1,325 research outputs found

    An improved Monte Carlo method for direct calculation of the density of states

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    We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the probabilities associated with move proposal only--we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang-Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties.Comment: 7 pages, 4 figures. to appear in Journal of Chemical Physic

    Saddles in the energy landscape: extensivity and thermodynamic formalism

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    We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular the temperature dependence of the energy and fractional order of sampled saddles.Comment: 4 pages, 1 figur

    Enumeration of distinct mechanically stable disk packings in small systems

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    We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small systems because this enables us to enumerate nearly all distinct MS packings. We measure the probability to obtain a MS packing at packing fraction ϕ\phi and find several notable results. First, the probability is highly nonuniform. When averaged over narrow packing fraction intervals, the most probable MS packing occurs at the highest ϕ\phi and the probability decays exponentially with decreasing ϕ\phi. Even more striking, within each packing-fraction interval, the probability can vary by many orders of magnitude. By using two different packing-generation protocols, we show that these results are robust and the packing frequencies do not change qualitatively with different protocols.Comment: 4 pages, 3 figures, Conference Proceedings for X International Workshop on Disordered System

    Building the Emotionally Learned Negotiator

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    This piece reviews three recent books on the significance of emotion in negotiation and dispute resolution (Fisher & Shapiro: Beyond Reason: Using Emotions as You Negotiate; Peter Ladd: Mediation, Conciliation and Emotion: A Practitioner\u27s Guide for Understanding Emotions in Dispute Resolution; and Lacey Smith: Get It! Street-Smart Negotiation at Work: How Emotions Get You What You Want), situating each work within a theory of practice for emotionally learned negotiators. After discussing the how the appearance of emotional sterility became synonymous with professionalism (and the toll this has taken on professional interaction), the piece sets forth a functional theory of emotion in negotiation based on four elements: emotion as (1) ether, (2) obstacle, (3) episteme, and (4) instrument. To cast emotion as ether (the ether of human experience) is to understand the inevitability of emotional impacts on negotiated exchange. For many, emotion in negotiation is encountered as an obstacle (that which obstructs mechanical application of established negotiating techniques). The more sophisticated negotiator recognizes emotionality as episteme (the medium of insight by which we consult interests and hypothesize about others) - a means for better understanding herself, the people she deals with, and a good deal else about the world. Finally, the emotionally learned negotiator uses emotion not only epistemologically but also instrumentally (as a tool for achieving desired ends), taking affirmative steps to help manage the emotional climate within a negotiation. She uses her emotional skills to mitigate undesired emotions and engender preferred emotions within herself and other participants: to soothe, bolster, win respect, build trust, and encourage creativity. The emotionally learned negotiator thus uses emotions not only as tools of knowing, but as instruments of persuasion. The new series of books on the subject offer strategies by which negotiators can learn to better integrate emotional skills into negotiation, among the most emotionally-charged of professional spheres. While the three books share the central premise that emotionality plays a critical role in the unfolding dynamics of all negotiations, each offers its own primary lesson. Lacey Smith\u27s business-oriented Get It! examines how the emotions of hope and fear can be both tools and obstacles to the interest-based bargaining method we first learned in Roger Fisher\u27s classic, Getting to Yes. Fisher and Shapiro\u27s Beyond Reason takes the Getting to Yes method to the next level of sophistication, providing a taxonomy of core emotional concerns that underlie individual negotiators\u27 behavior, and with it a Seven-Elements - like structure from which to prepare, advance, and overcome emotional obstacles in each negotiating context. Peter Ladd\u27s Mediation, Conciliation and Emotions expands the analysis of emotional content in a negotiation from the individual to the shared experience, exploring the establishment of emotional climates that arise between individuals and offering empirically based counsel for mediators and conciliators about how to help remedy undesirable emotional climates and create emotional climates more conducive to problem-solving. No book has all the answers we need, but each makes a valuable contribution to the field

    On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

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    We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.Comment: 21 pages, 4 figure

    A test of non-equilibrium thermodynamics in glassy systems: the soft-sphere case

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    The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential energy landscape. The existence of such a relation offers the unique possibility for testing the recently proposed extension of the liquid free energy to glassy out-of-equilibrium conditions and the associated expression for the temperature of the configurational degrees of freedom. We demonstrate that the non-equilibrium free energy provides an exact description of the soft-sphere pressure in glass states
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