Dynamical Response of Nanomechanical Oscillators in Immiscible Viscous Fluid for in vitro Biomolecular Recognition

Dynamical response of nanomechanical cantilever structures immersed in a viscous fluid is important to in vitro single-molecule force spectroscopy, biomolecular recognition of disease-specific proteins, and the detection of microscopic dynamics of proteins. Here we study the stochastic response of biofunctionalized nanomechanical cantilevers beam in a viscous fluid. Using the fluctuation-dissipation theorem we derive an exact expression for the spectral density of the displacement and a linear approximation for the resonance frequency shift. We find that in a viscous solution the frequency shift of the nanoscale cantilever is determined by surface stress generated by biomolecular interaction with negligible contributions from mass loading.Comment: 4 pages, 2 figures, RevTex4. See http://nano.bu.edu/ for related paper

Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods

In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller. However, in certain applications, no prior information regarding buyers' preferences is known. To address this issue, we consider uncertain valuations and formulate the problem in a robust optimization framework: the objective is to minimize the maximum regret. For a special case of revenue-maximizing pricing problem we present a solution method based on mixed-integer linear programming formulation

The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the autocorrelation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers.Comment: Submitted to Nanotechnology April 26, 200

On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers

The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties of solutions depend onthe suction parameter. Furthermore, making use of the fourth--order Runge--Kutta scheme together with the shooting method, numerical solutions are obtained.Comment: 15 page

The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid

Soft systems methodology: a context within a 50-year retrospective of OR/MS

Soft systems methodology (SSM) has been used in the practice of operations research and management science OR/MS) since the early 1970s. In the 1990s, it emerged as a viable academic discipline. Unfortunately, its proponents consider SSM and traditional systems thinking to be mutually exclusive. Despite the differences claimed by SSM proponents between the two, they have been complementary. An extensive sampling of the OR/MS literature over its entire lifetime demonstrates the richness with which the non-SSM literature has been addressing the very same issues as does SSM

Knowledge management: a review of the field and of OR's contribution

This paper examines the field of knowledge management (KM) and identifies the role of operational research (OR) in key milestones and in KM's future. With the presence of the OR Society journal Knowledge Management Research and Practice and with the INFORMS journal Organization Science, OR may be assumed to have an explicit and a leading role in KM. Unfortunately, the origins and the evidence of recent research efforts do not fully support this assumption. We argue that while OR has been inside many of the milestones there is no explicit recognition of its role and while OR research on KM has considerably increased in the last 5 years, it still forms a rather modest explicit contribution to KM research. Nevertheless, the depth of OR's experience in decision-making models and decision support systems, soft systems with hard systems and in risk management suggests that OR is uniquely placed to lead future KM developments. We suggest that a limiting aspect of whether OR will be seen to have a significant profile will be the extent to which developments are recognized as being informed by OR

Quid pro quo:reflections on the value of problem structuring workshops

Attracting clients who are willing to invest in using a problem structuring method (PSM) can be particularly difficult for the emerging generation of modellers. There are many reasons for this, not least that the benefits of a problem structuring intervention are vague and evidence of benefits are often anecdotal for example, claims of constructing a deeper understanding of the problem or building the commitment of a group to implementing an outcome. This paper contributes to the evaluation of problem structuring methods by reflecting on the quid pro quo that a client and problem structuring modeller can enjoy from collaboration. The paper reflects on 21 cases, where Journey Making (a problem structuring method) was used with 16 organizations to help managers agree a suite of actions to tackle a complex strategic issue. The reflections are clustered around those benefits that pertain to: PSMs in general; PSMs that use computer-supported workshops; the Journey Making methodology

Hele-Shaw beach creation by breaking waves: a mathematics-inspired experiment

Fundamentals of nonlinear wave-particle interactions are studied experimentally in a Hele-Shaw configuration with wave breaking and a dynamic bed. To design this configuration, we determine, mathematically, the gap width which allows inertial flows to survive the viscous damping due to the side walls. Damped wave sloshing experiments compared with simulations confirm that width-averaged potential-flow models with linear momentum damping are adequately capturing the large scale nonlinear wave motion. Subsequently, we show that the four types of wave breaking observed at real-world beaches also emerge on Hele-Shaw laboratory beaches, albeit in idealized forms. Finally, an experimental parameter study is undertaken to quantify the formation of quasi-steady beach morphologies due to nonlinear, breaking waves: berm or dune, beach and bar formation are all classified. Our research reveals that the Hele-Shaw beach configuration allows a wealth of experimental and modelling extensions, including benchmarking of forecast models used in the coastal engineering practice, especially for shingle beaches