Diffusion and Flexibility in Networks

该奖项由材料研究和数学科学部门共同资助，隶属于NSF范围内的数学科学优先领域。原子网络的性质在很大程度上取决于存在的约束，其中包括固定的键长和角度。 这一理论研究扩展了以往的静态研究工作，研究约束对网络动态行为的影响。 重点将放在被包装在一起的粘性球体的扩散上。 约束理论也将扩展到有限温度，因为它涉及到网络玻璃的热性能。 约束理论用硬约束取代了网络中的强力。 这使得刚性区域，无应力和应力，被确定，以及铰链的位置，特别是附近的刚性相变，在那里整个网络从柔性到刚性transforms.The目前的理论约束网络在三维的限制是必要的，包括债券弯曲力无处不在沿着与中心力。 虽然这适用于某些网络，但已发现它限制了更广泛的应用。 因此，我们将开发一个通用的刚性网络在三维的一般理论，目的是找到一个非常整数的算法。 这将被添加到软件上的灵活性，这是免费提供给学术用户在网站上已经建立在flexweb.asu.edu。扩散在球包可以实验研究使用共聚焦显微镜，它被发现，某些区域被锁定，使没有扩散发生在实验的时间，而扩散运动是可能在其他地区。 我们将预测这些区域，使用一个单一的初始配置，以确定约束条件，和理论概括以上。 这样的方法将提供静态和动态之间的桥梁。一个新的模型将被引入，将允许的约束的影响，以跟踪随着温度的增加，通过玻璃化转变温度。 这将把当前的限制提高到零温度，并允许熵效应被包括在内。 势是由低温下粘球锁定在一起构成的，因此约束理论是适用的，但随着温度的升高，熵效应变得重要，并且可以通过物理学来跟踪。 这项工作将有助于解释玻璃脆性的差异，因为通过粘度可以看出，大块玻璃是由熔体形成的。新的理论，开发了更广泛的影响，特别是生物分子，其中功能往往与灵活性和扩散运动。 当温度升高到室温以上时，天然状态的蛋白质会展开，从而发生变性，因此熵效应很重要。该奖项由材料研究和数学科学部门共同资助，隶属于NSF范围内的数学科学优先领域。原子网络的性质在很大程度上取决于存在的约束，其中包括固定的键长和角度。 这一理论研究扩展了以往的静态研究工作，研究约束对网络动态行为的影响。 重点将放在被包装在一起的粘性球体的扩散上。 约束理论也将扩展到有限温度，因为它涉及到网络玻璃的热性能。 约束理论用硬约束取代了网络中的强力。 这使得刚性区域，无论是无应力和应力，以及铰链的位置，特别是附近的刚性相变，整个网络从柔性到刚性transforms.The新的理论，开发有更广泛的影响，特别是生物分子，其中功能往往是与灵活性和扩散运动。 当温度升高到室温以上时，天然状态的蛋白质会展开，从而变性，因此熵效应很重要。

This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area.The properties of networks of atoms are determined to a large degree by the constraints present, which include fixed bond lengths and angles. This theoretical research extends previous work on statics to study the effect of constraints on dynamical behavior of networks. The emphasis will be on the diffusion of sticky spheres that are packed together. The theory of constraints will also be extended to finite temperature as it relates to the thermal properties of network glasses. Constraint theory replaces the strong forces in a network by hard constraints. This allows the rigid regions, both unstressed and stressed, to be determined, as well as the location of the hinges, especially near the rigidity phase transition, where the whole network transforms from flexible to rigid.The present theory of constrained networks in three-dimensions is restricted by the necessity to include bond bending forces everywhere along with central forces. While this is appropriate for some networks, it has been found to be restrictive to wider applications. We therefore will develop a general theory for the rigidity of generic networks in three-dimensions, with the aim of finding a very integer algorithm. This will be added to the software on flexibility that is available free to academic users at the website that has been set up at flexweb.asu.edu.Diffusion in sphere packs can be studied experimentally using a confocal microscope, and it is found that certain regions are locked so that no diffusion occurs over the time of the experiment, while diffusive motion is possible in other regions. We will predict these regions, using a single initial configuration to determine constraints, and the theory as generalized above. Such an approach will provide a bridge between statics and dynamics.A new model will be introduced that will allow the effect of constraints to be tracked as the temperature increases up through the glass transition temperature. This will lift the current restriction to zero temperature, and allow entropic effects to be included. The potential is constructed with the sticky spheres locked together at low temperature, so that constraint theory is applicable, but as the temperature is increased, entropic effects become important and can be tracked thermodynamically. This work will help to explain the differences in the fragility of glasses as seen through the viscosity as a bulk glass is formed from the melt.The new theory that is developed has broader implications, particularly to bio-molecules, where function is often associated with flexibility, and diffusive motion. Proteins in the native state unfold as the temperature is increased above room temperature to become denatured, and so entropic effects are important.%%%This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area.The properties of networks of atoms are determined to a large degree by the constraints present, which include fixed bond lengths and angles. This theoretical research extends previous work on statics to study the effect of constraints on dynamical behavior of networks. The emphasis will be on the diffusion of sticky spheres that are packed together. The theory of constraints will also be extended to finite temperature as it relates to the thermal properties of network glasses. Constraint theory replaces the strong forces in a network by hard constraints. This allows the rigid regions, both unstressed and stressed, to be determined, as well as the location of the hinges, especially near the rigidity phase transition, where the whole network transforms from flexible to rigid.The new theory that is developed has broader implications, particularly to bio-molecules, where function is often associated with flexibility, and diffusive motion. Proteins in the native state unfold as the temperature is increased above room temperature to become denatured, and so entropic effects are important.***