Asymmetric and symmetric double bubbles in an inhibitory ternary system

نویسندگان

  • Xiaofeng Ren
  • Juncheng Wei
چکیده

An inhibitory ternary system contains two terms in its free energy: the interface energy that favors micro-domain growth and the longer ranging confinement energy that prevents unlimited spreading. In a parameter regime where two constituents are small in size compared to the third constituent and the longer ranging energy does not dominate, there is a double bubble like stable critical point of the energy functional. The two minority constituents occupy the two bubbles of the double bubble respectively, and the majority constituent fills the background. A special way of perturbing an exact double bubble leads to a restricted class of perturbed double bubbles that can be described by internal variables which are elements in a Hilbert space. The exact double bubble is non-degenerate in this class and nearby there is a perturbed double bubble that locally minimizing the free energy within the restricted class. This perturbed double bubble satisfies three of the four equations for critical points of the free energy; namely the three equations involving the curvature and the inhibitor variables on its three boundary curves. However it does not satisfy the 120 degree angle condition at its triple points. By translating and rotating the entire restricted class of perturbed double bubbles, one finds a particular direction and location in the domain of the problem where the locally minimizing perturbed double bubble in this specific restricted class also satisfies the 120 degree condition. This approach can handle both asymmetric and symmetric double bubbles.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Asymmetric and Symmetric Double Bubbles in a Ternary Inhibitory System

A ternary inhibitory system contains two terms in its free energy: the interface energy that favors micro-domain growth and the longer ranging confinement energy that prevents unlimited spreading. In a parameter regime where two constituents are small in size compared to the third constituent and the longer ranging energy does not dominate, there is a double-bubble-like stable stationary point ...

متن کامل

A double bubble assembly as a new phase of a ternary inhibitory system

A ternary inhibitory system is a three component system characterized by two properties: growth and inhibition. A deviation from homogeneity has a strong positive feedback on its further increase. In the meantime a longer ranging confinement mechanism prevents unlimited spreading. Together they lead to a locally self-enhancing and self-organizing process. The model considered here is a planar n...

متن کامل

A double bubble in a ternary system with inhibitory long range interaction

The free energy of a ternary system with a self-organization property includes an interface energy and a longer ranging, inhibitory interaction energy. In a planar domain, if the two energies are properly balanced and two of the three constituents make up an equal but small fraction, the free energy admits a local minimizer that is shaped like a perturbed double bubble. Most difficulties in the...

متن کامل

Dosimetric evaluation of a treatment planning system using pencil beam convolution algorithm for enhanced dynamic wedges with symmetric and asymmetric fields

Background: The dosimetric performance of Eclipse 6.5 three dimensional treatment planning system (3DTPS) is evaluated by comparing the calculated and measured dose in two dimensions following the guide lines of American Association for Physicists in Medicine Task Group 53. Materials and Methods: The calculations were performed by the 3DTPS for symmetric as well as asymmetric fields for standar...

متن کامل

Accuracy Evaluation of Isogray TPS Dose Calculations in Symmetric and Asymmetric Fields of the Elekta Compact Linear Accelerator

Introduction: Radiation therapy is one of the most important methods of cancer treatment. Radiation therapy uses symmetric and asymmetric fields in which the radiation dose distribution is different. To calculate the dose distribution, computer treatment planning systems are used which must have acceptable calculations accuracy. The aim of this study was to investigate the accuracy of the dose ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013