We use Monte Carlo simulations to study the influence of dipolar interaction and polydispersity on the magnetic properties of single-domain ultrafine ferromagnetic particles. From the zero field cooling (ZFC)/field cooling (FC) simulations we observe that the blocking temperature T(B) clearly increases with increasing strength of interaction, but it is almost not effected by a broadening of the distribution of particle sizes. While the dependence of the ZFC/FC curves on interaction and cooling rate are reminiscent of a spin glass transition at T(B), the relaxational behavior of the magnetic moments below T(B) is not in accordance with the picture of cooperative freezing.

With the aim to study the relationship between protein sequences and their native structures, we adopt vectorial representations for both sequence and structure. The structural representation is based on the Principal Eigenvector of the fold's contact matrix (PE). As recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence is represented through a Hydrophobicity Profile (HP), using a generalized hydrophobicity scale that we obtain from the principal eigenvector of a residue-residue interaction matrix and denote it as interactivity scale. Using this novel scale, we define the optimal HP of a protein fold, and predict, by means of stability arguments, that it is strongly correlated with the PE of the fold's contact matrix. This prediction is confirmed through an evolutionary analysis, which shows that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N -dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call Vectorial Protein Space. In this way, we define a unified framework for sequence to sequence, sequence to structure, and structure to structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences with sequences and sequences with structures.

The use of Henkel plots as a tool to analyze the type and strength of interaction between particles in fine magnetic particle systems is wide spread. It is commonly accepted that noninteracting systems in general show linear Henkel plots, while interacting systems show curved plots. Using extensive Monte Carlo simulations Henkel plots for noninteracting and interacting systems of particles that show different anisotropies are studied. It is found that a direct relation between linearity and noninteraction exists only for systems of uniaxial particles at low temperatures, while particles with cubic anisotropy always show positive deviation of the Henkel plot in the whole range of temperatures. On the other hand, dipolar interaction always results in negative deviation. In the case of particles with cubic anisotropy and dipolar interaction, the deviation changes gradually from positive to negative with increasing strength of the interaction.

We introduce a new approach to build microscopic engines on the atomic scale that move translationally or rotationally and can perform useful functions such as pulling of a cargo. Characteristic of these engines is the possibility to determine dynamically the directionality of the motion. The approach is based on the transformation of the fed energy to directed motion through a dynamical competition between the intrinsic lengths of the moving object and the supporting carrier.PACS numbers: 66.90.+r, 45.40.Ln, 87.16.Nn The handling of single atoms and molecules has become widespread in science [1], but the challenge still remains to further 'tame' them and make single molecules perform useful functions. Nanoscale technology has been predicted almost 40 years ago [2], but inspite of a growing interest in atomic scale engines, such as biological motors [3,4], ratchet systems [3,[5][6][7], molecular rotors [8][9][10][11], and molecular machinery in general [12], a real breakthrough concerning the construction of a man-made nanoscale counterpart of the 'steam engine' has not occured yet. This has mainly been due to the fact that we still miss the crucial link of how to transform energy to directed motion on this scale.In this Letter we propose possible basic principles of such an engine. The main advantages of this novel approach are: (a) the same concept applies for both translational and rotational motions, (b) the directionality of motion is determined dynamically and does not require spatial asymmetry of the moving object or of the supporting carrier, (c) the velocity obtained can be varied over a wide range, independent of the direction, and (d) the engine is powerful enough to allow for the transportation of a cargo.The proposed engine consists in general of two parts: the supporting carrier and the moving object. Achieving motion of the engine is based on dynamical competition between the two intrinsic lengths of the carrier and the object. This competition is used to transform initially fed energy to directed motion. To exemplify the concept, we use below a simple model system of a chain in a periodic potential, namely a Frenkel-Kontorova type model [13]. But we would like to emphasize that this choice as example is solely motivated by the simplicity of the model rather than by experimental requirements. In particular, the particles are not meant to be single atoms and the springs are not meant to be single chemical bonds. The sole purpose of the model system is to address in a simple manner the following questions: (a) What is the minimal size of the engine? (b) How are the direction and velocity of the motion determined? (c) How powerful is the engine? The important questions of possible physical realizations will be addressed towards the end of the Letter.In the model system, as already mentioned, the supporting carrier is taken as an isotropic surface, and the moving object as a chain of N identical particles on the surface. Each particle i has a mass m and is located at coordinate x i . For simplicity...

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point degree-degree correlated undirected random networks without self-edges or multiple edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution P(j,k) , which allows one to fix an arbitrary degree distribution P(k) and an arbitrary average nearest neighbor function k_{nn}(k) simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks [P(k) proportional, variantk;{-gamma}] and empirical complex networks [ P(k) taken from network] as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field-like manner.

The scaling behavior of linear polymers in disordered media modeled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p(c) is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior; i.e., different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers mu(q) and enhancement exponents gamma(q), which depend on q. Our numerical results suggest that the relation mu(1)=p(c)mu between the first moment mu(1) and its regular lattice counterpart mu is valid.

We study optimal paths in disordered energy landscapes using energy distributions of the type P(log(10) E)=const that lead to the strong disorder limit. If we truncate the distribution, so that P(log(10) E)=const only for E(min) < or =E < or =E(max), and P(log(10) E)=0 otherwise, we obtain a crossover from self-similar (strong disorder) to self-affine (moderate disorder) behavior at a path length l(x). We find that l(x) proportional, variant[log(10)(E(max)/E(min))](kappa), where the exponent kappa has the value kappa=1.60 +/- 0.03 both in d=2 and d=3. We show how the crossover can be understood from the distribution of local energies on the optimal paths.

We investigate the dynamics of a classical particle in a one-dimensional two-wave potential composed of two periodic potentials, that are time-independent and of the same amplitude and periodicity. One of the periodic potentials is externally driven and performs a translational motion with respect to the other. It is shown that if one of the potentials is of the ratchet type, translation of the potential in a given direction leads to motion of the particle in the same direction, whereas translation in the opposite direction leaves the particle localized at its original location. Moreover, even if the translation is random, but still has a finite velocity, an efficient directed transport of the particle occurs. PACS numbers: 05.60.Cd, 05.40.−a, 87.16.NnA particle subject to a spatially asymmetric but on large scale homogeneous potential displays a symmetric diffusive motion, since the sole violation of the x → −x symmetry is not sufficient to cause a net directional transport. As already noted more than 100 years ago by Curie [1], the additional breaking of time reversal t → −t symmetry [e.g. by dissipation] may lead to a macroscopic net velocity, so that in this case directed motion can result in the absence of any external force. Such systems, known as thermal ratchets [2], have been subject of much activity, both theoretical [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and experimental [19][20][21][22][23][24][25], partly motivated by possible applicability to biological motors [26][27][28].In this Letter we study the classical dynamics of a particle in a one-dimensional two-wave potential. The total potential is composed of two periodic potentials, that are time-independent and of equal amplitudes and periodicities. One of the potentials is externally driven performing a translational motion with respect to the other. It is shown that if, in addition to the broken time reversal symmetry, the spatial symmetry is broken for one of the potentials, the relative translation can result in a twofold behavior: (i) Translation in one direction causes a deterministic motion of the particle in the same direction, whereas (ii) translation in the opposite direction leaves the particle localized at its original location. Thus, the total potential acts as a ratchet in the original sense. Moreover, an efficient directed transport occurs even if the translation is random but still has a finite velocity. The reason for the directed transport is the existance of points of irreversibility in the particle trajectory. The high rate transport stems from the fact that if the particle once gains a distance which is an integer multiple of the potential period, this distance is preserved, different from former ratchet systems driven by random fluctuations.We consider a simple ratchet type potential Π(x), which is assumed to be continuous but not necessarily differentiable. It has a periodicity b, so that Π(x+b) = Π(x) ∀x, an amplitude Π 0 = max Π(x) = − min Π(x), and one minimum is located at x = 0, i.e. Π(0) = −Π 0 . We a...