenzzentren. Auch eine inhaltliche Verzahnung mit den bereits existierenden Arbeitsschwerpunkten von WissGrid steht noch aus. Insgesamt ist es wünschenswert, wenn klar erkennbar wird, wie sich das PG in WissGrid einbringen und integrieren will, inklusive Nennung des Ergänzungs-bzw. Erweiterungspotentials für WissGrid und seine Arbeitspakete. • Diese Frage ist u.E. falsch gestellt. Wir wünschen uns, diese organisatorischen Fragen ZUSAMMEN mit WissGrid zu klären. Wir meinen, das ist besser, als wenn wir einseitige Vorschläge unterbreiten. Sollte WissGrid an einer Kooperation mit uns interessiert sein, so werden wir hier sicher eine gute, von beiden Seiten getragene Lösung finden. Wir würden unsere Ideen gerne unter dem Dach von WissGrid realisieren.

By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion equation, as well as by particle simulations. The connection between these levels of description is provided by the Fokker-Planck equation describing the particle dynamics. PACS numbers:

In this paper we study the Hamiltonian dynamics of charged particles subject to a non-selfconsistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov equation is a diffusion equation in the velocity space, but homogeneous in the physical space. We obtain a diffusion matrix, quadratic with respect to the electric field, which can be related to the diffusion matrix of the resonance broadening theory and of the quasilinear theory, depending on whether the typical autocorrelation time of particles is finite or not. In the self-consistent deterministic case, we show that the asymptotic distribution function is homogenized in the space variables, while the electric field converges weakly to zero. We also show that the lack of compactness in time for the electric field is necessary to obtain a genuine diffusion limit. By contrast, the time compactness property leads to a "cheap" version of the Landau damping: the electric field converges strongly to zero, implying the vanishing of the diffusion matrix, while the distribution function relaxes, in a weak topology, towards a spatially homogeneous stationary solution of the Vlasov-Poisson system.