Fuel Efficient Computation in Passive Self-Assembly

In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which particles are modeled by four-sided squares with glue types assigned to each tile edge. The assembly process is driven by positive and negative force interactions between glue types, allowing for tile assemblies floating in the plane to combine and break apart over time. We refer to this type of assembly model as passive in that the constituent parts remain unchanged throughout the assembly process regardless of their interactions. A computationally universal system is said to be fuel efficient if the number of tiles used up per computation step is bounded by a constant. Work within this model has shown how fuel guzzling tile systems can perform universal computation with only positive strength glue interactions. Recent work has introduced space-efficient, fuel-guzzling universal computation with the addition of negative glue interactions and the use of a powerful non-diagonal class of glue interactions. Other recent work has shown how to achieve fuel efficient computation within active tile self-assembly. In this paper we utilize negative interactions in the tile self-assembly model to achieve the first computationally universal passive tile self-assembly system that is both space and fuel-efficient. In addition, we achieve this result using a limited diagonal class of glue interactions

Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically step-flow growth. The breakdown of the metastable step-flow occurs through the formation of a mound of critical width proportional to L_c=1/sqrt(l_es), the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with L_c. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change L_c significantly. Standard continuum theories cannot be used to evaluate the activation energy of the critical mound and the instability time. The dynamics of a mound can be described as a one dimensional random walk for its height k: attaining the critical height (i.e. the critical size) means that the probability to grow (k->k+1) becomes larger than the probability for the mound to shrink (k->k-1). Thermal detachment induces correlations in the random walk, otherwise absent.Comment: 10 pages. Minor changes. Accepted for publication in Phys. Rev.

Rejection in Łukasiewicz's and Słupecki's Sense

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic

Conformational mechanism for the stability of microtubule-kinetochore attachments

Regulating the stability of microtubule(MT)-kinetochore attachments is fundamental to avoiding mitotic errors and ensure proper chromosome segregation during cell division. While biochemical factors involved in this process have been identified, its mechanics still needs to be better understood. Here we introduce and simulate a mechanical model of MT-kinetochore interactions in which the stability of the attachment is ruled by the geometrical conformations of curling MT-protofilaments entangled in kinetochore fibrils. The model allows us to reproduce with good accuracy in vitro experimental measurements of the detachment times of yeast kinetochores from MTs under external pulling forces. Numerical simulations suggest that geometrical features of MT-protofilaments may play an important role in the switch between stable and unstable attachments

How to determine local elastic properties of lipid bilayer membranes from atomic-force-microscope measurements: A theoretical analysis

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this article.Comment: 14 pages, 9 figures, REVTeX4 style. New version corresponds to the one accepted by PRE. The result section is restructured: a comparison to experimental findings is included; the discussion on the influence of adhesion between AFM tip and membrane is extende

Negative Interactions in Irreversible Self-Assembly

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles

Competing mechanisms for step meandering in unstable growth

The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear stability analysis of Bales and Zangwill [Phys. Rev. B {\bf 41}, 4400 (1990)]. In the presence of edge diffusion a local instability mechanism related to kink rounding barriers dominates, and the meander wavelength is set by one-dimensional nucleation. The long-time behavior of the meander amplitude differs in the two cases, and disagrees with the predictions of a nonlinear step evolution equation [O. Pierre-Louis et al., Phys. Rev. Lett. {\bf 80}, 4221 (1998)]. The variation of the meander wavelength with the deposition flux and with the activation barriers for step adatom detachment and step crossing (the Ehrlich-Schwoebel barrier) is studied in detail. The interpretation of recent experiments on surfaces vicinal to Cu(100) [T. Maroutian et al., Phys. Rev. B {\bf 64}, 165401 (2001)] in the light of our results yields an estimate for the kink barrier at the close packed steps.Comment: 8 pages, 7 .eps figures. Final version. Some errors in chapter V correcte