<i>Introductory Statistical Mechanics</i>

Bowley, R. M.; Sánchez, Mariana; Knox, Robert

doi:10.1063/1.881981

Cited by 37 publications

(54 citation statements)

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“…However, there exists a powerful method by which the motion of these resonators can be calibrated via observation of their random thermal motion. This is known as thermomechanical calibration and is performed by invoking the equipartition theorem, which establishes a relationship between the thermal energy of a device and its mean squared amplitude of motion [37]. Many of the detection methods mentioned above are sensitive enough to measure the thermal motion of devices on the micro or nanoscale.…”

Section: Introductionmentioning

confidence: 99%

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

et al. 2013

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We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.

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Section: Introductionmentioning

confidence: 99%

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

et al. 2013

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“…This balance is exactly what the thermodynamic potential called the free energy describes. At equilibrium, the free energy is minimal [11]. By considering a small displacement of a particle in a system at equilibrium, Einstein was able to show [13,17] that D = k B T /ζ, where k B is Boltzmann's constant, T is the temperature and ζ is a property of the medium.…”

Section: Diusionmentioning

confidence: 99%

MRI based radiotherapy planning and pulse sequence optimization

Sjölund¹

2015

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Radiotherapy plays an increasingly important role in cancer treatment, and medical imaging plays an increasingly important role in radiotherapy. Magnetic resonance imaging (MRI) is poised to be a major component in the development towards more eective radiotherapy treatments with fewer side eects. This thesis attempts to contribute in realizing this potential.Radiotherapy planning requires simulation of radiation transport. The necessary physical properties are typically derived from CT images, but in some cases only MR images are available. In such a case, a crude but common approach is to approximate all tissue properties as equivalent to those of water. In this thesis we propose two methods to improve upon this approximation. The rst uses a machine learning algorithm to automatically identify bone tissue in MR. The second, which we refer to as atlas-based regression, can be used to generate a realistic, patient-specic, pseudo-CT directly from anatomical MR images. Atlas-based regression uses deformable registration to estimate a pseudo-CT of a new patient based on a database of aligned MR and CT pairs.Cancerous tissue has a dierent structure from normal tissue. This aects molecular diusion, which can be measured using MRI. The prototypical diusion encoding sequence has recently been challenged with the introduction of more general gradient waveforms. To take full advantage of their capabilities it is, however, imperative to respect the constraints imposed by the hardware while at the same time maximizing the diusion encoding strength. In this thesis we formulate this as a constrained optimization problem that is easily adaptable to various hardware constraints.

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“…This reservoir can also act as a heat bath, thus allows energy transfer as well [23]. Simply, a grand canonical can be seen in Figure 3 as an open system in contact with a reservoir [22]. …”

Section: Grand Canonical Ensemblementioning

confidence: 99%

“…Energy transfer is allowed with the heat bath, but particle transfer is impermissible. Heat bath can be described as a system with a relatively large heat capacity, in so much that its temperature remains constant in spite of any energy transfer [22]. Since the energy transfer can be shown between the system and the heat bath, exact energy of the system is unknown.…”

Section: Canonical Ensemblementioning

confidence: 99%

Sürüler Probleminin Topluluk Bağlamı Açısından Modellenmesi

Kok¹,

Çellek²,

Koşun³

et al. 2016

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

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Robotic swarms have been modeled in a myriad of ways. One property of the swarms is their multitude. As their numbers increase to uncountable numbers, the thermostatistical mechanics may come into play. Authors took advantage of this fact so as to generate global statistics for the swarm. Three distinct ensembles are explained and formulated. When isolated, the swarms behave as if microcanonical ensemble reigns. But when a predator or a prey appears, transitions are observed depending on the conditions. Therefore, both the formulations and the transitions are all contingent. Finally, observed probabilities were discussed. Keywords: Swarm modeling, Statistical physics, Ensembles, Robotics Sürüler Probleminin Topluluk Bağlamı Açısından Modellenmesi ÖzSürü robotları yüzlerce farklı şekilde modellenmiştir. Kalabalık olmaları sürülerin bir özelliğidir. Sayılamayacak kadar çok sayıya ulaştıklarında, termo-istatiksel mekanik devreye girebilir. Yazarlar bu avantajı kullanarak sürü robotları için evrensel istatistik oluşturmak istediler. Üç temel topluluk açıklandı ve formüle edildi. Sürüler izole edildiklerinde mikrokanonik uyum ortama hakim olurken, ortama av veya avcı girişi olur ise, duruma bağlı olarak değişimler gözlemlenir. Bu yüzden formulasyonlar ve geçişler şarta bağlıdır. Son olarak gözlemlenen olasılıklar tartışıldı.

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Introductory Statistical Mechanics

Cited by 37 publications

References 0 publications

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

MRI based radiotherapy planning and pulse sequence optimization

Sürüler Probleminin Topluluk Bağlamı Açısından Modellenmesi

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