ACTA PHYSICA POLONICA A MODIFIED KRATZER-FUES FORMULA FOR ROTATION-VIBRATION ENERGY OF DIATOMIC MOLECULES*

An extension of the Kratzer-Fues approach to analytical calculation of the rotation-vibration energy of diatomic molecules is proposed. The eigen -v a l u e s f r o m t h i s a p p r o a c h a r e a p p l i e d i n c a l c u l a t i o n o f t h e r o t a t i o n a l a n d rovibrational energies and in evaluation of molecular constants of selected diatomic molecules, resulting in satisfactory reproduction of experimental frequencies over a wide range of rotational states. In contrast to our previous proposition the rotational dependence of vibration energy is taken into account. An additional set of fitted parameters which include equilibrium distance and dissociation constant was also employed

Homeostatic competition drives tumor growth and metastasis nucleation

We propose a mechanism for tumor growth emphasizing the role of homeostatic regulation and tissue stability. We show that competition between surface and bulk effects leads to the existence of a critical size that must be overcome by metastases to reach macroscopic sizes. This property can qualitatively explain the observed size distributions of metastases, while size-independent growth rates cannot account for clinical and experimental data. In addition, it potentially explains the observed preferential growth of metastases on tissue surfaces and membranes such as the pleural and peritoneal layers, suggests a mechanism underlying the seed and soil hypothesis introduced by Stephen Paget in 1889 and yields realistic values for metastatic inefficiency. We propose a number of key experiments to test these concepts. The homeostatic pressure as introduced in this work could constitute a quantitative, experimentally accessible measure for the metastatic potential of early malignant growths.Comment: 13 pages, 11 figures, to be published in the HFSP Journa

Patient-Specific Prosthetic Fingers by Remote Collaboration - A Case Study

The concealment of amputation through prosthesis usage can shield an amputee from social stigma and help improve the emotional healing process especially at the early stages of hand or finger loss. However, the traditional techniques in prosthesis fabrication defy this as the patients need numerous visits to the clinics for measurements, fitting and follow-ups. This paper presents a method for constructing a prosthetic finger through online collaboration with the designer. The main input from the amputee comes from the Computer Tomography (CT) data in the region of the affected and the non-affected fingers. These data are sent over the internet and the prosthesis is constructed using visualization, computer-aided design and manufacturing tools. The finished product is then shipped to the patient. A case study with a single patient having an amputated ring finger at the proximal interphalangeal joint shows that the proposed method has a potential to address the patient's psychosocial concerns and minimize the exposure of the finger loss to the public.Comment: Open Access articl

Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p

Modified Kratzer-Fues Formula for Rotation-Vibration Energy of Diatomic Molecules

An extension of the Kratzer-Fues approach to analytical calculation of the rotation-vibration energy of diatomic molecules is proposed. The eigen-values from this approach are applied in calculation of the rotational and rovibrational energies and in evaluation of molecular constants of selected diatomic molecules, resulting in satisfactory reproduction of experimental frequencies over a wide range of rotational states. In contrast to our previous proposition the rotational dependence of vibration energy is taken into account. An additional set of fitted parameters which include equilibrium distance and dissociation constant was also employed

Expansion of the Rotational Energy of Diatomic Molecules into a Continued Fraction

A new expansion of the rotational energy of diatomic molecules, in the form of a continued fraction has been investigated. The considered formula is applied in calculation of molecular constants and reproduction of rotational spectra of rigid-, semirigid- and van der Waals-type molecules. A physical interpretation of semiempirical expansion parameters is proposed and a connection between the method considered and the Dunham approach is also discussed